Reciprocity in Economics and International Relations · Introduction Reciprocity in Economics...

Introduction Reciprocity in Economics Reciprocity in International Relations A Cobb-Douglas Example Experiments Conclusion

Reciprocity inEconomics and International Relations:

Taking Stock and Discussing Strategic Implications forLeadership

Michael Eichenseer

Presentation - TU Bergakademie Freiberg

October 10, 2019

Reciprocity in Economics and International Relations Michael Eichenseer

Reciprocity

Donald Trump, Vampire Bats & Adam Smith


“reciprocal, one of my favouritewords”

Donald Trump

Source: https://www.sueddeutsche.de/politik/aktuelles-lexikon-reziprok-1.4384933

Reciprocity in Economics and International Relations Michael Eichenseer 1


Vampire batsFemale vampire bats (Desmodus rotundus) have reciprocalfood-sharing relationships not only with kin but also with non-kin(Carter et al., 2017).



“in a nation of hunters, if any one has a talent formaking bows and arrows better than his neighbor hewill at first make presents of them, and in return getpresents of their game. By continuing this practice

he will live better than before and will have nooccasion to provide for himself, as the surplus of his

own labor does it more effectually”

Adam Smith, 1976, p.220 as cited by Ashraf et al. (2005)



Outline of this Presentation

Part I

Going in search of reciprocity, taking stock of the literature:

• Micro-level of individual preferences in(experimental-)economics.

• Is there evidence that these results can be transferred to thelevel of international relations (IR)?

Part II

What are the strategic implications of reciprocity for leadership?

• A Cobb-Douglas example considers the level of public goodcontributions and the first-mover advantage.

• Finally, I briefly present whether these pattern are reflected inexperimental public goods games that incorporate leadership.


Economics


Economists referred reciprocity to a broad range ofeconomic outcomes:

• Gift exchange in labor markets (Akerlof, 1982).

• Employee theft (Giacalone and Greenberg, 1997).

• Informal insurance (Coate and Ravallion, 1993).

• Public goods supply (Sugden, 1984).

Increasing evidence with the spread of experimental economics:

• Ultimatum game (Guth et al., 1982): responders reject lowoffers (less than 20 % of the surplus) with a large probability(Fehr and Schmidt, 2006) which indicates negative reciprocity.

• By contrast, gift-exchange games (Fehr et al., 1998) and trustgames (Berg et al., 1995) indicate positive reciprocity.



Reciprocity in the Sequential Prisoner’s Dilemma I

• In this sequential version of the Prisoner’s Dilemma gameplayers move one after the other.

• Correspondingly, the second player has the means ofreciprocally responding to the first player’s action.• Clark and Sefton (2001) show that a substantial fraction of

second movers make use of this opportunity:• About 90% of the experimental subjects respond with

defection to the first mover’s defection whereas 58% use thecooperative action if the first mover cooperated.

• Cooperation, however, decreases with repetition of the gameand the extent of reciprocity diminishes with rising monetarycosts of cooperation.



Reciprocity in the Sequential Prisoner’s Dilemma II

Type Behavior

Conditional cooperator (CC) Cooperates only if the other player also cooperatesSelfish (SF) Never cooperates (free-rider)

Altruist (AL) Always cooperatesMismatcher (MM) Does the opposite of the other player



Reciprocity in the Sequential Prisoner’s Dilemma III

Miettinen et al. (2017): strategy method to determine the reactionon cooperation as well as defection for every individual→ classify discrete behavioral types:

• 47% free-riders/ unconditional defectors

• 38% conditional cooperators

• 9% altruists

• 6% missmatchers.

→ A substantial fraction of subjects can be classified asconditional cooperators in the sequential prisoner’s dilemma.



Reciprocity in Public Goods Games I

• Workhouse model to study cooperation in experimental publicgoods games: voluntary contribution mechanism (VCM) withindividual payoffs

πi = yi − gi + αN∑j=1

gj .

• Croson (1996): strong positive correlation to both, others’contributions and to the beliefs about others’ contributions→ indicates positive reciprocity and is contrary to a standardcrowding-out hypothesis. Subjects increase their contributionsif others do so or they expect others to do so.

• Sonnemans et al. (1999) and Keser and Van Winden (2000)comparing partner and stranger matching: pattern ofconditional cooperation emerges.



Strategy Method (Fischbacher et al., 2001)



Reciprocity in Public Goods Games III

• Conditional cooperation is a cross-culturally robustphenomenon with a varying fraction of conditional cooperators(Kocher et al. (2008); Herrmann and Thoni (2009))

• Can be observed from early on (Hett et al., 2018).

• However, mapping most subjects’ contributions relative to theaverage contribution of the remaining subjects reveals thattheir contributions are below the 45 degree line when using thestrategy method → ”selfish-biased conditional cooperation”.

• When individual contributions instead of an average of others’contributions are revealed, subjects align to a low contribution(Hartig et al., 2015).



Type stability across games (Eichenseer and Moser, 2019)

• Explore the within subject stability across the sequentialprisoner’s dilemma and the public goods game.

• Subjects classified as conditional cooperators in the prisoner’sdilemma match others’ contributions in the public goods gameto a signicantly larger degree compared to other types. Graph

• Conditional relative frequencies: 93.3% of the subjects whoare classified as CC in the prisoner’s dilemma, are alsoclassified as CC in the public goods game. Venn Numbers

• However, individuals classified as ‘selfish’ in the prisoner’sdilemma, are classified as ‘selfish’ only in around 34.6% of thecases in the public goods game. Venn Numbers



Costly and decentralized punishment

• Punishment opportunity induces higher PG contributions onaverage.

• “homo reciprocans has the opportunity to discipline thosesubjects who are selfish or insufficiently motivated by positivereciprocity” (Fehr and Gachter, 1998).

• Evolutionary perspective: a small fraction of people couldinduce selfish types to cooperate (Gintis et al., 2003).

• The possibilty of punishing others and the threat of beingpunished have an impact on conditional cooperation(Kirchkamp and Mill, 2018). More

• Dispositional free riders “do not free ride onpunishment ofothers” (Weber et al., 2018). More



Models of reciprocity I

Intention-based reciprocity: Rabin (1993): players sacrificemonetary payoffs to reward kind intentions and punish unkindintentions → players form beliefs about the other player’s actionsand hold beliefs on the other player’s beliefs about own actions.→ Dufwenberg and Kirchsteiger (2004) incorporate updating ofbeliefs.

Outcome-based reciprocity: e.g. Fehr and Schmidt (1999) andBolton and Ockenfels (2000).

Mixed models: Charness and Rabin (2002) and (Falk andFischbacher, 2006, for extensive form games) combine intentionsand distributional concerns.



Models of reciprocity II

Type-based reciprocity: kindness towards another player dependson the other player’s type (Levine, 1998).

Emotional state-based reciprocity: Cox et al. (2007).

Norm-based reciprocity:

• Utility from following societal norms (e.g. Kimbrough andVostroknutov (2016)).

• Sugden (1984) formulates a a “reciprocity principle”:people in a PGG feel a moral obligation to either follow anadapted version of a Kantian “categorical imperative” or ifothers contribute less: at least the minimum contribution ofthe group → individual maximizes utility subject to a “moralconstraint” that includes an obligation for reciprocal behavior.


International Relations


Reciprocity and International Relations

• Direct linkage is the work of Elinor Ostrom who promoted theintegration of elements of behavioral economics likereciprocity into economically minded rational choice theory(Ostrom, 1998).

• Likewise, theorists like Axelrod described reciprocity as amean of achieving cooperation among egoists by formalizingthe argument through an iterated Prisoner’s Dilemma(Axelrod, 1981).

• Liberal school of institutionalism: Robert Keohane (1986) hasdescribed the immanent meaning of reciprocity for liberalistinstitutionalism in answering “Why is there no war of allagainst all?” → Limited cooperation in large parts due toreciprocity.



Reciprocity in the Liberal School (Keohane)

• Two different kinds of reciprocity:• “diffuse reciprocity”: not always clear whether it is an

exchange of equivalent values and moreover the sequence ofthe exchange is less obvious. No expectation of an immediatepayback → creating trust and show good will.

• “specific reciprocity”: contingent exchange of equivalent itemsin a pre-specified sequence e.g. in international tradenegotiations.

• Chance of transferring diffuse reciprocity into specificreciprocity → preconditions like powerful common interests,fear of future retaliation or international regimes.

• Successful specific reciprocity may create trust and lead todiffuse reciprocity in other domains.

• Prosperous institutions are rooted on both grounds.



Empirical Examples and Evidence for Reciprocity I

Is there evidence for reciprocal behavior between nations?

• For a considerable number of pairs of bilateral interactions(cooperation/ non-cooperation) between countries reciprocalpatterns can be detected in a time series (Frank et al., 2018).• Reciprocal behavior in military conflicts:

• Superpower relations between the United States and the SovietUnion (Goldstein, 1991).

• Bosnia Conflict (Goldstein and Pevehouse, 1997) .• Middle East (Goldstein et al., 2001).• India and Pakistan (Rajmaira, 1997).• Adherence to international law in times of war during the 20th

century (Morrow, 2007) → noncompliance is almost alwaysmutual.



Empirical Examples and Evidence for Reciprocity II

• Diplomacy and International Negotiations• Since the 19th century diplomatic privileges and immunity

have been granted on the basis of reciprocity which is alsorooted in the Vienna Convention of 1961 (Hestermeyer, 2009).

• Expulsion of diplomats is commonly based on the reciprocityprinciple.

• Visa reciprocity is a very stable pattern (Czaika et al., 2018).• International agreements oftentimes explicitly refer to the

principle of reciprocity e.g. Basic Principles Agreementbetween Nixon and Brezhnev in 1972 (Keohane, 1986).

• Arms control during the cold war resembles a specific form ofreciprocity (Bernauer, 2013).

• International law (Simma, 2008). More

• Foreign policy attitudes of the electorate (Bechtel and Scheve,2013; Tingley and Tomz, 2014). More


Strategic Implications of Reciprocity-

A Cobb-Douglas Example


The Framework I

• Two countries L and F have preferences over privateconsumption and public good consumption of Cobb-Douglastype which is given by vi = xiG for i = L,F where xi denotesprivate consumption.

• In addition, a reciprocity term enters additive in the utilityfunction such that: ui = vi + ϕi (gF , gL).

• The public good G is produced by a summation technology,i.e. G = gL + gF . Public good productivity is equal to 1 suchthat gi = wi − xi .

• Let us further assume like in Buchholz and Sandler (2017)that the reciprocity component is given byϕi (gF , gL) = αi (gL − gL)(gF − gF ) with gF and gL beingreference values for country F and L respectively.



The Framework II

• We assume equal endowments wi = w of both countries.

• For simplicity, we assume that each country considers thepublic good supply of the other country as the point ofreference.

• The additive separable utility function is then given by:

ui = xiG + αi (gi − gj)(gj − gi ). (1)

Setting gi = gj , gj = gi , G = gi + gj and gi = wi − xi yields:

ui = (wi − gi )(gi + gj)− αi (gi − gj)2 (2)


Nash Equilibrium


The Nash Equilibrium I

Country i for i = L,F maximizes utility ui which is given by (1):ui = (wi − gi )(gi + gj)− αi (gi − gj)

2 with respect to gi such thatthe first-order condition (f.o.c., herafter) is:

∂ui∂gi

= −(gi + gj) + (wi − gi )− 2αi (gi − gj) = 0 (3)

Solving (3) for gi gives us:

gi =wi − (1− 2αi )g j

2 + 2αi(4)

and due to symmetry:

gj =wj − (1− 2αj)g i

2 + 2αj. (5)



The Nash Equilibrium II

Inserting the reaction function of j, g rj which is given by (5) in (4)

gives:

gi =wi

2 + 2αi− 1− 2αi

2 + 2αi

wj − (1− 2αj)g i

2 + 2αj(6)

Solving this term for gi gives:

gi =(2 + 2αj)wi − (1− 2αi )wj

3 + 6αj + 6αi(7)

and due to symmetry:

gj =(2 + 2αi )wj − (1− 2αj)wi

3 + 6αi + 6αj. (8)



The Nash Equilibrium III

In the case of equal endowments, public good contributions gi andgj are independent of the reciprocity parameters αi and αj :

gi =(2 + 2αj)w − (1− 2αi )w

3 + 6αj + 6αi=

(1 + 2αj + 2αi )w

3 + 6αj + 6αi=

1

3w (9)

and due to symmetry: gj = 13w .

Countries’ PG contributions are strictly larger than zero andcountries can afford their contribution as gi ,j = 1

3w < w . Publicgood supply thus is G = 1

3w + 13w = 2

3w and utilities are:

ui =

(w − 1

3w

)2

3w − αi

(1

3w − 1

3w

)2

=4

9w2(= uj) (10)

→ reciprocity term does not alter the Nash equilibrium in ourexample.


Stackelberg Equilibrium


The reaction function of the follower

Maximizing the utility of the followeruF = (wF − gF )(gL + gF )− αF (gF − gL)2 which is given by (2)with respect to gF gives the f.o.c.:

∂uF∂gF

= −(gF + gL) + (wF − gL)− 2αF (gF − gL) = 0. (11)

This yields the reaction function:

gRF =

wF − (1− 2αF )gL

2 + 2αF(12)

such that crowding-in occurs, i.e. ∂gF∂gL

> 0 for αF >12 .



Public good contribution of the leader I

The leader’s utility is given by (2) :uL = (wL − gL)(gL + gF )− αL(gL − gF )2. Inserting gR

F in theutility function of the leader yields:

uL = (wL − gL)

(gL +

wF − (1− 2αF )gL

2 + 2αF

)− αL

(gL −

wF − (1− 2αF )gL

2 + 2αF

)2

(13)

which can be rewritten as:

uL = (wL−gL)

(wF

2 + 2αF+

1 + 4αF

2 + 2αFgL

)−αL

(3

2 + 2αFgL −

wF

2 + 2αF

)2

.

(14)



Public good contribution of the leader II

Maximizing uL with respect to gL gives the f.o.c.:

∂uL∂gL

= −(

wF

2 + 2αF+

1 + 4αF

2 + 2αFgL

)+ (wL − gL)

1 + 4αF

2 + 2αF

− 2αL

(3

2 + 2αFgL −

wF

2 + 2αF

)3

2 + 2αF= 0. (15)

Solving the f.o.c. for gL yields:

gL =(1 + 4αF )(2 + 2αF )wL − (2 + 2αF − 6αL)wF

2(1 + 4αF )(2 + 2αF ) + 18αL. (16)

In the case of equal endowments, i.e. w = wi = wj , this reducesto:

gL =8αF

2 + 8αF + 6αL

2(1 + 4αF )(2 + 2αF ) + 18αLw . (17)



Public good contribution of the leader III

Obviously, the public good contribution of the leader is positive ifeither one of the two countries has reciprocal preferences. For ourspecial case, inserting the public good contribution of the leaderinto the reaction function of the follower gives:

gF =w

2 + 2αF− (1− 2αF )

2 + 2αF

8αF2 + 8αF + 6αL

2(1 + 4αF )(2 + 2αF ) + 18αLw (18)

and gL > gF holds as soon as:

gL =8αF

2 + 8αF + 6αL

2(1 + 4αF )(2 + 2αF ) + 18αLw >

1

3w (19)

such that the leader contributes more than the follower as soon ashis contribution exceeds the one of a player in the Nash-Game.



Total public good supply

Total public good supply in the Stackelberg Case, G = gL + gFthen is using eq. (17) and (18):

G =w

2 + 2αF+

(1 + 4αF )

2 + 2αF

8αF2 + 8αF + 6αL

2(1 + 4αF )(2 + 2αF ) + 18αLw . (20)

→ An improvement to the Nash equilibrium, i.e. G > 23w occurs if

αF >12 .

→ The leader contributes more than the follower in this case (as0 < ∂gF

∂gL< 1).


Numerical Example


Stackelberg Equilibrium:

Nash Equilibrium: gL = 13w ; gF = 1

3w ; G = 23w

Calc1 Calc2



A brief look into Experiments: Contributions



Contribution ratio (CR = gFgL

)

Source: Eichenseer (2019)Reciprocity in Economics and International Relations Michael Eichenseer 32

Conclusion


Conclusion I

• Reciprocity is wide-spread both in (Experimental)Economicsand International Relations.

• Both in the public discussion and theoretical literaturereciprocity is regarded as a key to successful cooperation→ argument of crowding-out looses its importance.

• In addition, reciprocity apparently alters the balance of powerin the leader-follower game.

• Without reciprocity, the leader is in a fortunate position andconsequently contributes less than the follower(s). Inanticipation of a reciprocal response of the follower(s) thisgame now turns.



Conclusion II

• The first-mover position of the leader becomes unfavorable –a “leader curse”.

• Followers’ reciprocity thus not only is a reliable remedy tostand one’s ground in a strategically unfavorable position butit also allows to exploit the leader to a certain extent.

• So, why lead? Why should one choose to be the leader?→ A first answer might be that the leader does not fare worsecompared to simultaneous play, he only improves less.→ Better to swallow the bitter pill if no one else did.


Thank you for your attention!

References I

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Bolton, G. E. and A. Ockenfels (2000). Erc: A theory of equity, reciprocity, andcompetition. American Economic Review 90(1), 166–193.

Buchholz, W. and T. Sandler (2017). Successful leadership in global publicgood provision: Incorporating behavioural approaches. Environmental andResource Economics 67(3), 591–607.

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Carter, G. G., D. R. Farine, and G. S. Wilkinson (2017). Social bet-hedging invampire bats. Biology letters 13(5), 20170112.

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Clark, K. and M. Sefton (2001). The sequential prisoner’s dilemma: Evidenceon reciprocation. The Economic Journal 111(468), 51–68.

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References III

Eichenseer, M. (2019). Leading by example in public goods experiments: Whatdo we know? Available at SSRN 3441638 .

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Falk, A. and U. Fischbacher (2006). A theory of reciprocity. Games andEconomic Behavior 54(2), 293–315.

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Fehr, E., E. Kirchler, A. Weichbold, and S. Gachter (1998). When social normsoverpower competition: Gift exchange in experimental labor markets.Journal of Labor Economics 16(2), 324–351.

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Ostrom, E. (1998). A behavioral approach to the rational choice theory ofcollective action: Presidential address, american political science association,1997. American Political Science Review 92(1), 1–22.

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References VIII

Weber, T. O., O. Weisel, and S. Gachter (2018). Dispositional free riders donot free ride on punishment. Nature Communications 9(1), 1–9.

Contribution paths by SPD classification in FGF Back

Venn diagrams of SPD and FGF-T (refinement of Thoniand Volk (2018)) Back

Types in SPD and FGF-T (refinement of Thoni and Volk(2018)) Back

Kirchkamp and Mill (2018): impact of punishment power onconditional cooperation

• Individuals who have the possibility of punishing others, showa pattern of more conditional cooperation.• The threat of being punished has opposite effects:

• Extensive margin: the number of free-riders increases.• Intensive margin: intensity of conditional cooperation increases→ positive overall effect.

Weber et al. (2018): relation between positive and negativereciprocity:• Subjects classified as free-riders cooperate only when

punishment is possible.• Conditional cooperators also cooperate in the absence of

punishment.• Positive (conditional cooperation) and negative (punishment)

reciprocity are not correlated.• Dispositional free riders “do not free ride on punishment of

others”

Back

International law (Simma, 2008) Back

• Reciprocity involved in the law making process and theemergence of customary international law.

• Claims put by states that initiate the process of law-makingdepend on the expectation of the acceptance of claims byother states.

• Expectations of reciprocity may bring about mutual restraintand encourage self-limitation of the actors involved.

• Reciprocity is governing every international agreementespecially with regard to the reservations, termination andsuspension of multilateral treaties and the observance of law.

Reciprocal principles apply for example to the mutual recognitionand enforcement of judgments, the granting of copyright to foreignauthors in the Bern Convention and the accepting of thecompulsory jurisdiction of the International Court of Justice.

Reciprocity in the foreign policy attitudes of theelectorate Back

• On-going discussion between realists and liberals to whatextent social preferences/norms in the electorate do and shallcarry over to foreign policy (Kertzer et al., 2014).• Bechtel and Scheve (2013) using survey evidence from France,

Germany, UK and the US:• CCs more sensitive to # of participants in the agreement and

the share of emissions covered by it, i.e. support increases morepowerful if more involved. → “ the sensitivity of public supportto design features reflects underlying norms of reciprocity”.

• Tingley and Tomz (2014) mTurk US survey:• most US citizens have an attitude of positive reciprocity when

other countries cut their emissions i.e. respond positively whilethey would not advocate to increase emissions if others did.

• public support for reciprocal response based on tradesanctions/blaming and shaming when an other countryincreases emissions (especially if treaty violated).

Numerical Example 1 Back I

To illustrate this, let us first consider a non-reciprocal leader and areciprocal follower (αL = 0, αF = 1). Then the public goodcontribution of the leader is according to (17):

gL =8 + 8

2(1 + 4)(2 + 2)w =

16

40w =

4

10w

and the follower contributes according to (18):

gF =w

2 + 2− 1− 2

2 + 2

16

40w =

14

40w =

7

20w

such that gL > gF , i.e. the leader contributes more. Total publicgood supply is G = gL + gF = 3

4w . Consequently, the utilities ofboth countries are:

uSL =6

10

3

4w2 =

9

20w2 >

4

9w2 = uN

Numerical Example 1 Back II

and

uSF =13

20

3

4w2 −

(1

20

)2

w2 =39

80w2 −

(1

20

)2

w2 >4

9w2 = uN .

Both countries attain a larger utility compared to the Nash case,the leader, however, attains a lower utility compared to thefollower’s one as:

uSL = 0.45w2 < 0.485w2 = uSF

Numerical Example 2 Back I

Let us now consider the case where both have reciprocalpreferences (αL = 1, αF = 1). Then the public good contributionof the leader is according to (17):

gL =8 + 8 + 6

2(1 + 4)(2 + 2) + 18w =

22

58w =

11

29w

and the follower contributes according to (18):

gF =w

2 + 2− 1− 2

2 + 2

11

29w =

10

29w

such that gL > gF , i.e. the leader contributes more again. Totalpublic good supply is G = gL + gF = 21

29w .Consequently, the utilities of both countries are:

uSL =18

29

21

29w2 −

(1

29

)2

w2 ≈ 0.4483w2 >4

9w2

Numerical Example 2 Back II

and

uSF =19

29

21

29w2 −

(1

29

)2

w2 ≈ 0.4733w2 >4

9w2.

Both countries attain a larger utility compared to the Nash case,the leader, however, once more attains a lower utility compared tothe follower’s one as: uSL ≈ 0.4483w2 < 0.4733w2 ≈ uSF .

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Reciprocity in Economics and International Relations · Introduction Reciprocity in Economics...

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