Sergio Beraldo

(University of Naples “Federico II” & ICER)

Lectures delivered at the University of Prague (VSE)

October 2011 III - IV

Outline of the courseI: InstitutionsII: CoordinationIII: Cooperation 1IV: Cooperation 2V: Institutional structure and economic

performance

III LECTURE

Cooperation

CooperationFor mutually beneficial exchange to

take place it is necessary that trading partners do cooperate

Institutions which ensure an acceptable level of cooperation are necessary

The problem of cooperationIn many social situations in which your

opponent is behaving in such a way as to make the achievement of a cooperative outcome possible, it may seem contrary to your self-interest to resist the temptation of cheating

There are gains to be made by resisting such a temptation

Indeed: a surplus may be generated if selfishness (or lack of confidence) were put aside;

The problem of cooperationD.C. North, Journal of Economic

Perspectives, 1991 → Individuals will usually find it worthwhile to cooperate with other players when:

the play is repeated they possess complete information about the other

player's past performance there is a small number of players

[Think at earliest economies characterized by local exchange within a village – kin or reputation ensure compliance]

The problem of cooperationNorth (1991) → Cooperation is difficult to sustain

when: the game is not repeated (or there is an endgame); information on the other players is lacking there is a large number of players

Notice : the productivity gains coming from specialization and division of labour can only be reaped if there emerges an institutional structure solving the problem of human cooperation under the latter conditions

Anonymous exchange requires cooperative individuals

Are human beingscooperative beings?

“Evolution is based on a fierce competition between individuals and should therefore reward only selfish behaviour...yet we observe cooperation on many level of biological organization. Genes cooperate in genomes. Chromosomes cooperate in eukaryotic cells. Cells cooperate in multicellular organisms. There are many example of cooperation among animals. Humans are the champions of cooperation...cooperation is the decisive organizing principle of human society. The question of how natural selection can lead to cooperative behaviour has fascinated evolutionary biologists for several decades” (Nowak, Science, 2006)

Are human beingscooperative beings?

“Human societies…are based on a detailed division of labour and cooperation between genetically unrelated individuals in large groups”, (Fehr&Fischbacher, Nature, 2003)

"The evolution of cooperation among non-related individuals is one of the fundamental problems in biology and social sciences.", (Hauert et al., Science, 2002)

The standard framework for the study of cooperation: the Prisoner’s dilemma

CooperateCooperate DefectDefect

CooperateCooperate 1,11,1 9,09,0

DefectDefect 0,90,9 5,55,5

Player 1

Player 2

How can cooperation emerge in an evolutionary setting?

M. Nowak (Science, 2006) discusses five possible routes:Direct reciprocityIndirect reciprocityNetwork reciprocitykin selectionGroup selection

Nowak (2006) shows that in any of these cases cooperation can emerge if the cost to benefit ration of the cooperative act is below a certain threshold

Direct reciprocityExperimental evidence: individuals do cooperate even in one

shot interactions or in the last stage of a repeated game (Gintis & Bowles, 2003)

To explain how cooperation did evolve it is necessary to take into account that for individuals living in small groups of hunter-gatherers (humans until 10.000 years ago) it would have been relatively simple to avoid punishment by joining a different group (Gintis and Bowles, 2003)

The evidence that cooperation among animals is actually based on reciprocity is scarce (Silk, 2005; Fehr & Fischbacher, 2003; Hammerstein, 2003; Clutton-Brock, 2009)

Hammerstein (2003) – Genetic and cultural evolution of cooperation, MIT press: “After three decades of worldwide research on reciprocal altruism and related phenomena, no more than a modest number of animal examples have been identified”

How is it possible to extend the folk theorem from a group of two to a group of n individuals? (public good game – if you do not cooperate you are actually punishing also who cooperates)

Direct reciprocity: I scratch your back and you’ll scratch mine

Trivers, The Quarterly Review of Biology, 1971.

Folk Theorem;Nowak (2006) → prob. of another encounter

between the same two individuals> cost/Benefit ratio of the cooperative act

As n increases it becomes more and more difficult for cooperation to evolve

Stated in different terms: the probability that a proper number of individuals be sufficiently forward looking shrinks as n increases (Bowles & Gintis, 2003; Beraldo & Turati, 2011)

Indirect reciprocity: I make a point of going to other people’s funeral otherwise they won’t come to mine (Yogi Berra,

baseball player) Remember yogi bear, the Hanna-Barbera’s cartoon, (however

cartoonists denied they were inspired by Berra). Berra is well known for his Yogiism, often taking the form of either obvious tautology or a paradoxical contradiction.

However, the sentence above is less paradoxical of what may seem

Indirect reciprocity – based on status or reputationIR has recently obtained considerable attentionSocial sciences → cooperation when interaction is not

face to faceEvolutionary biology → Nowak and Sigmund, Nature,

2005: → “humans not only feel strongly about interactions

involving them directly, they also judge the actions between third parties (e.g. gossip), indirect reciprocity is therefore likely to be connected with the origins of moral norms and has probably played a pivotal role in the evolution of collaboration and communication (language)”

Open problemsActual debate: does indirect reciprocity work in sustaining cooperation in an evolutionary environment?

How does it actually work? What is a reliable model of cooperation based on indirect reciprocity?

Two competing modelsThe image-scoring model (Nowak and Sigmund,

Science, 1998);The good standing model (Sugden, 1986)The difference is that the latter distinguishes

between justified and unjustified defection, while the former does not;

Although computer simulations point out that the standing model would perform better under a wide set of circumstances, it is often maintained that it requires individuals with an implausibly large capacity of processing recursive information (e.g. Engelmann and Fischbacher, Games and Economic Behaviour, 2009) .

Open ProblemsGood standing model → B’s standing does matter

Help, Not Help

b, -c

t = m t = m + 1

Help, Not Help

b, -c

A B

CC A

Open Problems – Good standing Recursive information: a potential donor k

should not only know the behaviour of j in his last interaction as a donor, i.e. whether j cooperated or defected; as k’s behaviour has to be contingent on j’s standing, k should be aware of the standing of j', the potential recipient with whom j last interacted as a potential donor. As the standing of j' depended on the choice made when j' acted as potential donor of j'', k should be aware of j''’s standing at the time, and so on.

Is recursive information necessary for the standing model to work?It is possible to prove that the standing model does not require recursive information (see Beraldo S., International Review of Economics, 2011)

Does indirect reciprocity work?Adam Smith (1763/1978) was the first to

suggest that cooperative practices emerge whenever the cost of acquiring a good reputation is more than offset by the material gains accruing from it. Any economist would still agree that the need of displaying a good image is (at least partially) driven by the desire of reaping the fruits accruing from market interaction. A good standing or image, in other words, pays.

Greif, A., 1989. Reputation and coalitions in medieval trade: evidence on the Maghribi traders. Journal of Economic History, 49, 857-882. (overseas commerce made possible by indirect reciprocity)

Does indirect reciprocity work?As the development of a far than

rudimentary language is a necessary condition for large scale cooperation based on it, indirect reciprocity is certainly not suitable to provide a convincing explanation for the widespread level of cooperation observed in nature (e.g. de Waal., 2006)

Does indirect reciprocity work?In a forthcoming book, Sam Bowles and Herbert

Gintis (2010) argue that indirect reciprocity is also unable to give account of the evolution of the biological traits which make humans a cooperative species, since, as soon as human communities get larger, high quality information is no more available and the rate of errors in perception becomes excessively high for indirect reciprocity to work

Does indirect reciprocity work?Cooperation is not a single phenomenon with a

unified causal explanation. Even if a form of reciprocity based on status or reputation is inadequate to provide a consistent account of the biological bases of our attitude to cooperate, there are reasons to believe that it helps in drawing a reliable picture of the forces sustaining cooperative practices in many social and economic environments [In this respect, the standing model, starting from more realistic hypotheses about human behaviour, seems to be the preferred candidate to catch the basic aspects of how reputation works and is affected by one’s conduct]

Kin Selection: I will jump into the river to save two brothers or eight cousins (J.B.S.Haldane, biologist)!

Hamilton, Journal of Theoretical Biology, 1964; natural selection favours cooperation when the donor and the recipient are genetically related

Hamilton’s rule: coefficient of genetic relatedness (probabiliy of sharing a gene) > C/B

The selfish gene (Richard Dawkins, 1976)Kin selection is unable to explain why

individuals do cooperate with those who are not genetically related to them

Es: why do individuals donate resources under conditions of anonimity? (e.g., blood donations)

Network reciprocity – Group selection

Network reciprocity: cooperators give rise to clusters

Group selection: groups of cooperators fare better than groups of defectors

To sum upNo one of the five routes analyzed by

Nowak can explain the emergence of cooperation without dropping one of the following two hypotheses:

well-mixedness;Anonimity

This problem is fundamental as anonymity and well-mixedness are typical of many economic, social and biological environments

Two further hypotheses for the evolution of cooperationThe green beard hypothesis (Dawkins, 1976),

and the hypothesis of voluntary participation (e.g. Tullock, 1985; Hauert et al. 2002, 2007).

The green beard hypothesis → the evidence is very limited (Keller and Ross, 1998); its general applicability, has been deeply questioned (Fehr and Fischbacher, 2005)

The voluntary participation hypothesis → if the Prisoner’s Dilemma payoffs are retained, cooperation remains a (weakly) dominated strategy; in pairwise interaction the only effect is that of replacing the defection equilibrium with one of non-participation

No more prisoners of the dilemmaTheorists have generally used the Prisoner’s

Dilemma as the paradigm model of cooperation problems. In doing so, they may have set themselves an unnecessarily difficult challenge. Furthermore, by neglecting the existence of all those situations in which the problem of cooperation is less intractable than in the simple Prisoner’s Dilemma, the analysis risks to be both incomplete theoretically and dangerous socially (Worden and Levin, 2007)

No more prisoners of the dilemmaAmong the restrictive features of the

Prisoner’s Dilemma, a prominent one is that, in any given interaction, an individual must act either pro-socially or anti -socially; there is no opportunity to be simply a social

Clutton-Brock (2009) → “social animals are seldom constrained to cooperate with particular partners and can develop profitable relationships and terminate unproductive ones”

This is even more true for humans, given their higher cognitive capacities

No more prisoners of the dilemmaAs emphasized before Adam Smith’s

pointed out that honest behaviour is profitable for the individuals performing it whenever the opportunity is given of terminating trading relationships with untrustworthy partners

The voluntary participation hypothesis adds an asocial strategy, that of opting out of the interaction. However, in anonymous settings with pairwise interaction, if the Prisoner’s Dilemma payoffs are retained, the only effect is to replace the defection equilibrium with one of non-participation

No more prisoners of the dilemmaBeraldo and Sugden (2010) propose a

voluntary participation model which retains the dyadic form of the Prisoner’s Dilemma;

In their model the benefit that each player derives from the cooperative activity (given the other’s cooperation) is an independent realisation of a random variable, known to the relevant player before the game is played.

Modelling the payoffs from the cooperative outcome as subject to random variation is consistent with the evidence that both in humans and among animals, the outcome of many strategic situations implying gains through joint activity, depends on subject to subject variation (e.g. Johnson et al., 2002)

ResultsBeraldo and Sugden (2010) show that - provided

the upper bound of the distribution of cooperative benefit is not too low - there is an equilibrium in which beneficial cooperation occurs. The non-participation option plays an essential part in this result, as it holds down the equilibrium frequency of cheating and this allows cooperation to persist

In their model, cooperative behaviour does not depend on benevolence, reciprocity or fear of punishment; it occurs because the benefit that an individual would derive from mutual cooperation is sometimes great enough to make it worthwhile to run the risk that the opponent will cheat

The modelLarge number of individuals, interacting

anonymously in an indefinitely long sequence of periods.

In each period, individuals are randomly matched to play a two-player game.

In a representative game between players i and j, the benefits from cooperation xi and xj are independent realizations of a random variable X whose distribution f(.) is continuous with support [xmin , xmax].

Each player knows its own benefit but not that of the other player. Given this knowledge, it chooses one of three options – to cooperate (C), to cheat (D), or not to participate (N).

Payoff matrix [Beraldo-Sugden, 2010]

NN CC DD

NN 0, 00, 0 0, 00, 0 0, 00, 0

CC 0, 00, 0 xxii, , x xjj --bb, , aa

DD 0, 00, 0 aa, -, -bb --cc, -, -cc

Player 1

Player 2

xmax > a > xmin 0; b > a > c > 0.

Payoff matrix

xmax > a > xmin →C or D may be the better response to C, depending on the realization of X.

b > c → D is better than C as a response to D.

a > 0 → cheating gives a higher payoff than non-participation if the opponent cooperates;

c > 0 → the opposite is the case if the

opponent cheats; b > a → implies that the benefit from cheating a cooperating co-player is less than the cost inflicted on the latter.

NN CC DD

NN 0, 00, 0 0, 00, 0 0, 00, 0

CC 0, 00, 0 xxii, , x xjj --bb, , aa

DD 0, 00, 0 aa, -, -bb --cc, -, -cc

ResultsIf xmax > ab/c (more intuitively: provided that

the upper tail of the distribution of cooperative benefit is not too short), there is at least one interior or boundary equilibrium in which both C and D are played with positive probability.

These equilibria are ESS

Some Comments If participation in a potentially cooperative activity is voluntary, the frequency of cheating can be held down to a level at which some mutually beneficial cooperation can occur even in anonymous well-mixed populations

Cooperative behaviour may not depend on benevolence, reciprocity or fear of punishment; it may occur because the benefit that an individual would derive from mutual cooperation is sometimes great enough to make it worthwhile to run the risk that the opponent will cheat

Cooperation is seen as a risky strategy, worthwhile only if the probability that any occasional opponent will cheat is sufficiently low

In the game, getting to the cooperative outcome may be in some occasions so valuable for the players involved, that each of them would risk cooperation rather than loosing the chance of getting such an advantage, even if by so doing it is unavoidable to get exposed to the risk of being cheated

DiscussionThere are differences between this

framework, some of the evidence gathered by zoologists so far, and various strategic situations envisaged by game-theorists.

First note that: some apparently cooperative behaviours are forms of mutualism, in which any individual maximizes its own fitness and any effect on the fitness of others is coincidental and does not contribute to the selection pressures maintaining the behaviour (e.g. Clutton-Brock, 2002, 2009).

Suricata Suricatta.

suricata suricatta, small mammals living in arid areas of southern Africa (Clutton Brock et al., 1999). Going on guard when no other individual is guarding, may have immediate, direct benefits. In cases like these, variously termed as mutualism, by-products or mutual benefits, acts by one individual confer immediate benefits to the actor and (only) coincidentally to others

Snowdrift game (R. Sugden, 1986)

DigDig Not DigNot Dig

DigDig V- CV- C11,,

V-CV-C22

V- CV- C11, V, V

Not digNot dig V, V- CV, V- C11 0,00,0

Player 1

Player 2V → Benefir to get out of the snowdriftC1 → cost to dig alone player 1;C2→ cost to dig alone for player 2

even if the relevant player is sure that the opponent defects, it is in her interest to dig: it is so important to get out of the snowdrift that each player would rather do all the digging himself rather than remain stuck.

Stug-hunt game

HareHare StagStag

HareHare 2,22,2 2,02,0

StagStag 0,20,2 3,33,3

Player 1

Player 2

Each player may be tempted to follow a smaller prey instead of obeying to a concerted plan suitably devised to catch a deer - the relevant player does better by cooperating only if the opponent cooperates too.

Cooperation in animal societiesIt is now clear that there are substantial

differences between humans and animals. In animal societies, where some apparently cooperative behaviours are indeed forms of mutualism, cooperation is mostly based on kin, being therefore quite rare in groups consisting of genetically unrelated individuals (Clutton-Brock, Science, 2009)

A different view based on empathy

The age of empaty