Heath the Structure of Intergenerational Cooperation

The Structure ofIntergenerationalCooperation

JOSEPH HEATH

The problem of anthropogenic climate change has generated renewedinterest in the issue of intergenerational justice, or more generally, thequestion of what we owe to future generations. This is primarily becausethe costs of carbon abatement are upfront, while the most significantbenefits (which is to say, the most important costs averted) will begin tobe felt only in about a century. Thus the central question we face is howmuch sacrifice we—all those living now—should be willing to make inorder to improve the quality of life of people, many of whom will be bornsometime after we are dead.

This question is one that philosophers have found particularlyintriguing, not least because the two most important contemporaryapproaches to normative political theory, namely, utilitarianism andcontractualism, appear to produce answers to this question that arepreposterous. Since future people vastly outnumber those who are livingin the present, and since it is possible to make productive investmentsnow that will generate very long, if not infinite, streams of futurerewards, any simplistic application of the utilitarian calculus suggeststhat we should be investing pretty much everything we produce; we maynot even be entitled to meet our own subsistence requirements.1 Thisseems overly demanding. Yet if utilitarianism seems too demandingwhen applied in an intergenerational context, contractualism seems

I would like to thank the Social Sciences and Humanities Research Council of Canadafor financial support of this work. My thanks also to audiences at Queens University andDuke University for critical feedback, as well as the referees and editors of Philosophy& Public Affairs.

1. This was shown by Tjalling C. Koopmans, “On the Concept of OptimalEconomic Growth,” Pontificae Academiae Scientiarum Scripta Varia 28 (1965): 225–300.The easy solution is to impose a temporal discount rate, but this is a measure thatmany utilitarians resist.

© 2013 Wiley Periodicals, Inc. Philosophy & Public Affairs 41, no. 1

quite the opposite. Indeed, in some of its formulations contractualismseems to imply that we owe absolutely nothing to future generations.2

Typically this is motivated by the thought that there is no possibility ofmutually beneficial cooperation between generations, because reciproc-ity is impossible since benefits can flow only forward in time.3 (This issometimes referred to as the “nonreciprocity problem.”)4 If there is nosuch thing as intergenerational cooperation, then it follows that there isno place for a social contract to determine how the benefits and burdensof cooperation are to be assigned. Yet the theory of justice, according tothe contractualist, is just the set of principles used to effect this assign-ment, so the implication seems to be that intergenerational relations arenot governed by principles of justice.

According to critics of contractualism, when John Rawls characterizedthe basic structure of society as institutionalizing a “fair system of coop-eration between generations over time,”5 he was making a fundamental

2. I use the term “contractualism” and not “contractarianism” because the formula-tions that are often thought to have this problem include not only David Gauthier’s but alsoJohn Rawls’s, since they both conceive of justice as a set of principles designed to allocatethe benefits and burdens of cooperation. The primary difference is that Gauthier appliesthis framework to particular interactions, whereas Rawls conceives of society in general asa “cooperative venture for mutual advantage.” John Rawls, A Theory of Justice, rev. ed.(Cambridge, Mass.: Harvard University Press, 1999), p. 4. Both, however, are committed tothe view that there is a system of intergenerational cooperation in place. Rawls writes, “Thelife of a people is conceived as a scheme of cooperation spread out in historical time. It isto be governed by the same conception of justice that regulates the cooperation of con-temporaries” (p. 257). Naturally, versions of contractualism that put less emphasis oncooperation, such as T. M. Scanlon’s, do not have the same problem. See Rahul Kumar,“Wronging Future People: A Contractualist Proposal,” in Intergenerational Justice, ed. AxelGosseries and Lukas Meyer (Oxford: Oxford University Press, 2009).

3. For a sample, see Brian Barry, A Treatise on Social Justice, vol. 1, Theories of Justice(Berkeley: University of California Press, 1989), p. 189; Derek Parfit, Reasons and Persons(Oxford: Oxford University Press, 1984), p. 524; Robert Goodin, Protecting the Vulnerable(Chicago: University of Chicago Press, 1985), p. 177; Edward Page, “Fairness on the Day afterTomorrow: Justice, Reciprocity and Global Climate Change,” Political Studies 55 (2007):225–42; Gustaf Arrhenius, “Mutual Advantage Contractarianism and Future Generations,”Theoria 65 (1999): 25–35; Stephen Gardiner, “A Contract on Future Generations,” in Gos-series and Meyer, Intergenerational Justice; Claus Dierksmeier, “John Rawls and the Rightsof Future Generations,” in Handbook of Intergenerational Justice, ed. Joerg Chet Tremmel(Cheltenham: Edward Elgar, 2006), p. 79.

4. For a critical survey, see Hugh McCormick, “Intergenerational Justice and the Non-Reciprocity Problem,” Political Studies 57 (2009): 451–58.

5. John Rawls, Justice as Fairness: A Restatement, ed. Erin Kelly (Cambridge, Mass.:Harvard University Press, 2001), p. 160.

32 Philosophy & Public Affairs

mistake, because it is impossible for noncontemporaneous generationsto cooperate with one another. It is this claim about the impossibility ofintergenerational cooperation that I will be concerned to evaluate in thisarticle. Without taking a position on the larger normative question ofwhat we owe to future generations, my objective in what follows willsimply be to show that the supposed problem for contractualism is notreally a problem, since the “nonreciprocity” problem stems from theadoption of an overly narrow, direct conception of reciprocity. Coopera-tion, however, can also be sustained by systems of indirect reciprocity,where there is no requirement that the person to whom one supplies abenefit be the person from whom one receives a benefit. Thus I will showthat there is no problem in principle, or in practice, with a system ofintergenerational cooperation in which benefits flow only one way.

The framework that I will be adopting in addressing the issue of inter-generational justice will be that of “just savings.”6 A few observationsabout this are in order. First, this is not a standard allocative justiceframework, in recognition of the fact that we do not literally distributegoods between present and future people (by, for example, buryinggoods in time capsules). What we do, instead, is divide up our economicefforts between the production of consumption goods and of investmentgoods. Producing investment goods requires that we forgo consumptionin the present, but it generates benefits down the line, by making it easierto produce consumption goods in the future. This is the primary eco-nomic mechanism through which present generations can benefit futuregenerations.7 And since it is the savings rate that determines how eco-nomic activity is to be partitioned between the production of consump-tion and investment goods (since it creates the pool of capital availablefor investment), the question of what we owe to future generations istypically formulated as a question about how high the savings rateshould be.8 There are, of course, other ways in which present generationsbenefit future ones. Technological innovation, cultural production, andinstitution building are all prominent examples. Yet none of these is felt

6. Rawls, A Theory of Justice, p. 252.7. The other important mechanism is cultural. See Peter J. Richerson and Robert Boyd,

Not by Genes Alone (Chicago: University of Chicago Press, 2005).8. Here I am following Frank Ramsey, “A Mathematical Theory of Saving,” Economic

Journal 38 (1928): 543–59; Koopmans, “On the Concept of Optimal Economic Growth”; andof course Rawls.

33 The Structure of IntergenerationalCooperation

to give rise to any particular questions of justice, simply because thedownstream benefits are typically produced as by-products of self-interested or narrowly altruistic action (i.e., action aimed at benefitingone’s immediate descendants). We create new technology, for instance,with the primary intention of benefiting ourselves; the fact that itbecomes available to all subsequent generations is just a positive sideeffect. The savings rate is different, because in order to save, presentgenerations must actually forgo consumption, which seems to be, atleast prima facie, contrary to their interest.

For those who approach this complex of issues from an environmen-tal perspective, the focus on savings may be somewhat puzzling. As far asthe environment is concerned, the central issue seems to be one ofdepletion, not accumulation. Of course the objection is easily disarmedif one is willing to tolerate the “economism” of treating depletion as atype of dissaving. More substantively, unless one is committed to a“strong sustainability” thesis, which does not tolerate compensation forvarious forms of environmental destruction or natural resource con-sumption, then one is committed to the view that investment goods andenvironmental goods can be traded off against one another.9 Forexample, depletion of a nonrenewable fuel source can be compensatedby improvements in engine efficiency—after all, it is not the fuel thatfuture generations are interested in, but rather the amount of usefulenergy that it can be used to produce. Thus it is worth keeping in mindthat the issue of climate change arises in a broader context. If thingscontinue more or less as they have been, the future generations who areharmed by climate change are still likely to be vastly better off than weare now.10 Climate change stands poised to depress the rate of growth,not eliminate it. The central problem is the adaptation that human

9. On weak versus strong sustainability, see Alan Holland, “Sustainability: ShouldWe Start from Here?” in Fairness and Futurity, ed. Andrew Dobson (Oxford: OxfordUniversity Press, 1999).

10. For example, to see the projections under the widely used “DICE model,” seeWilliam Nordhaus and Joseph Boyer, Warming the World (Cambridge, Mass.: MIT Press,2000), p. 143. There is, of course, the small chance that some sort of catastrophic scenariowill unfold, which is not taken into account in these models. This is counterbalanced,however, by the possibility of a technological “magic bullet” that will resolve the problemat very low cost, which is also not taken into account in the models. Thus an approach thatignores both possibilities—on the grounds that they cancel each other out—is not entirelyimplausible, especially given that we have no idea how to assign probabilities to either.


populations will have to make in response to climate change, mostnotably, the mass migration of people away from equatorial and low-altitude regions.11 Thus the “just savings” framework seems to be theappropriate one for discussing the issues raised by climate change. It is,in any case, the framework within which almost all policy discussions areconducted, and so anyone hoping to bring normative reflections to bearupon questions such as the appropriate level of carbon taxation will beobliged to formulate claims in these terms.

The article proceeds as follows. First, I offer a brief survey of the criti-cism of the contractualist approach that has become standard in theliterature. In the following section (II), I show that cooperation can besustained intergenerationally through a system of indirect reciprocity.This is an entirely formal demonstration, however, and various criticshave expressed reasonable concerns about the applicability of suchmodels to the real world. I will therefore go on to show (in section III) thatthere are real systems of cooperation that have the exact same structure,most obviously, pay-as-you-go pension schemes. I will then briefly con-sider how this example can be used to respond to many of the standardobjections that are raised against the model in the literature (in sectionIV). Finally, I will argue that the rate of savings in our society is sustainedthrough such a system (in section V). I do not draw any particular nor-mative conclusions from this exercise. My goal is simply to present aclear outline of how the existing system of intergenerational cooperationin our society functions in order to show that the standard objection tocontractualism is without merit.

I. THE CASE AGAINST CONTRACTUALISM

“Cooperation,” in the sense in which it is being used here, is a technicalterm used to describe situations in which a group of individuals, byexercising restraint in their pursuit of individual self-interest, is able toachieve an outcome that is better for all of them.12 The possibility of

11. See Nicholas Stern, The Economics of Climate Change (Cambridge: CambridgeUniversity Press, 2007), pp. 457–506.

12. This is, it should be noted, narrower than the everyday sense of the term. For asurvey of different definitions, see Raimo Tuomela, Cooperation (Dordrecht: Kluwer, 2000),pp. 21–23. The narrow definition was introduced by game theorists, primarily to distinguishdilemmas of cooperation (where the optimal outcome was out of equilibrium) from those


cooperation arises in situations where the strategic equilibrium of aninteraction is Pareto-suboptimal (which is to say, worse for at least oneperson and better for no one). In these situations, as Rawls noted, indi-viduals have both a common interest (in maximizing the benefits ofcooperation) and a conflict of interest (over how these benefits are to bedistributed). A “theory of justice,” again in the technical sense of theterm, constitutes a set of principles designed for the specific task of“choosing among the various social arrangements which determine thisdivision of advantages.”13 It is the function of these principles to bringabout the agreement required to induce individuals to act in a nonmaxi-mizing fashion (i.e., to refrain from defecting, or to respect the con-straints required to achieve the cooperative outcome).

The paradigm instance of a potentially cooperative interaction is theprisoner’s dilemma (PD), which is a two-person interaction in which thePareto-superior outcome can be achieved only if both players select astrongly dominated strategy. Figure 1 shows the familiar normal-formrepresentation of such an interaction. This is a highly schematic repre-sentation of an interaction such as the one described by David Hume

that merely required coordination (i.e., choice among multiple equilibria). For example,see Robert Boyd and Peter Richerson, “Culture and Cooperation,” in Cooperation andProsocial Behavior, ed. Robert A. Hinde and Jo Groebel (Cambridge: Cambridge UniversityPress, 1991), p. 27. This game-theoretic sense is sometimes referred to as “altruistic coop-eration”: see, e.g., Samuel Bowles and Herbert Gintis, A Cooperative Species (Princeton,N.J.: Princeton University Press, 2011). In this article I will be focusing on establishing thepossibility of intergenerational cooperation in this narrower sense, simply because itis the only type of cooperation that is thought to pose any sort of a problem inthe intergenerational case.

13. Rawls, A Theory of Justice, p. 4.

Player 2

Player 1

c

c

d

(2,2) (0,3)

(3,0) (1,1)

d

Figure 1. Prisoner’s dilemma.


involving two farmers who could help each other bring in the harvest,but “for want of mutual confidence and security” fail to do so.14 Antici-pating that the one who moves second will defect, the first mover defectsas well, and so the two wind up with the inferior (d,d) outcome.

In situations of this type, both parties have an incentive to somehowrestructure their interaction in order to motivate each to choose thecooperative option of helping the other with his harvest (c). The mostunproblematic way of doing this—the one emphasized by Hume—is toembed this interaction in a larger sequence of potentially cooperativeinteractions, then make future cooperation contingent upon coopera-tion in the present. Thus the farmers might agree to help each other out,not just this year but every year. This deprives the second mover of theincentive to defect, since he knows that the first is likely to cooperatewith him again next year only if he upholds his part of the bargain. Thusthe parties are able to realign their external incentives in such a way as tomake cooperation instrumentally rational.

The other option, emphasized in different ways by both Rawls andDavid Gauthier, is that individuals might possess some psychologicaldisposition or faculty that makes them willing to cooperate even in one-shot PDs, so long as they have reasonable assurances that the otherplayer will do the same. (Rawls describes this as the quality of “reason-ableness”; Gauthier has a more dispositional conception, which herefers to as “constrained maximization.”)15 Thus the second mover,having agreed to help out the first, would be psychologically disposed tocarry through on this commitment, despite having the opportunity todefect. Knowing that the second is so disposed, the first would also bewilling to cooperate. Thus the two farmers would be able to sustaincooperation even in the absence of appropriate external incentives,since each would be motivated by what one might call a “sense ofjustice.” How one specifies this sense need not detain us here—there area variety of proposals in the literature. The important point is simply thatmost contractualists presuppose something like this, some deviationfrom canonical rational choice theory, as an explanation for the

14. David Hume, A Treatise of Human Nature, ed. L. A. Selby-Bigge (Oxford: Clarendon,1978), p. 521.

15. John Rawls, Political Liberalism, exp. ed. (New York: Columbia University Press,2005), p. 49; David Gauthier, Morals by Agreement (Oxford: Clarendon, 1984).


phenomenon of “large-scale cooperation among genetically unrelatedindividuals” in human societies.16

The contractualist intuition, that principles of justice arise because ofthe need to specify the modalities of cooperative interaction, is plausibleonly when conjoined with the view that the major social institutions inany society—what Rawls refers to as the “basic structure”—have as theirprimary function the provision of some cooperative benefit, which iswhy they can all be assessed from the standpoint of justice. In particular,the important structural features of the economic and political system,such as property rights and the provision of public goods financedthrough taxation, are all analyzed as systems of cooperation. And indeed,one can tell a fairly plausible story about how all of these institutionalarrangements provide benefits that are enjoyed by all, and yet are vul-nerable to individual defection. Everyone benefits, for example, from theorderliness provided by the state through its enforcement of the criminallaw, and yet everyone has an incentive on various occasions to break thislaw and to avoid the obligations that must be discharged in order tosustain it (payment of taxes, performance of jury duty, and so on). Thusthere is a strong sense in which the law-abiding, tax-paying citizens of anation are involved in a large-scale system of cooperation with oneanother, in which each refrains from taking advantage of certain oppor-tunities that are available to free ride and, in so doing, provides a benefitthat is enjoyed by all of the others.

There are many people who find this sort of contractualism unintui-tive, because it is both narrow in its focus on cooperation and norma-tively minimal. At the very least, this account of justice requiressupplementation with some other account that articulates our moralobligations in cases that do not involve cooperation (such as altruisticaction, where we benefit some other without any expectation of receiv-ing a benefit ourselves).17 For many contractualists, of course, it is animportant conceptual point to show that in restricting greenhouse gas

16. Ernst Fehr and Urs Fischbacher, “The Nature of Human Altruism,” Nature 425

(2003): 785–91, at p. 785.17. Hume, for example, argued that the contract idea provided only an account of

“artificial virtue,” which should be supplemented by the usual list of “natural virtues.” SeeDavid Gauthier, “David Hume, Contractarian,” Philosophical Review 88 (1979): 3–38. Rawlsclaims that it provides a “political” conception of justice, which is supplemented at theindividual level with a private comprehensive doctrine. See Rawls, Political Liberalism.


emissions, we are not just “being nice” to future generations (as anaccount in terms of altruism would suggest) but instead ensuringthat our basic institutions respect fair terms of interaction. And yet, asfar as the problem of climate change is concerned, there would seem tobe no need to get into such issues, simply because the accumulationof greenhouse gases in the atmosphere is the result of a collectiveaction problem, and any proposed solution would seem to requiresome sort of cooperation. Furthermore, disagreement over how thebenefits and burdens of such a scheme should be allocated is a majorimpediment to progress.18 Thus a contractualist theory of justice wouldappear to be ideally suited to addressing the issue—and the norma-tively minimal presuppositions would seem particularly attractive ina global context, where there is very little agreement about how muchaltruistic concern we are obliged to exhibit toward others, and muchgreater agreement about what constitutes fair terms of interactionin cooperative schemes.

There is, however, a major impediment to the application of the con-tractualist analysis. Even if one is willing to grant the basic picture,expanding the analysis to include the presence of multiple generationsseems to present a challenge. Past, present, and future generations donot seem to cooperate in any significant sense of the term. First of all, thebenefits seem to flow only one way—following time’s arrow, from thepresent to the future. While we (those alive today) have received enor-mous benefits from our ancestors, we are unable to return the favor,since we are (according to the usual understanding) unable to benefitthe dead.19 Furthermore, we are generally thought to be under an obli-gation to pass along some of these benefits to future generations, eventhough it is unclear what we stand to gain from doing so. Thus therelationship does not seem to be cooperative in any sense of the term.On the contrary, it seems more like Gauthier’s thought experiment ofpeople living by the side of a river, each of whom benefits when thosewho live upstream refrain from polluting it, but each of whom lacks an

18. There are, as Stephen Gardiner emphasizes, two major dimensions of disagree-ment: first, with respect to the distribution of burdens across generations; and second, withrespect to the allocation of carbon allocation permits in the present. See Gardiner, A PerfectMoral Storm (New York: Oxford University Press, 2012), p. 7.

19. Axel Gosseries, “A-t-on des obligations envers les morts?” Revue Philosophique deLouvain 101 (2003): 80–104.


incentive to refrain from doing so himself.20 Various people here are in aposition to benefit various other people, yet no one is in a position toengage in any mutually beneficial interaction (that is to say, interactionin which the parties are symmetrically positioned), and so everyone isoutside the scope of any potential social contract. Gauthier himselfgrants that principles of justice do not govern the relations of individualsin such circumstances (and that they are, subject to a few minorquibbles, basically free to pollute).21 But are these not precisely the cir-cumstances that present and future people find themselves in?

On the basis of this sort of analysis, Brian Barry has concluded that the“circumstances of justice” (i.e., “the normal conditions under whichhuman cooperation is both possible and necessary”) are absent in theintergenerational case: “Whether or not the circumstances of justiceobtain among nations is an empirical matter. They may or they may not.Whether or not they obtain between the generations of those currentlyalive at one time and their successors is a logical matter. They cannot.The directionality of time guarantees that, while those alive can maketheir successors better or worse off, those successors cannot do anythingto help or harm the current generation.”22 As a result, in Barry’s viewthere simply is no prisoner’s dilemma in the intergenerational context,because there is no possibility of mutual benefit. Yet as Stephen Gardinerobserves, “if, in the intergenerational setting, we depart from the pris-oner’s dilemma model, then the traditional contract approach seems tobe undercut, and in a particularly deep way: its basic analysis of theproblem appears not to apply.”23 Daniel Attas has echoed these senti-ments, claiming that the “absence of mutuality between generationsposes an insurmountable problem to any contractarian theory that aimsto ground obligations on the idea of mutual advantage.”24 Gustaf Arrhe-nius has claimed, on this basis, that “intergenerational justice remains

20. Edward Page says exactly this: “Members of earlier generations seem, in this sense,to be in a similar situation to those living in an upstream community who have just realizedthat their industrial and agricultural sectors are polluting the environment of many distantcommunities living downstream without having to bear any costs themselves.” Page,Climate Change, Justice and Future Generations (Cheltenham: Edward Elgar, 2007), p. 105.

21. Gauthier, Morals by Agreement, pp. 212–13.22. Barry, A Treatise on Social Justice, 1:189.23. Gardiner, “A Contract on Future Generations,” pp. 78–86.24. Daniel Attas, “A Trans-Generational Difference Principle,” in Gosseries and Meyer,

Intergenerational Justice, p. 197.


an embarrassment for contractarians and will, I surmise, continueto be so.”25

So to summarize the case against contractualism: the living cannotcooperate with the dead, or with those who have not yet been born. As aresult, any theory that ties the claims of justice to the existence of coop-erative relations between individuals will be committed to the view thatwe have no obligations of justice toward future generations. In the past,this may not have been such a problem, because self-interested actiongenerated consequences for future generations that were largely posi-tive. But with the growing importance of environmental problems, thisneglect becomes no longer tolerable. In order to articulate the logic ofour concerns, however, we must get away from the idea that justice isconcerned with dividing up the benefits and burdens of cooperation, orthat it operates within some shared “basic structure.”

In the rest of this article, I will try to show that the first claim is false. Wecan and do cooperate with those who are not yet born. Or more specifi-cally: we often act cooperatively, where doing so only makes sense if weare presuming that future generations will also act cooperatively. Thismakes them participants in the system of reciprocity. Critics of contractu-alism have overlooked this because they are working with an overlynarrow conception of cooperation. There are two central points that tendto be missed. First, many critics fail to realize that cooperation need not besustained through direct reciprocity; it can also be sustained throughindirect reciprocity.26 Because of this, neither “time’s arrow” nor the“absence of mutuality between generations” precludes the possibility ofcooperation. Second, critics fail to appreciate the importance of intergen-erational overlap, combined with the fact that people undergo a lengthyperiod of dependency at both the beginning and at the end of their lives.If one generation died the moment the next was born, then there would beno possibility of cooperation. Humans, however, are not like eels.27 As a

25. Arrhenius, “Mutual Advantage Contractarianism and Future Generations,” p. 34.26. See André Masson, Des liens et des transferts entre générations (Paris:

EHESS, 2009), p. 77.27. That is, we do not die at the time that our children are born. On the other hand, Tim

Mulgan introduces a science fiction thought experiment in which people do reproduce likeeels. Mulgan, “A Minimal Test for Political Theories,” Philosophia 28 (2001): 283–96. Hethen asserts that they would still have obligations toward future generations (and that theability to account for such obligations is a “minimal test” for the acceptability of a politicaltheory). This seems to me to beg the question against any nonrealist view of these


result, we have no choice but to enter into a complex web of cooperativerelations, one that stretches from the past into the distant future. Histori-cally, this system of cooperation has been sustained primarily throughintrafamilial altruism. With the development of capitalism and thewelfare state, however, it has become a central feature of the basic struc-ture of society. Thus I will end by showing that the rate of savings achievedin capitalist economies, which constitutes the central mechanismthrough which the older generations benefit the younger, is based upon asystem of indirect reciprocity between overlapping generations.

II. THE STRUCTURE OF COOPERATION

To begin with, I would like to set aside any special assumptions thatcontractualists (or others) might like to make about the motivationalforce of the “sense of justice.” Let us assume that individuals act in apurely instrumental fashion, in accordance with the canons of standardrational choice theory. My objective in this section will be to show thatcooperation among noncontemporaneous generations can be sustainedeven under these (worst-case) assumptions. In the next section, when Imove on to “real world” considerations, I will consider the impact ofloosening this assumption.

As mentioned above, the standard way of inducing instrumentallyrational agents to cooperate is to introduce a system of reciprocity. WithHume, we may imagine that the two farmers agree to help each other outwith the harvest, not just this year, but in this and every subsequent year.Formally, this is represented as a repeated PD. The payoffs in such agame are the sum of the payoffs in each individual stage game, dis-counted in a way that reflects both the time-preference of the playersand their beliefs about the probability that the game will end. A strategyin this game is a set of actions specifying an action for a player at eachstage, for each possible history of play. This allows players to respond toeach other’s moves by making the action at stage t depend upon theother player’s actions at any previous stage. A set of strategies is in equi-librium if each player’s action is (or would be) a utility-maximizing

obligations, since a possible world in which human beings had the reproductive biology offish would most certainly be one in which elements of human psychology—includingattitudes toward our offspring—differed quite dramatically from those in the actual world.


response to the action of the other player, at the time at which it isplayed. (The “or would be” qualification is important, as it indicates thatthe relevant equilibrium concept is subgame-perfection—the equilib-rium strategy set must prescribe utility-maximizing actions both on andoff the equilibrium path in order to eliminate noncredible threats.)28

It is easy to show that repeated play of actions that are in equilibriumin the stage game will also be in equilibrium in the repeated game. Sincemutual defection (d,d) is the sole equilibrium of the one-shot PD, thestrategy pair ([d,d,d, . . .], [d,d,d, . . .])—i.e., “defect forever”—will be anequilibrium of the repeated game. If one player is always defecting, thenit will never be in the interest of the other player to start cooperating.Conversely, simple cooperation remains out of equilibrium, for the samereason that it is out of equilibrium in the stage game. If the expectedstrategy pair is ([c,c,c, . . .], [c,c,c, . . .]), then either player could benefit bydefecting at any stage game. If, however, the players adopt strategies inwhich cooperation is conditional upon a history of successful coopera-tion, then it is possible to sustain a strategy profile of actions that wouldbe out of equilibrium in the stage game. In particular, if both playersadopt a strategy of the form “play c, and continue to play c as long as theother player plays c; if the other plays d, then play d forever,” then anequilibrium path in which both players choose c can be sustained as anequilibrium of the repeated game (as long as the discounted sum offuture cooperative benefits outweighs the one-shot benefit of defection).

This is known as a “trigger” or a “grim” strategy. It is sometimes felt tobe implausible, since the punishment sequence associated with defec-tion is completely relentless. It becomes less implausible when oneobserves that universal defection is, and always will be, a possible equi-librium of the repeated game, because it is the sole equilibrium of thestage game. Furthermore, the trigger strategy does not call upon playersto perform a non-utility-maximizing action; it simply shifts expectationstoward a Pareto-suboptimal equilibrium. In other words, it does notcall for “costly punishment”; it just stipulates that cooperation willcollapse when someone defects. This is perfectly credible, since nonco-operation is, in a sense, the default outcome of most human interactions.Furthermore, a less relentless set of strategies, such as tit for tat

28. For a textbook presentation, see Drew Fudenberg and Jean Tirole, Game Theory(Cambridge, Mass.: MIT Press, 1991), p. 73.


(“cooperate at first, then respond to cooperation with cooperation,defection with defection”), is not a subgame-perfect equilibrium,because the punishment is not credible. (Punishing someone this roundjust ensures that you will be punished back the next round, so you arebetter off cooperating. Since the other player can see this, he will defect,in which case you’re better off defecting. Thus tit for tat played againstitself is not a subgame-perfect equilibrium of the repeated game.)29

What sustains cooperation with the trigger strategy is a system ofdirect reciprocity. Both players cooperate in the expectation that doingso will induce the other to cooperate again in the next round. It is worthobserving, though, that in order to sustain the cooperative equilibrium,the identity of the player who cooperates in the subsequent round isactually not essential; what matters is simply that cooperating nowinduces someone else to cooperate later. To see this, consider a multi-player game with, say, eight players. At the beginning of the first round,players are matched up in pairs and given a repeated PD to play. Natu-rally, universal adoption of a trigger strategy will be able to sustain acooperative equilibrium in each of these games. Now suppose that at theend of each stage the players are reshuffled so that each is assigned a newpartner to play the next PD. Suppose also that the trigger strategy ismodified slightly so that it now prescribes cooperation unless a playerdefects, in which case it specifies that everyone matched with that playerin subsequent rounds should defect on that player forever. Universaladoption of this modified trigger strategy is an equilibrium, one thatresults in everyone cooperating in all games.30 Players refrain fromdefecting, not because they expect the person that they are harming todefect in the future, but because they expect the players with whom theywill be matched in subsequent rounds to defect.

Cooperation of this sort is said to be sustained through a system ofindirect reciprocity.31 Player x confers a cooperative benefit upon y, not

29. Or, to speak more precisely, it is a Nash but not a subgame-perfect equilibrium(because it contains a noncredible threat). For an especially clear discussion, see HerbertGintis, Game Theory Evolving (Princeton, N.J.: Princeton University Press, 2000), p. 133. Seealso Eric Rasmusen, Games and Information, 4th ed. (Oxford: Blackwell, 2007), pp. 131–32.

30. For a textbook presentation of the underlying model, see Fudenberg and Tirole,Game Theory, pp. 172–73.

31. Joerg Chet Tremmel, A Theory of Intergenerational Justice (Sterling, Va.: Earthscan,2009), states that indirect reciprocity is only possible if individuals are not selfish (p. 194).Gosseries also seems to assume that indirect reciprocity can only be sustained by moral


because he expects y to benefit him in the future, but because heexpects some other player z to benefit him. The logic of these interac-tions is sometimes described in terms of the desire on the part of indi-viduals to maintain their reputation or their good standing in thecommunity. This is, however, somewhat misleading. In both games,cooperation can be sustained only if the actions that individuals chooseare publicly observable (or observable enough), so that others candevelop strategies that are conditional upon the history of past play. Wetend simply to assume that when two individuals are playing againsteach other repeatedly, they will know what each has done in the pastround, whereas when the players get reassigned there may be some lossof information. But it is easy to stipulate in either game that informationeither be transmitted or not. Thus there is nothing special about theinformational structure that sustains cooperation in a system of indirectreciprocity. It is simply the identity of the players that changes—and asone can see, the identity of the players makes no difference to the stra-tegic properties of the equilibrium.

Let us now modify the game slightly in order to make the structure ofthe intergenerational case more apparent. Imagine that the eight playersare seated in a big circle and instructed to play a variant of a public goodsgame. At the beginning of each stage, they are given two tokens, oneworth $2 and another worth $5. They have two options: the first is toplace the $5 token in the account of the person to their left, the second isto place the $2 token in their own account. They only get to play onetoken. At the end of the round, the amount in each player’s account isrecorded, the tokens are collected, and the game is repeated. In thisgame, the cooperative strategy is obviously to deposit $5 in the accountof the person to one’s left. If everyone does this, then each person gets $5

and the group as a whole gets $40 per round. Putting the $2 in one’s ownaccount is a form of defection. If everyone else is cooperating, then youget $7 that round instead of only $5 (and the person to your left, if shecooperates, gets $0). But if everyone does this, then the group as a wholegets only $16 per round.

commitment: Gosseries, Penser la justice entre les générations (Paris: Flammarion, 2004),p. 149. The model elaborated above shows why this is not the standard view among econ-omists and game theorists (and, for that matter, evolutionary biologists).


For reasons that should be apparent, a trigger strategy is able tosustain a cooperative equilibrium in this game. Individuals may beinstructed to cooperate with the person on their left unless that persondefects, in which case one should defect on that person in perpetuity.Universal adoption of this strategy is subgame perfect.32 What is note-worthy about this game is that it features an absence of mutualitybetween individuals—players help only those to their left, and arehelped only by those to their right. Furthermore, the person on the left ispowerless to either help or harm the person from whom she expects toreceive cooperative benefits—she wields no effective threat and has nobenefits to offer. She relies entirely upon the person on the right of thatperson to deter defection. Thus there is no reciprocity between the indi-viduals in any proper subset of the group, yet the group as a whole isclearly engaged in a cooperative interaction.

The structure of this interaction should be enough to disarm theanxiety about the absence of mutuality or the asymmetry of relationsbeing an impediment to cooperation. It takes only a slight modificationto disarm the further anxiety about time’s arrow. Suppose that at the endof each round, the person at the head of the circle is asked to leave thegame (call this “dying”). The remaining players are asked to move overone chair to the left (call this “aging”). Finally, a new player is brought into fill the empty chair (call this “being born”). Once again, there is noproblem maintaining cooperation in this game, even using the sametrigger strategy that was employed in the previous version. The only realdifference in the way this game plays out is that the oldest player—theperson in the eighth position, who expects to die next round—cannot bemotivated to cooperate, and so will defect. But this does not affect any-thing. The expectation of defection does not set off a cascade of defec-tions, because neither the player in position seven nor the one inposition one has anything to gain from defecting. And it does not gen-erate any punitive defection in the next round, because the eldest playeris no longer there to be defected on. Thus cooperation can be sustainedat the slightly lower level of aggregate payment, where the group as a

32. It should be noted that defection by a single individual generates a cascade thatcauses all eight players to defect for the rest of the game. But this is not required in order tosustain the equilibrium. Again, for a textbook presentation, see Fudenberg and Tirole,Game Theory, pp. 171–72.


whole receives $37 per round (with the eldest receiving $7 and theyoungest receiving $0 in the first round).

So here we have a system of cooperation, supported by indirect reci-procity in a multiplayer game with overlapping generations. Older gen-erations receive benefits from younger ones, but are powerless to eitherhelp or harm them. Furthermore, this system is one that ties all of theplayers into a single cooperative system, not just those who are con-temporaries. This is because the cooperation of each generationdepends not just upon the anticipated cooperation of the generationone stage younger, but upon the anticipated cooperation of allyounger, future generations, including those yet unborn. (With birthand death, the overall system need not be a loop, but can be a lineextending out indefinitely into the future. Note that “indefinite” is notthe same thing as “infinite.” A finitely repeated game in which there isuncertainty about when the game will end is formally identical to aninfinitely repeated game.)33 What makes the system of cooperationhang together is not just the actions chosen, but the expectationsplayers have about what actions will be chosen. Thus future genera-tions may show up as virtual participants in the cooperative system,simply because expectations about what they will do, when they finallyget a chance to act, may be essential to holding together the equilib-rium in the present.

To see this, consider what would happen if a referee were toannounce at some point that the game was to continue for three morerounds, but that it would then end. Obviously this would generate uni-versal defection in the final round, since there would be no possibilityof punishing those who defected at that point. But if everyone is goingto be defecting in the final round, then there is also no way of punishingthose who defect in the penultimate round. Since everyone can see this,everyone can be expected to defect in that round as well. But this makesit impossible to punish anyone who defects in the antepenultimateround, and so everyone will defect then as well. As a result, theannouncement that the game will end at some specific point in thefuture immediately transforms universal defection into the sole

33. See Rasmusen, Games and Information, p. 132. See also Larry Samuelson, “A Noteon Uncertainty and Cooperation in a Finitely Repeated Prisoner’s Dilemma,” InternationalJournal of Game Theory 16 (1987): 187–95.


subgame-perfect equilibrium (simply by changing expectations).34 Thisis true regardless of how far off in the future the end of the game is.Thus the referee could just as easily say that the game would end in tenor twenty rounds, and it would have the same effect. This is why coop-eration in the present is sustained, in a very real way, not just by theparticipation in the cooperative scheme of those currently alive, butalso by the anticipated cooperation of those not yet born.

III. GETTING REAL

In the game outlined above, each player provides a cooperative benefitto the player who is one stage older than her (i.e., on the left), andreceives a cooperative benefit from the player who is one stage younger(i.e., on the right). One could run the lines of cooperation in the otherdirection (i.e., from left to right, or from older to younger). I have chosenthis game, however, because it has the same structure as the system ofcooperation in our society that currently sustains the savings rate. Thismay strike some people as surprising, since it is commonly assumed thatit must be older, past generations who have been saving in order toproduce benefits for younger, future generations, and therefore thatcooperation runs “downstream,” from older to younger. The fact that thesystem runs the other direction is one of its counterintuitive features,and is therefore one of the reasons that it has been widely misunder-stood. Thus Gardiner analyzes the intergenerational problematic onanalogy with “successive crews of a vessel at sea,” where “the earliercrews are required to hand over the ship to their immediate successors ingood working order.”35 The question is then what incentive any “genera-tion” has to do more than the minimum amount of work necessary tokeep it afloat until the time they get off. The answer, in a downstream

34. This is a well-known result in game theory. It is the transformation of an infinitelyrepeated PD into a finitely repeated one. See Rasmusen, Games and Information,pp. 129–30.

35. Gardiner, “A Contract on Future Generations,” p. 103. He presents this as a possibleinterpretation of Gauthier, even though Gauthier is quite explicit that cooperation runsupstream (Gauthier, Morals by Agreement, p. 100). Gosseries has a very similar thoughtexperiment involving a train (Penser la justice entre les générations, pp. 168–71). Part of thereason for this approach to the problem, with Gosseries, is that he conceives of the prin-ciple of reciprocity in moral terms. Thus his suggestion is that, having received somethingfrom our ancestors, we owe something to our descendants.


model like this, is “not much.” But this is not how intergenerationalcooperation works in our society.

Part of the problem comes from a tendency to think that, because thesavings rate is sustained by a system of intergenerational cooperation,saving itself must be the cooperative behavior. This is not true: people donot save because it benefits younger people or future generations; theysave because it benefits themselves.36 First and foremost, people save inorder to finance their own future consumption, primarily during retire-ment.37 The benefit to future generations is entirely a by-product of thisself-interested action. The cooperative behavior (i.e., the action thatdeserves to be labeled “c” in the game tree diagram) occurs on the part ofyoung people, when they agree to honor the promissory notes that wereissued to their elders, thereby allowing the latter to continue consuminglong after they have ceased to make any productive contribution to theeconomy. To adopt Gardiner’s analogy, one should imagine each gen-eration, after having rowed the boat for a while, expecting to continue onfor a while as passengers while the younger generation rows. With thismodification, it is not difficult to see why the earlier generation mightwant to hand the boat over in good condition. What is more difficult tosee is why the younger generation should be willing to carry their eldersalong as deadweight, rather than simply throwing them overboard assoon as the boat has been handed over. This is what the account ofintergenerational cooperation aims to explain.

Before getting into the details of this, however, I would first like to setaside some anxieties that may have arisen over the somewhat formalnature of the model presented in the previous section. It is one thing toknow that perfect rational utility-maximizers can sustain systems ofintergenerational cooperation, but it is quite another to claim that realpeople can do so. It may be helpful to observe, therefore, that there arevarious systems of cooperation in place in our society that have precisely

36. Incidentally, this is true primarily of capitalist economies. In the former communiststates, saving was subject to state planning, with the ambition typically being to spurindustrialization by pushing the savings rate higher than the rate that individuals them-selves would choose: see, e.g., Robert C. Allen, Farm to Factory (Princeton, N.J.: PrincetonUniversity Press, 2003), pp. 61–64.

37. This consumption should be taken to include the flow of services they receive fromowner-occupied housing. It should be noted that most people do not even manage to saveenough for their own retirement, much less set anything aside for future generations.


this structure. This is most obvious in the case of unfunded defined-benefit pension schemes (i.e., pensions that are financed on a pay-as-you-go basis). In such a system, the pension deductions taken fromactive employees are not saved or invested; they are simply used to makepayments to those who are currently retired. Some money will be setaside in order to handle anticipated increases in expected liabilities, dueto things such as variation in cohort size, but overall the plan will nothave savings adequate to cover its liabilities.

Thanks to the financial crisis in 2008, I am currently a participant insuch a plan. Stylizing only somewhat, one can say that every month afairly large portion (over 5 percent) of my salary is deducted from mypaycheck and essentially handed over to one of my emeritus col-leagues.38 What I get in return, at least for the moment, is very little. At theend of the year, I am sent a letter telling me what my own anticipatedmonthly pension will be, based on my current salary and accumulatedyears of service. But this is nothing more than a promise, and a weak oneat that. It is hostage to all of the vicissitudes of employee-employer bar-gaining over the next twenty years. So why do I agree to this? (In particu-lar, why did I voluntarily join the plan when I was a young facultymember, before the age at which it became mandatory?) It is because Iam confident that when I am older and retired there will be a new gen-eration of young professors who are willing to do the same thing for methat I am currently doing for my emeritus colleagues. But why should Iexpect the next generation to be willing to hand over 5 percent of theirsalary to me? Certainly not out of gratitude for the fact that I am doing sonow, to the benefit of my older colleagues. It is because I expect them toexpect that they will someday have younger colleagues who will do thesame for them, that is, that the chain of cooperation will continue on intothe future unbroken (or that the pension scheme will remain, as they say,a “going concern”).

The value of this example is that a pension system like this obviouslyhas the structure of a system of intergenerational cooperation sustained

38. This presentation is somewhat stylized, since private pension plans in most juris-dictions are now required by regulation to fund the majority of their liabilities. This is so thatthe plan can be “wound down” in an orderly fashion if the need arises. Thus the only purepay-as-you-go plans are in the public sector. Nevertheless, even funded plans retain sig-nificant pay-as-you-go features. These become apparent when the plans suffer significantinvestment losses, creating a shortfall that current employees are expected to make up.


by indirect reciprocity. It can therefore be appealed to as a way ofdisarming many of the doubts that have been raised by critics of con-tractualism about the realism or appropriateness of the relevant game-theoretic models. First of all, it is clearly a system of cooperation. The“defect” strategy, in this case, is for each individual simply to save for hisor her own retirement. This is Pareto-inefficient, because uncertaintyabout our own time of death creates a risk of either over- or undersaving.If everyone saves, using average life expectancy at the time of retirementas a guide, this will result in a significant fraction of the populationoutliving their savings. If individuals agree to pool their retirementsavings, however, they can take advantage of the law of large numbersin order to drastically reduce the chances of anyone running out ofsavings.39 This is the insurance mechanism at the core of a life annuity(and a defined-benefit pension is essentially a bundle of collectivelypurchased life annuities). Hence the value to me of the pension scheme.If life expectancy increases by ten years between now and the time of myretirement, whatever individual savings plans I may have had would bethrown into disarray, yet the promise made to me by the pension planwould still stand.

The second important thing to observe about this pension scheme isthat the cooperative arrangement cannot be sustained by any propersubset of the total set of cooperators—such as those who are alive rightnow. Closing it off at any point would leave the younger generationcontributing but not receiving anything. Thus one could not set up apay-as-you-go pension scheme that was designed to run for onehundred years and then stop; it must continue indefinitely into thefuture. Because of this, the total set of cooperators must be taken toinclude future generations, including those yet unborn, and this means,in turn, that the “circumstances of justice” obtain between us and them.

IV. RESPONSE TO OBJECTIONS

Consider now some of the objections that have been directedtoward this type of “overlapping generations” model of intergenera-tional cooperation.

39. See Joseph Heath, “The Benefits of Cooperation,” Philosophy & Public Affairs 34

(2006): 313–51, at p. 324.


A. Doubts about the Punishment Scheme

Gardiner has expressed reservations about whether, in an arrangementof this sort, any future generation would ever defect (and, thus, whetherthe threat of defection is really doing any work in sustaining the suppos-edly “cooperative” system). He writes, “It is not clear that it would actu-ally pay the later group to withhold cooperation for the sake of past badtreatment once it actually achieves causal parity, when this withholdingdamages its interests still further.”40

Two responses are in order here. First, whether or not the interactionis cooperative does not depend on whether there is a credible punish-ment scheme in place; it depends on the underlying structure of theinteraction having the properties of a PD. In other words, what makes itcooperative is the fact that the individuals have an incentive to free ride,but are able to achieve a Pareto-superior outcome if they all refrain fromdoing so. This is why experimental subjects brought in to play a one-shotpublic goods game are described as “cooperating” and “defecting,” eventhough threats are precluded by the very structure of the game. Theiterated PD model happens to rely on a punishment scheme to securecooperation at each stage game, but if internal constraints, such as the“sense of justice,” are able to accomplish the same thing, then so muchthe better for everyone involved. Unfortunately there is no agreementover how to model such constraints without losing track of the sense inwhich the interaction is cooperative, and so the standard game-theoreticmodel remains the best way of bringing out the most important struc-tural feature of the interaction, which is the fact that the system of coop-eration, in order to remain a system of cooperation, must extend outindefinitely into the future.41

But that having been said, I do want to offer some defense of theiterated PD model, simply because when dealing with large-scale,anonymous interactions, people do tend to act more instrumentally, and

40. Stephen Gardiner, “The Pure Intergenerational Problem,” Monist 86 (2003): 481–501, at p. 490.

41. The “orthodox” view, as defended by Ken Binmore among others, is that any suchinternal factors should simply be written into the agent’s utility function, with the impli-cation that the interaction is not genuinely cooperative. See Ken Binmore, Playing Fair:Game Theory and the Social Contract (Cambridge, Mass.: MIT Press, 1994), 1:112. This is, inmy view, a mistake. See Joseph Heath, Following the Rules (New York: Oxford UniversityPress, 2008), pp. 82–84.


so external incentives are likely to play an important role in sustainingany such system of cooperation. To the extent that the model seemsimplausible, it is usually because the nature of the punishment mecha-nism is misunderstood or mischaracterized. Under the “trigger” strat-egy, the expectation is not that the younger generation is going to pursuea non-utility-maximizing course of action, or that they will go out of theirway, harming their own interests, in order to punish their elders. Thesuggestion is simply that they will stop cooperating, so that defection byan older generation would have the effect of shifting expectations towarda noncooperative equilibrium. In other words, the claim is not that theyounger generation will retaliate, but rather that the system of coopera-tion will fall apart.

So a pay-as-you-go pension scheme is an example of a system ofintergenerational cooperation, regardless of whether a trigger strategy isthe best way of representing the incentive structure that motivates indi-viduals to cooperate. What makes it cooperative is simply the fact that itis mutually advantageous, yet the participants each could benefit fromadopting a free-rider strategy. And yet, it is hardly unrealistic to thinkthat the trigger strategy captures something of the incentive structurethat holds it together.42 If one cohort of faculty members refused to makeany payments into the pension plan for a period of, say, a decade, andreduced the benefits being paid to current retirees to cover the shortfall,it is quite unlikely that they would themselves be able to retire with fullpensions merely by imploring younger generations to ignore the breachof trust or to let “bygones be bygones.” The more likely outcome of suchflagrant defection would be the dissolution of the pension scheme,which is to say, a reversion to the noncooperative baseline of individualretirement savings (or a defined-contribution plan). This is just anotherway of describing the trigger strategy.43

42. As Gintis has observed, one can find examples of individuals playing trigger strat-egies in a wide variety of economic contexts. Obvious examples include employers firingemployees who shirk, lenders refusing any further loans to borrowers who have defaulted,and customers refusing to make any further purchases from a firm that has sold themshoddy goods. See Gintis, Game Theory Evolving, p. 135. Gintis refers to these as “contin-gent renewal contracts”—where the individual either renews the cooperative arrangementor else discontinues it permanently—and observes that they are “among the most preva-lent exchanges in market economies” (p. 136).

43. A more sophisticated criticism—one not based on a misunderstanding ofthe model—would be that the punishment sequence that supports the cooperative


The other point that tends to get overlooked is that real people areactually more punitive in response to perceived unfairness or freeriding than agents in rational choice models. They routinely committhemselves to, and engage in, costly retaliation. In the iterated PDmodel, no one ever goes so far as to play a non-utility-maximizingaction; they merely withdraw their cooperation. In real life, people willoften engage in “altruistic punishment,” where they act in ways that aredetrimental to their own interests in order to punish someone else.44

The best-known example of this is the ultimatum game, where stan-dard theory predicts that the second player will accept any offer,regardless of how small. Yet what really happens is that players rejectoffers that they perceive to be unfair, even though this involves burningmoney. Thus the idea that the cooperation of future generations isnot conditional on our own, because they cannot ever plausibly beexpected to defect, is overly sanguine. Indeed, it seems to me equiva-lent to the now thoroughly discredited notion that people will acceptany positive offer in an ultimatum game.

B. Doubts about Backward Induction

Arrhenius has expressed some doubts about the validity or realism ofthe backward induction argument that makes present cooperationdependent upon the anticipated cooperation of all future generationsin the iterated PD model.45 But again, the pension example would seemto belie these concerns. Suppose the government were to announcethat my university was to be closed down in twenty years, with no pro-vision for taking over the pension scheme. Would I continue to makepension payments, knowing that by the time I retire there will be nomore younger professors around to give me 5 percent of their salary?Certainly not. But suppose the date of closure were pushed back to forty

equilibrium is not credible because it is not “renegotiation proof.” See Fudenberg andTirole, Game Theory, p. 180. The intuition here is that the punishment would not occurbecause the offenders could talk their way out of it. But since renegotiation-proofness buildsthe Pareto principle into the solution concept, it cannot be appealed to in this context.

44. See Ernst Fehr and Simon Gächter, “Altruistic Punishment in Humans,” Nature 415

(2002): 137–40.45. Arrhenius, “Mutual Advantage Contractarianism and Future Generations,”

pp. 39–40. The model he criticizes is Joseph Heath, “Intergenerational Cooperation andDistributive Justice,” Canadian Journal of Philosophy 27 (1997): 361–76.


years. Does this change anything? I can now expect that there will beyounger faculty around when I am retired. But will they be willing togive me 5 percent of their salary? It is hard to see how I could have anyreasonable expectation of this, since they know that by the time they areretired, there will be no more younger faculty around. The same logicapplies no matter how far back the closure date is pushed. And even ifsome faculty members have doubts about the validity of backwardinduction, their investment advisers and benefit negotiators most cer-tainly do not. Thus it would not be unreasonable to expect to see “pre-emptive defection,” which is the tangible manifestation of backwardinduction reasoning. Naturally, longer stretches of time introducegreater uncertainty, so one might see cooperation continue under theassumption that “things might change.”46 (It is worth recalling, in thiscontext, that a finitely repeated game with uncertainty about when thegame will end is equivalent to an infinitely repeated game.)47 Peoplemay continue to cooperate simply because they think there is a goodenough chance that they will benefit from the system of reciprocity. Butif there really is no uncertainty, it seems plausible to suppose that coop-eration will completely unravel.

This is, however, mainly empirical speculation. Even if one finds thistype of backward induction reasoning implausible, it does not decide thequestion of whether there are systems of intergenerational cooperationin place in our society. After all, cooperation need not be sustained by thethreat of defection among the parties; it can be sustained by an honorcode, or by the force of law, or by some other mechanism entirely. Andregardless of the specific mechanism, it is simply a fact about pay-as-you-go pension schemes that they involve cooperation between presentand future generations. To see this, consider the argument that is oftenmade by critics of these pension arrangements that they are nothing butglorified Ponzi schemes (since both use money from new members topay off old members). What makes the comparison misleading is the factthat in a Ponzi scheme, the last generation of “investors” foreseeably

46. This is basically because uncertainty transforms the finitely repeated PD back intoan infinitely repeated PD. See Fudenberg and Tirole, Game Theory, pp. 384–85; Rasmusen,Games and Information, p. 132.

47. This is why it can be rational to invest in stock market bubbles and even pyramidschemes. Even though the end is foreseeable, uncertainty about when the end will occurcan make it rational to invest—with the intention of getting out before the end occurs.


loses its money. Pay-as-you-go pensions are not like this, simply becausethere is no reason to think that any one generation is going to wind uplosing money (or being suckered). But this is true only because the chainof cooperation extends indefinitely into the future.

It is also worth keeping in mind that critics who express doubts aboutthe possibility of intergenerational cooperation have an obligation toprovide some alternative account of what motivates individuals, likemyself, who are participating in institutions that, at least superficially,seem to have this structure. If my pension scheme is not a system ofcooperation extending out indefinitely into the future, then what is itexactly? For it not to be a system of intergenerational cooperation, itwould have to be the case that my contributions are not motivated by theexpectation of reciprocity (i.e., the benefits that I will someday receive).But how could that be? Since I am giving away over 5 percent of mysalary, it cannot be self-interested in any obvious way. The only alterna-tive hypothesis is that I am acting altruistically, to the benefit of myemeritus colleagues. This implies that, should the pension scheme beabruptly canceled, leaving me to live out my retirement in penury, Iwould not feel in any way cheated, since it was not the expectation ofreciprocity that was driving my contributions. This is (needless to say?)not my self-understanding, nor that of anyone I have ever discussedpension issues with.

C. Time Bomb Arguments

There is also the claim, made by several critics, that contractualists areunable to exclude the possibility of one generation constructing aso-called time bomb, “where an action beneficial to the present genera-tion has a devastating effect on some distant future generation, but nodirect effect on intervening generations.”48 The availability of this optionis thought to undermine the possibility of cooperation between genera-tions, because it does an end run around the generational overlap that issupposed to keep each generation on the straight and narrow. A suffi-cient number of critics find this argument persuasive, and it deservesa detailed response.

48. Tim Mulgan, Future People (Oxford: Clarendon, 2006), p. 30; see also Gosseries,Penser la justice entre générations, pp. 97–98.


Unfortunately, despite the fact that many critics find it intuitivelyquite powerful, the argument has never been given a precise formula-tion. There are three possible interpretations that could be given to it.First, critics might be claiming that construction of a time bomb is a typeof free-rider strategy, which defeats the effectiveness of generationaloverlap at sustaining cooperation in a repeated PD. For example, onemight imagine adding a third strategy to the PD (call it “e”) that gives theperson who plays it a free-rider payoff right away, but, instead of givingthe sucker payoff to his immediate opponent, gives it to some otherperson several rounds later. The intuition, then, is that a player could getaway with playing such a strategy because it does not give anyone anincentive to punish him right away (since no one is injured), and by thetime someone is injured, it is too late to do anything about it. Thisintuition, however, rests on a misunderstanding of the trigger strategy. Itimplies that individuals switch to the punishment sequence only out ofa desire to retaliate for injuries they have received. This is not the case(since retaliation is a form of non-utility-maximizing action). One cansee this clearly in a system of indirect reciprocity, where the persondoing the punishing is typically not the person who has suffered from thedefection. The trigger strategy does not impose punishment; it merelyshifts expectations away from cooperation toward defection in responseto free riding. Thus one could easily sustain cooperation in response tothe introduction of a time bomb option to the PD by amending thetrigger strategy to read: “play c, and continue to play c as long as theother player plays c; if the other plays d or e, then play d forever.” Thisstrategy is obviously able to sustain a cooperative equilibrium, andmakes it impossible for anyone to free ride by constructing a time bomb.

Second, critics may be claiming that, outside of game theory, with realcognitive-warts-and-all human agents, cooperation may not be sustain-able, because this free-rider strategy is likely to be adopted by presentgenerations, who anticipate that it will go unpunished. The properresponse to this claim is the one made above: that real human agentsmight not adopt such a strategy even if it were available (for the samereason that they cooperate in one-shot public goods games), and thatone cannot count upon real agents being more forgiving of freeriding (for the same reason that one cannot count on people to acceptlowball offers in ultimatum games). Thus the time bomb argumentfails to show that cooperation cannot be sustained intergenerationally;


it is simply an intuition that falls apart when any attempt is made to giveit precise formulation.

This leaves us with a third possibility: that the time bomb may not bea free-rider strategy at all, but merely a move within the system of inter-generational cooperation toward an arrangement that favors the inter-ests of present generations over future ones.49 But then this is no longera criticism of the basic contractualist framework, since the critic is essen-tially granting that intergenerational cooperation is possible. The sug-gestion is simply that the contractualist does not have the normativeresources required to condemn cooperative arrangements that are self-serving from the standpoint of present generations. In response, thecontractualist merely has to show that the time bomb is unjust, accord-ing to whatever principles of justice he or she is using to determine theproper distribution of the benefits and burdens of cooperation withinthe intergenerational scheme. In other words, the contractualist neednot show that construction of a time bomb in this sense is contrary to theself-interest of present generations (it is not); she need only show that itis unfair to future generations.

This point is sufficiently subtle that it perhaps merits further elabora-tion. The folk theorem for the iterated PD establishes that there are aninfinite number of possible “cooperative” equilibria (i.e., equilibriumoutcomes with payoffs better than the noncooperative baseline). For thepayoff matrix in Figure 1, with appropriate discounting and normaliza-tion, any payoff in the space bounded by (1,1), (1,21⁄2), (21⁄1,1), and (2,2) canbe produced through some combination of strategies that will be inequilibrium.50 For instance, a payoff of (21⁄4,11⁄2) can be obtained by thestrategy profile ([c,c,c,d,c,c,c,d . . .], [c,c,c,c,c,c,c,c . . .]) backed up bythe “trigger” threat of universal defection in response to deviation fromthe pattern. This equilibrium is obviously nice for player 1, since it allowshim to exploit player 2 with impunity every fourth round. We are there-fore inclined to describe it as cooperative yet unfair. Many critics,however, seem to think that it is incumbent upon the contractualist toshow that the adoption of an unfair arrangement of this sort will lead to

49. This is the structure of the argument in Avner de Shalit, Why Posterity Matters(London: Routledge, 1995), p. 96; and Arrhenius, “Mutual Advantage Contractarianism andFuture Generations.”

50. See Fudenberg and Tirole, Game Theory, p. 153.


the collapse of cooperation. Thus, for example, Arrhenius criticizes theiterated PD model of intergenerational cooperation on the grounds thatit “leaves room for” strategies that “involve negative consequences thatonly stay in effect for a limited time” and therefore are still better thanuniversal defection.51 Gardiner also criticizes the model, on the groundsthat mere “unfairness to future generations” cannot be shown toprovoke universal defection.52 But this is not a bug; it is a feature of themodel (and the existence of strategies such as the one Arrhenius sketchesout need not be demonstrated; that they exist is a trivial consequence ofthe folk theorem).53 To exclude the possibility of such strategies would beto commit oneself to the self-evidently false claim that cooperation canonly be sustained if the terms are perfectly just.54 Thus one suspects thatthe criticism involves some misunderstanding of the contractualistmodel. The concept of cooperation is intended only to fix the properscope of the principles of justice (namely, that they apply to the “feasibleset” of possible cooperative outcomes). It does not purport to explainhow people choose a particular cooperative arrangement. (On the con-trary, as the folk theorem shows, it radically underdetermines thatchoice, since there will typically be an infinite number of cooperativearrangements, some of them perfectly fair, most of them quite unfair.) Itis the willingness of all parties to accept common principles of justicethat serves as the basis for choosing a particular one of these arrange-ments. Thus if one player comes along and proposes some arrangementthat generates some measure of cooperative benefit, yet violates theprinciples of justice, then the problem with the proposal—and the basisfor its rejection—is simply that it violates the principles of justice.

D. Doubts about the Significance of Upstream Cooperation

Critics have questioned whether systems of intergenerational coopera-tion with an “upstream” (or “ascending”) flow of benefits matter all thatmuch. Gardiner, for instance, makes the significant admission that, if“earlier groups know that they will eventually be at the mercy of their

51. Arrhenius, “Mutual Advantage Contractarianism and Future Generations,” p. 30.52. Gardiner, “A Contract on Future Generations,” p. 104.53. See, e.g., Gintis, Game Theory Evolving, pp. 126–27.54. For useful discussion (on narrow and broad compliance), see Gauthier, Morals by

Agreement, p. 178.


successors,” this would undermine his critique of the contractualistanalysis of intergenerational relations. “Still,” he says, “it is doubtful towhat extent it characterizes many contemporary relationships betweengenerations.”55 This ignores the fact that government pensions, such asSocial Security in the United States, are all unfunded, or pay-as-you-go.Furthermore, public health insurance has very much the same struc-ture—most of it involves a pure transfer from the young and healthy tothe old and infirm. This is quite explicit in the case of Medicare in theUnited States, where almost the entire population pays into the programthroughout their working lives, yet they are unable to draw benefits untilreaching the age of sixty-five. Again, the reason that people are willing topay into it (i.e., largely oppose attempts to dissolve the system) is thatthey anticipate being able to draw from it when they are retired. But sincethe plan is unfunded, there is no basis for this anticipation other than theexpectation that younger workers will continue in their willingness tocontribute. (In the case of Medicare the cooperative dimension is evenmore apparent, since it is based entirely upon an implicit promise. Unlikestate pensions, where you at least get a piece of paper saying how muchyou can expect to draw, in the case of Medicare there is not even a pieceof paper.) Since Social Security and Medicare spending together make upmore than 8 percent of GDP in the United States, explicitly pay-as-you-gosystems of intergenerational cooperation—which leave elderly groupsentirely “at the mercy of their successors”—constitute a significantfraction of the economy, and of individual lifetime consumption.

Far more important than these government programs, however, is thefact that the entire system of retirement savings, whereby people accu-mulate monetary balances over the course of their working lives, whichthey then convert to consumer goods after having withdrawn from theworkforce, is essentially a system of upstream cooperation. The directionin which cooperation flows is more difficult to discern in this case,however, because it is obscured by a money illusion. It therefore requiresa bit more explication in order to be laid bare.

V. JUST SAVINGS

Individual retirement saving—either through funded pension schemesor through individual savings accounts—is sometimes presented as

55. Gardiner, “The Pure Intergenerational Problem,” pp. 490–91.


though it were radically different from unfunded, pay-as-you-goschemes. In the latter case the elderly are portrayed as being a burdenupon younger generations, receiving unproductive transfers, while inthe former case they are presented as being self-sufficient, able toprovide for their own needs without burdening the young. Yet if onelooks at it from the standpoint of economic fundamentals, one can seethat the two arrangements are, of necessity, equally burdensome. Nomatter how you organize it—whether through pay-as-you-go or privatesavings—the fact remains that a certain percentage of the population ata certain age stops producing, and yet continues to consume (in manycases at a very high level) until death. As a result, there is a huge transferof goods and services from the young to the old. In the past, people haveeither continued working until death or else relied upon the support oftheir children. Yet in our society the elderly for the most part rely onstrangers to supply their needs. They are able to do so because of asystem of intergenerational cooperation, which allows them to producemore than they consume when they are young, “save” the difference,and then cash in these savings when they are old. The important thing tosee is that the money with which they pay for goods and services later inlife is not itself a good. It is nothing but a promissory note, not so differ-ent in kind from the annual letter that I receive from my pension fundtelling me how much I can expect to receive in monthly payments. Whenpeople save for their retirement, what they are essentially doing is accu-mulating promissory notes—not just from the bank or the mutual fund,which promises to allow them to redeem their savings, but from societymore generally, which promises them that these banknotes can later beexchanged for vegetables, clothes, housing, medical treatment, andnursing care. It is the credibility of this promise that, in turn, makes iteconomically rational to save a fraction of one’s income.

The system of intergenerational cooperation in question does notreally have a special name, other than simply capitalism, if one interpretsthis in terms of its core feature, namely, the ability of individuals to takemoney and use it as capital. To see how it motivates saving, consider acase where, instead of participating in a pension scheme, I decide to save5 percent of my income in order to support myself during retirement.What this means, in practice, is that during a certain period of myworking life, I will have to produce 5 percent more than I consume. Butwhat shall I do with the extra 5 percent? One strategy is to become a


hoarder—I could start stockpiling all the consumer goods that I expect toneed when I am older, or else some set of goods that I think I have areasonable chance of trading for consumer goods that I will need. Analternative is to become an investor. Instead of spending the money onconsumer goods, I could lend the money to someone who wants toproduce capital goods. In a sense, I am taking the extra 5 percent andusing it to produce goods that will not be consumed right away, but willinstead be used to produce consumer goods in the future. What I accept,in return for the loan, is a promise that I will be able to get a share of theconsumer goods that are to be produced. The advantage of this arrange-ment is that forgoing consumption now, in order to make productiveinvestments, reduces the amount of time and energy that will berequired to produce consumer goods later on. This makes it possible forthe borrower to promise to repay me not just the principal that I lenthim, but also accumulated interest. Thus the advantages of investing,rather than hoarding, correspond precisely to the advantages that comefrom putting money in a bank rather than hiding it under a mattress.This is what it means for money to serve as capital.

What is the cooperative benefit produced by this system? It isincreased labor productivity, and more generally, economic growth.56 Tosee this, consider a simplified example. Suppose that I am a farmer. Oneway of saving for my retirement would be to take 5 percent of my grainand hide it away in the basement. Suppose that this is the prevailingpractice in the community. Yet suppose also that my neighbors and Icould benefit from an irrigation system, which would increase cropyields by 30 percent. Unfortunately, the main canal would take manyyears to dig, and as a result no one has any individual incentive to do it.One way of solving this problem would be for all of us to take the timethat we had spent growing extra grain, and spend it instead digging thecanal, in return for a promise, to the effect that anyone who has spent

56. This is the problem with Gardiner’s argument, in “A Contract on Future Genera-tions,” p. 102, where he suggests that a particular generation might free itself from depen-dence upon the young by hoarding rather than investing. The availability of this option,however, does not undermine the contractualist analysis. In order to show that there is asystem of intergenerational cooperation in place, one need only show that investment isbetter than hoarding. The fact that investment allows individuals to earn interest on theirsavings, and therefore to consume, during their retirement years, several times more thanthey actually saved, is sufficient to establish this.


time working on the canal will be entitled to a grain ration once theproject is complete. Furthermore, imagine that the ration is more thancould be produced through individual hoarding (a promise not difficultto honor, given the way that the irrigation system increases crop yields).Thus an intergenerational arrangement could be proposed of the form,“we agree to invest now, if you promise to support us later.”57 This wouldbe mutually advantageous, because shifting production from consump-tion to investment goods makes it easier to produce consumption goodslater, and this “cooperative surplus” can be divided up in a way thatmakes the arrangement positive sum. Yet the younger generation has anobvious free-rider incentive. Once the canal has been dug, what is to stopthem from using it, yet refusing to honor the promises made to thosewho dug it?

One solution is to create a completely generalized system, wherepeople are credited not for having made specific investments, but forhaving produced more than they consumed, thereby making resourcesavailable for investment. And rather than issuing them ration cards orpromissory notes, one can simply give them money and pay them inter-est on their savings. Younger generations have an incentive to continuethis system of cooperation, as long as there are still productive invest-ments to be made, and to the extent that they themselves stand to gainfrom the integrity of the monetary system. Defection is, of course, stillpossible, either through debt repudiation or, more subtly, through infla-tion. Indeed, the central vulnerability that the elderly have toward theyoung is due to the effects of inflation, which can easily wipe out thevalue of all savings. Hyperinflation is therefore the central mechanism ofintergenerational defection. It says, in effect, “even though you producedmore than you consumed, in order to accumulate this cash balance, youwill no longer be entitled to exchange it for consumer goods equivalentto what you forewent.” The elderly are often hardest hit by inflation, butthey are not singled out. By destroying the value of savings generally, andweakening the integrity of the money system, young people wind up

57. Contracts with this annuity-like structure were extremely common in Europebefore the emergence of capitalism. Farmers would often transfer land title to theirchildren, in return for a lodging and rations, typically specified in great detail. SeeC. G. Lewin, Pensions and Insurance before 1800 (East Lothian, Scotland: Tuckwell Press,2003). Corrodies—commonly sold by monasteries in order to finance capital projects—also had this structure.


being denied access to a system of mutually beneficial cooperation. Thusthe consequences of defection, with respect to the value of money, arenot so different from the consequences of dissolution of a pay-as-you-gopension scheme.

It is worth noting as well that the force of the “backward induction”argument can be seen in the way that investors can be “spooked” by thethreat of credit default, sovereign debt repudiation, inflation, or currencyweakness (all of which have the effect of undermining the value ofsavings). It takes an extraordinary amount of trust to get an investmentsystem going—because people are forgoing present consumption inreturn for nothing more than a promise (a certificate of deposit, a bond,a sum of fiat currency, and so on). Thus when it seems like a nation isgoing to be unable to hold a currency peg, or that a firm will not be ableto repay a set of bonds, or that a bank will be unable to redeem deposits,there may be a “rush for the exit” among investors. This is often preemp-tive defection—exactly what one would expect if the iterated PD modelprovided an accurate picture. This is one of the reasons why financialinstability is rampant—because decisions are often based on expecta-tions rather than “fundamentals.” Of course, the end result is collectivelyself-defeating, in the sense that investors force the default that theyfeared. But this is, again, just a reflection of the fact that the interactionhas the structure of an iterated PD.

Thus the entire savings-and-investment system in our society hasimportant features in common with a pay-as-you-go pension system.This structure is obscured by a money illusion, which leads us to think ofmoney that is saved as having been hoarded rather than as having beenspent by someone else on the production of capital goods. Cooperationis required in order to allow savers to “cash out” at a later point in time,converting the money balance into consumption goods (the honoring ofsuch requests is what deserves to be labeled “c” in the game treediagram). The advantage of having such a system in place is that itenlarges the pool of funds available for investment, making it individu-ally rational to save (or, more accurately, increasing the incentive tosave). Young people in general have no incentive to deviate from thisarrangement, because they themselves stand to benefit from it, when thenext generation takes over the major productive tasks in the economy.

Once this system of cooperation is in place, environmental degrada-tion of the sort associated with climate change clearly becomes an issue


of justice, which is to say, it is a question that concerns how the benefitsand burdens are to be divided up within an ongoing system of coopera-tion. Older generations claim certain entitlements (namely, the accumu-lated returns on their savings) based on the amount of their earliercontributions to the pool of funds available for investment. Yet in thepresence of negative environmental externalities, the private benefit ofthese investments most certainly exceeds the social benefit. Thusclimate change raises obvious questions about what the terms are to be(or what the principles of justice require) in the system of intergenera-tional cooperation that underlies saving and investment. This is not tosay that we must adopt a particular set of climate change policiesbecause we fear that failure to do so will generate some sort of massdefection on the part of future generations. It is intended simply to showthat the circumstance of justice obtains between ourselves and all futuregenerations with respect to this issue, which is why, when we think aboutclimate change, we are compelled to apply principles of justice to thequestion rather than some less demanding set of norms, such as anobligation of generalized benevolence or a duty of assistance.58

VI. CONCLUSION

The view that intergenerational justice creates difficulties for contractu-alism, because the “absence of mutuality” between generations pre-cludes cooperation, has become widespread in the philosophicalliterature. I hope to have shown, in this article, that the view is basedupon a misunderstanding of several key features of both contractualismand the operations of a modern economy. (It is worth keeping in mindthat, whatever normative objections one may have to contractualism orto the principles of justice that a contractualist might recommend in theintergenerational case, none of it is relevant to the empirical question ofwhether or not we are involved in various systems of intergenerationalcooperation.) There are, as far as I can tell, three major reasons why somany philosophers have failed to see the system of intergenerationalcooperation that underlies many core features of the basic structureof our society:

58. I am assuming here that contractualism is being put forth as a “political” concep-tion of justice, in the Rawlsian sense, and not as a comprehensive moral view.


(1) The system is based upon indirect reciprocity, and so those whothink of cooperation in very narrow terms, on the model of directreciprocity, have difficulty discerning it.

(2) The cooperative benefits flow upstream—from younger toolder. The downstream benefits to future generations are allby-products. This is somewhat counterintuitive if one is thinkingabout the problem from a moralistic perspective. Because savingis the behavior that ultimately generates the benefits for futuregenerations, there is an inclination to think that people must besaving for moral reasons, and so any contractualist theory mustbe able to explain saving as a form of cooperative behavior. Thisinclination dissipates as soon as one realizes that almost allsaving is motivated by self-interest, or else narrow altruism (i.e.,toward one’s living descendants).

(3) Finally, the most important system of intergenerational coopera-tion, the one that underlies the savings system, is hidden behinda money illusion. This is what leads us to think of the elderly ashaving somehow freed themselves from dependence upon theyoung by virtue of having saved for their retirement. This givescertain economic transactions the appearance of being nonco-operative, when in fact they require an extensive system ofintergenerational cooperation.

There are no doubt many who will still dispute the normativeadequacy of contractualist approaches. In order to even debate thesequestions, however, it is first necessary to set aside the pseudoproblemabout intergenerational cooperation that has so far impeded discus-sion. What I hope to have shown in this article is that there is noimpediment to the application of contractualist principles to the ques-tion of just savings—understood broadly, to include the set of environ-mental problems and natural resource issues that are conventionallyaddressed within this framework. Whether or not everyone will appre-ciate the results of such an application is a question that must be leftto another day.


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Heath the Structure of Intergenerational Cooperation

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