evolution of social behavior: individual and group...

Evolution of Social BehaviorIndividual and Group Selection

Theodore C Bergstrom

ldquoA selector of sufcient knowledge and power might perhaps obtain from the genes at presentavailable in the human species a race combining an average intellect equal to that ofShakespeare with the stature of Carnera But he could not produce a race of angels For themoral character or for the wings he would have to await or produce suitable mutationsrdquo

mdashJBS Haldane (1932 p 110)

W hat can our evolutionary history tell us about human motivations andsocial behavior The genes that in uence our own behavior are copiesof copies of copies of genes that have guided our ancestors to survive

and to reproduce If sel sh behavior leads to reproductive success then we shouldexpect our genes to impel us toward sel shness Thus Richard Dawkins (1976pp 2ndash4) observed

If we were told that a man lived a long and prosperous life in the world ofChicago gangsters we would be entitled to make some guesses as to the sortof man he was Like successful Chicago gangsters our genes have sur-vived in some cases for millions of years in a highly competitive world Ifyou look at the way natural selection works it seems to follow that anythingthat has evolved by natural selection should be sel sh

Sir Alexander Carr-Saunders (1922) a sociologist who pioneered studies ofdemography and social evolution took an opposing view Carr-Saunders main-tained that evidence from primitive cultures suggests that prehistoric humansclustered into groups that inhabited well-dened areas between which migration

y Theodore C Bergstrom is the Aaron and Cherie Raznick Professor of Economics Universityof California at Santa Barbara Santa Barbara California

Journal of Economic PerspectivesmdashVolume 16 Number 2mdashSpring 2002mdashPages 67ndash88

was infrequent These groups usually managed to avoid overpopulation and theattendant scourges of war famine and disease Population densities remainedroughly constant and close to the levels that maximized per capita food consump-tion To support these claims Carr-Saunders offered evidence that in existingprimitive societies fertility is deliberately restrained by means of abortion infanti-cide and long-term sexual abstinence He argued that such reproductive restraintis inconsistent with sel sh maximization of individual fertility and must somehowbe explained by ldquogroup selectionrdquo

In an encyclopedic study of the spatial dispersion of animal populations VCWynne-Edwards (1962) proposed that this principle has far more ancient roots Hebelieved that in much of the animal kingdom species maintain population densi-ties at an ldquooptimal level for each habitat that they occupyrdquo Wynne-Edwards arguedthat group selection is possible because ldquoanimal (and plant) species tend to groupinto more or less isolated populationsrdquo who depend on food resources of aldquolocalized immobilerdquo character and that ldquothe local stock conserves its resources andthereby safeguards the future survival of its descendantsrdquo

Some biologists viewed Wynne-Edwardsrsquo book as academic heresy George CWilliams (1966) argued that the behavior that Wynne-Edwards cites as evidence forgroup selection is consistent with individuals maximizing their own long-run re-productive interests or those of close relatives For example individuals may nd itin their own reproductive interests to vary their birth rates inversely with populationdensity It also may be in an individualrsquos sel sh interest to defend territories thatexceed minimum requirements in normal years because the extra territory will becritically important in bad years Other biologists have attempted to provide formalunderpinnings for Wynne-Edwardsrsquos rather loosely argued proposition A detailedand interesting account of this controversy can be found in Sober and Wilson(1999)

The polar theories of individual and group selection make dramatically dif-ferent predictions about social interactions Individual selection theory suggests aworld populated by resolutely sel sh homo economicus and his zoological (andbotanical) counterparts By contrast a world shaped by group selection would likelybe inhabited by natural socialists with an instinctive ldquoKantianrdquo morality towardother members of their group Of course the localism that leads to group selectionwould also tend to produce unsavory impulses toward xenophobia and intertribalwarfare

Games and Social Interactions

Prisonersrsquo Dilemma GamesEvolutionary biologists game theorists and anthropologists have frequently

used the prisonersrsquo dilemma game as a research vehicle to explore the polarregions of individual and group selection theory and the interesting terrain that liesbetween A multiplayer prisonersrsquo dilemma is a game in which individuals may take

68 Journal of Economic Perspectives

actions that are in the words of JBS Haldane (1932) ldquosocially valuable butindividually disadvantageousrdquo Speci cally we consider a game that has two possi-ble strategies for each player cooperate and defect where the payoff to each playerdepends on her own strategy and the number of other players who play cooperateAn N-player prisonersrsquo dilemma is de ned to be a game in which 1) all N players arebetter off if all play cooperate than if all play defect and 2) given the actions ofothers every individual necessarily gets a higher payoff from playing defect thanfrom playing cooperate

The prisonersrsquo dilemma is especially useful for exploring the alternative the-ories of individual and group selection because for this game the two theoriespredict starkly different outcomes If individuals are selected to act in their own self-interest all will defect If they are selected to act in the group interest all willcooperate

Much of the literature of evolutionary biology focuses on the special class ofN -player prisonersrsquo dilemma games in which each playerrsquos payoff depends linearlyon the number of players who play cooperate This game was introduced tobiologists in 1932 by JBS Haldane one of the founders of modern populationbiology1 Economists will recognize Haldanersquos game as the linear ldquovoluntary con-tribution to public goodsrdquo game much studied in experimental economics (SeeLedyard 1995 for a good survey of this work) In this paper we will call this gamethe linear public goods game

In an N-player linear public goods game a cooperator bears a cost of c and byso doing confers a bene t of bN on each of the N players including herself2 Adefector bears no costs and confers no bene ts but receives the bene ts conferredby cooperators in her group Thus if the fraction of cooperators in the group is xeach cooperator gets a payoff of bx ndash c and each defector gets a payoff of bx Fora linear public goods game to be a prisonersrsquo dilemma it must be that all playersare better off if all cooperate than if all defect and that given the actions of otherseach player gets a higher payoff from defecting than from cooperating The rstcondition is satis ed if and only if b c By cooperating an individual adds bNto her own payoff at a cost of c Thus the second condition is satis ed if and onlyif bN c It follows that a linear public goods game is an N-player prisonersrsquodilemma game if and only if bN c b

Stag Hunt GamesIn one-shot prisonersrsquo dilemma games the socially optimal action is never a

best response for sel sh individuals But in many social interactions the action that

1 The notation used here is that of Cohen and Eshel (1976) who credit Haldane (1932) in pp 207ndash210of their appendix2 David S Wilson (1975) studies a variant of this game in which at a cost of c a cooperator confersexpected bene ts of bN on every player except for herself Results for one variant translate easily intocorresponding results for the other since Wilsonrsquos formulation of the game with costs c is equivalent tothe Haldane formulation with costs c 1 b N

Theodore C Bergstrom 69

best serves onersquos self-interest depends on the actions taken by others This suggeststhe usefulness of a second exploratory vehicle a simple two-person game known asthe stag hunt This game formalizes a story told by Jean Jacques Rousseau (1755[1950] p 428) of two hunters who could cooperate by jointly hunting a stag ordefect by individually hunting hare3 Table 1 is a game matrix for a stag hunt gamewhere entries represent payoffs to the row player In contrast to a prisonersrsquodilemma where defect is the best response regardless of the otherrsquos strategy in staghunt games defect is the best response to defect but cooperate is the best responseto cooperate Thus the stag hunt has two equilibria one where both playerscooperate and one where both defect

Evolutionary Dynamics and Group FormationWe will explore the evolutionary dynamics of populations in which individuals

are ldquoprogrammedrdquo perhaps genetically or perhaps by cultural experience to playeither cooperate or defect in a game We assume that the dynamics are payoff-monotonic (Weibull 1995) which means that for any two player types the typereceiving the higher payoff in the game will reproduce more rapidly

If the entire population participates in a single multiperson prisonersrsquo di-lemma game the prediction of payoff-monotonic dynamics is simple Since defec-tors always receive higher payoffs than cooperators they will reproduce morerapidly than cooperators and eventually the population will consist almost entirelyof defectors4

Population biologists like JBS Haldane (1932) and Sewall Wright (1945)proposed that cooperation is most likely to evolve in populations where socialinteraction takes place within relatively small subpopulations called demes wherethere is occasional but relatively infrequent migration between subpopulations Toinvestigate this conjecture biologists have studied a class of dynamic models known

3 An engaging paper by Brian Skyrms (forthcoming) makes a strong case that social thinkers should paymore attention to the stag hunt game4 The result that the proportion of defectors converges to one is less obvious than the result that thisproportion increases monotonically A proof is found in Weibull (1995) who credits this result to JohnNachbar (1990)

Table 1A Stag Hunt Game(entries are payoffs to row player)

Column Playerrsquos StrategyCooperate Defect

Row Playerrsquos StrategyCooperate 4 0

Defect 3 3


as haystack models5 In haystack models random group formation produces somegroups with more cooperators than others Although cooperators have feweroffspring than defectors in their own group all members of groups with morecooperators reproduce more rapidly Haystack models are designed to explorecircumstances under which the between-group advantage of cooperation can over-whelm the within-group advantage of defection

In a haystack model time is divided into discrete periods Each period has areproductive phase and a dispersal phase The reproductive phase begins with apopulation that is partitioned into a large number of groups During the repro-ductive stage which may continue for several generations asexual reproductiontakes place within each group Descendants of any individual are of the same typeas their ancestor The number of descendants of each founding group memberpresent at the end of the reproductive phase depends on that individualrsquos type andon the distribution of types in the founding group At the end of the reproductivephase comes the dispersal phase where the entire population is pooled and newgroups are randomly formed from the pooled population The process is repeatedas the newly formed groups reproduce and disperse once again

In a haystack model we de ne group formation to be nonassortative if theprobability distribution of types of the other members of onersquos group is indepen-dent of onersquos own type Where individuals in the overall population can be of eithertype C or type D let us de ne pi(M N ) to be the probability that a type i individualis assigned to a group of size N in which M of the other group members are type CsThe assignment is de ned to be nonassortative if pC(M N ) 5 pD(M N ) for allrelevant M and N If the overall population is large and groups are formed byrandom sampling without replacement from this population then matching will bealmost nonassortative There will be a slight difference between pC(M N ) andpD(M N ) because the other members of a cooperatorrsquos group are drawn from theoverall population less one cooperator while the other members of a defectorrsquosgroup are drawn from the overall population less one defector For a largepopulation size this difference can be shown to be negligible

Where Not to Look for CooperationIn a survey of the literature on group selection Alan Grafen (1984) states that

ldquowith random selection there is no selection for altruismrdquo Grafen does not offer aproof of this assertion6 However if we de ne ldquoaltruismrdquo to mean playing cooperatein a prisonersrsquo dilemma and ldquorandomrdquo to mean nonassortative then Grafenrsquos claimis equivalent to the following theorem

Proposition 1 Iron Rule of Selshness In a haystack model if matching isnonassortative and if reproductive rates are determined by a prisonersrsquo

5 The rst haystack model was introduced by John Maynard Smith (1964) and will be discussed below6 An earlier paper by David S Wilson (1975) showed for a quite speci c model that ldquorandomrdquo formationof groups must result in the elimination of altruism

Evolution of Social Behavior Individual and Group Selection 71

dilemma game among group founders then the only asymptotically stableoutcome is a population consisting entirely of defectors

To prove Proposition 1 we show that in each time period at the dispersal stage theexpected number of descendants of a defector exceeds that of a cooperator7 Thuseach time the haystacks are dispersed and reformed it will be with a higherproportion of defectors It follows that eventually the proportion of defectors in thepopulation becomes arbitrarily close to one

It is important to understand that Proposition 1 does not rule out the possi-bility that group selection can sustain cooperative behavior Instead this proposi-tion allows us to classify environments where selection can favor cooperation asfollows In a haystack model cooperation will survive only if either a) the gamebeing played is not a prisonersrsquo dilemma or b) matching is assortative

Haystack Models of Group Selection

Maynard Smithrsquos MiceJohn Maynard Smith (1964) introduced the rst formal model of ldquogroup

selectionrdquo in which seemingly altruistic behavior is sustained in equilibrium eventhough the matching process is nonassortative The key to Maynard Smithrsquos resultis that groups may remain intact for several generations before the population isdispersed and randomly regrouped Maynard Smith motivates his model with acharming story of ldquoa species of mouse which lives entirely in haystacksrdquo

A meadow contains many haystacks each of which is colonized every year byexactly two mice These mice and their descendants reproduce asexually through-out the summer until harvest time when the haystacks are cleared8 The dislodgedresident mice scramble out into the meadow and when new haystacks are built inthe next year each haystack is colonized by exactly two mice randomly selectedfrom the survivors of last yearrsquos breeding season If there are more than enoughmice to provide two founders for each new haystack the extra mice are consumedby predators

7 The expected number of descendants of a cooperator is yenM yenN pC (M N )IIC(M N ) which is the sumover all possible group con gurations of the probability that a cooperator belongs to that type of grouptimes her number of descendants in this case Similarly the expected number of descendants of adefector is yenM yenN pD(M N )IID(M N ) Since matching is nonassortative it must be that pC(M N ) 5pD(M N ) for all M and N Therefore the difference between the expected number of descendants ofa cooperator and that of a defector is equal to yenM yenN pC(M N )(IIC(M N ) 2 IID(M N )) If the gameis prisonersrsquo dilemma it must be that IIC(M N ) 2 IID(M N ) 0 for all M and N It follows thatyenM yenN pC(M N )(IIC(M N ) 2 IID(M N )) 0 and therefore in every period the expected numberof offspring of a cooperator is less than that of a defector8 In Maynard Smithrsquos (1964) telling mice reproduce as sexual diploids However his model is mathe-matically equivalent to one with asexual reproduction To ease exposition and to make this modeldirectly comparable to extensions introduced by Cohen and Eshel (1976) I present the equivalentasexual model here


In a haystack settled by two timid mice all descendants are timid and in ahaystack settled by two aggressive mice all descendants are aggressive In a haystacksettled by one mouse of each type the descendants of the aggressive mouseeliminate the descendants of the timid mouse and the number of its descendantsat harvest time is the same as the number in a haystack colonized by two aggressivemice Although timid mice do poorly when matched with aggressive mice haystacksinhabited entirely by timid mice produce more surviving offspring at harvest timethan do haystacks inhabited by aggressive mice Thus a haystack colonized by twotimid mice produces 1 1 K times as many descendants as does a haystack withaggressive mice

Since the reproduction rate enjoyed by a founding mouse depends on its owntype and that of its cofounder these rates can be represented as the payoffs in agame between the two mice who colonize each haystack If two aggressive micecolonize a haystack they will have a total of r descendants half of whom aredescended from each founder Thus each mouse has r 2 descendants If anaggressive mouse and a timid mouse colonize a haystack the timid mouse will haveno descendants and the aggressive mouse will have r descendants If two timid micecolonize a haystack they will have a total of r(1 1 K ) descendants and each willhave r(1 1 K ) 2 descendants In the game played by cofounders payoffs to therow player are shown in Table 2

If 0 K 1 the haystack game is a prisonersrsquo dilemma since regardless ofits cofounderrsquos type an aggressive mouse will have more offspring than a timidmouse If K 1 the haystack game is not a prisonersrsquo dilemma but a stag huntIf matched with a timid mouse a mouse will have more offspring if it is timid thanif it is aggressive But if matched with an aggressive mouse a mouse will have moreoffspring if it is aggressive than if it is timid

For the prisonersrsquo dilemma case with K 1 the only equilibrium is apopulation made up entirely of defectors For the stag hunt case with K 1 thereare two distinct stable equilibria one in which all mice are timid and one in whichall are aggressive We demonstrate this as follows Let the proportion of timid micein the population at time t be xt Since matching is random any mouse is matchedwith a timid cofounder with probability xt and with an aggressive cofounder withprobability 1 2 xt Given the payoffs in Table 2 the expected reproduction rate ofan aggressive mouse is xtr 1 (1 2 xt)r 2 and the expected reproduction rate of

Table 2The Haystack Game(entries are payoffs to row player)


Row Playerrsquos StrategyCooperate r(11K )2 0

Defect r r2


a timid mouse is xtr(1 1 K ) 2 Subtracting the latter expression from the formerwe nd that the difference between the expected reproduction rates of timid miceand of aggressive mice is proportional to x tK 2 1 Therefore timid mice reproducemore rapidly than aggressive mice if xtK 1 and aggressive mice reproduce morerapidly if xtK 1 These dynamics are illustrated by Figure 1 The graph on the leftshows the case where K 1 so that the game played between founders is a staghunt In this case when the proportion of timid mice is large timid mice reproducemore rapidly than aggressive mice and when the proportion of timid mice is smallaggressive mice will reproduce more rapidly Thus there are two stable equilibriaone in which all mice are timid and one in which all are aggressive (There is alsoan unstable equilibrium where the fraction 1K of mice are timid) The graph onthe right shows the case where K 1 so that the game played between foundersis a prisonersrsquo dilemma In this case aggressive mice always reproduce more rapidlythan timid mice and there is a unique equilibrium in which all mice are aggressive

According to Proposition 1 a population of cooperators will be stable only ifeither a) the game played is not a prisonersrsquo dilemma or b) matching is assortativeWe see that the survival of cooperation in Maynard Smithrsquos haystack model fallsinto the rst case If K 1 the game played between founders is a stag hunt ratherthan a prisonersrsquo dilemma and there are two stable equilibria one with cooperatorsonly and one with defectors only Where K 1 the game played between foundersis a prisonersrsquo dilemma and as Proposition 1 predicts the only stable equilibriumis a population of defectors

The Cohen-Eshel Linear Public Goods ModelDan Cohen and Ilan Eshel (1976) generalize Maynard Smithrsquos (1964) haystack

model in an instructive way They study haystack models with cooperators anddefectors where founding groups may be of arbitrary size and where reproductionrates vary continuously with the proportion of cooperators in the group Groupsremain intact for a xed length of time T and then are dispersed and new groupsare formed with nonassortative matching We will pay special attention to one ofthe cases that they study This is a linear public goods game in which x(t) is theproportion of cooperators in a group at time t and where cooperators in the groupreproduce at the instantaneous rate a 1 bx(t) and defectors reproduce at the ratea 1 bx(t) 2 c For this model Cohen and Eshel are able to solve the resultingdifferential equations and thereby determine when the more rapid growth rates ofgroups with more cooperators is suf cient to offset the fact that cooperatorsreproduce less rapidly within groups than defectors Their answer is expressed inthe following proposition

Proposition 2 Cohen-Eshel Theorem In the Cohen-Eshel linear public goodsmodel where groups are of size N and where T is the length of time for whichgroups remain intact i) If T is small there is a unique asymptotically stableequilibrium The equilibrium population is made up entirely of defectors ifbN c and entirely of cooperators if bN c ii) If T is suf ciently large


and b c 0 there exist two distinct stable equilibria one with sel shplayers only and one with altruists only

A heuristic explanation of part (i) is that if T is small the reproduction rateover the life of the group is approximately bx for defectors and bx 2 c forcooperators where x is the proportion of cooperators among the founders IfbN c this game is a prisonersrsquo dilemma If bN c then the game is not aprisonersrsquo dilemma since the private bene ts that an individual gets from cooper-ating exceed the cost of cooperation and so cooperate rather than defect is adominant strategy Thus we see that part (i) of Proposition 2 is consistent withProposition 1

Part (ii) is the more surprising result Where groups are suf ciently long-liveda population of cooperators can be sustained as a stable equilibrium even if thegame played between contemporaries is a prisonersrsquo dilemma To see how this canhappen let us suppose that T is large and ask whether a population of cooperatorscan be invaded by defectors A defector who joins N 2 1 cooperators in foundinga group will have fewer expected offspring than would a cooperator in a groupmade up entirely of cooperators The reason is that for large T a group that has atleast one defector among its founders will eventually consist almost entirely ofdefectors and thus the reproduction rate of every member of that group willeventually be lower than the reproduction rate of the normal population ofcooperators who live in communities founded by cooperators only This impliesthat if groups are suf ciently long-lived a mutant defector will have fewer descen-dants than the normal cooperators who live among cooperators Thus mutantdefectors cannot invade the population

How does part (ii) of the Cohen-Eshel theorem square with Proposition 1 Ifwe consider the game played between founders and if the survival duration T ofgroups is large then as we have seen the game that determines reproductive ratesover the lifetime of a group is not a prisonersrsquo dilemma Thus there is no con ictwith Proposition 1 It is also instructive to look at the situation another way We notethat the linear public goods game that determines instantaneous reproduction

Figure 1Dynamics of the Haystack Model


rates is a prisonersrsquo dilemma if bN c But after a group has been intact for somelength of time the individuals who participate in this game will not be nonassor-tatively matched but will tend to share common ancestry

Absolute and Relative Payoff Within GroupsThere is an interesting class of games in which every player gets a higher payoff

from cooperating than from defecting but where paradoxically it is also true thatwithin each group defectors receive higher payoffs than cooperators The root ofthis paradox is the difference between absolute and relative payoffs Consider anN -player linear public goods game where in a group with the fraction x ofcooperators cooperatorsrsquo payoffs are bx 2 c and defectorsrsquo payoffs are bx Bycooperating rather than defecting a player increases x by 1N and hence confersa bene t of bN on all group members including herself If bN c 0 theprivate bene ts she gets from cooperating exceed the cost of cooperation socooperating increases her absolute payoff But defectors enjoy all of the bene tsfrom cooperatorsrsquo efforts and bear none of the costs Therefore in any group thedefectors have higher payoffs than the cooperators

DS Wilson (1979) noticed this possibility and suggested that someone whocooperates when bN c but not when bN c be called a ldquoweak altruistrdquo whilesomeone who cooperates whenever b c be called a ldquostrong altruistrdquo Wilsonargued that ldquomany perhaps most group-advantageous traits such as populationregulation predation defense and role differentiationrdquo may be explained by weakaltruism Grafen (1984) responded that Wilsonrsquos ldquoweak altruismrdquo is not reallyaltruism since weak altruists cooperate only when it is in their self-interest asmeasured by absolute (but not necessarily relative) payoffs Grafen suggests thatWilsonrsquos weak altruism would be better called ldquoa self-interested refusal to bespitefulrdquo

Whether we speak of ldquoweak altruismrdquo or ldquorefusal to be spitefulrdquo it is interestingto determine whether natural selection favors maximization of absolute payoff or ofrelative payoffs when these two objectives con ict Cohen and Eshelrsquos Proposi-tion 2 offers an answer Where the lifetime T of groups is short a stable equilibriumpopulation of cooperators can be supported if and only if bN c Thus naturalselection favors maximization of absolute payoffs even at the expense of relativepayoffs However if groups remain intact for a long time maximization of absolutepayoffs is not unambiguously favored The Cohen-Eshel result is that for large Tthere exist two distinct equilibriamdash one populated by cooperators only and one bydefectors only

Variations on the Haystack ModelIn the haystack model groups survive in perfect isolation until they are

simultaneously disbanded More realistic models would allow migration betweengroups and would have asynchronous extinctions and resettlements Such modelshave been studied by Eshel (1972) Levins (1970) Levin and Kilmer (1974) andBoorman and Levitt (1980) In these models defectors reproduce more rapidly


than cooperators within their own group but groups face a higher probability ofgroup extinction the greater the proportion of defectors For some parametervalues a population of cooperators will be sustained in equilibrium This is morelikely if the size of founding populations is relatively small if the migration rate isrelatively small and if the difference between the extinction rates of sel sh andaltruistic groups is relatively large

Assortative Group Formation

In the prisonersrsquo dilemma defect always yields a higher payoff than cooperatebut everyone gets a higher payoff if matched with a cooperator rather than adefector Proposition 1 tells us that defection will prevail if types are matched atrandom to play prisonersrsquo dilemma But if matching is assortative rather thanrandom the cost of cooperation may be repaid by a higher probability of playingwith another cooperator

The Index of AssortativitySewall Wright (1921) de ned the assortativeness of mating with respect to a

trait as ldquothe coef cient of correlation m between two mates with respect to theirpossession of the traitrdquo Cavalli-Sforza and Feldman (1981) pointed out thatWrightrsquos correlation coef cient is equivalent to a matching process where thefraction m are assigned to their own type with certainty and the remaining fraction(1 2 m) mate at random9 For a population of cooperators and defectorsBergstrom (2002) de ned the index of assortativity a( x) to be the differencebetween the expected fraction of cooperators that a cooperator will encounter inher group and the expected fraction of cooperators that a defector will encounterHe shows that this de nition reduces to Wrightrsquos correlation coef cient m whenmatching is pairwise and a( x) is constant As we will see in some importantapplications a( x) is constant but there are interesting cases where it is not

Recall that in an N-player linear public goods game a player who cooperatesincreases the fraction of cooperators in her group by 1N and thus adds bN to thepayoff of each player including herself Therefore the net cost of cooperating isc 5 c 2 bN and the game is a prisonersrsquo dilemma whenever c 0 Proposi-tion 3 tells us that if the index of assortativity is positive then in haystack modelsindividuals in equilibrium will act as if they ldquodiscountrdquo bene ts to other groupmembers at a rate equal to the index of assortativity

9 Let Ii be an indicator variable that takes on value 1 if mate i has the trait and 0 otherwise Wrightrsquosassortativeness m is the correlation between I1 and I2 Thus m 5 (E(I1I2) 2 E(I1) E(I2))(s1s2)where si is the standard deviation of Ii Now E(I1I2) 5 xp( x) and for i 5 1 2 E(Ii) 5 x and si 5=x(1 2 x) Therefore m 5 ( xp(x) 2 x2)x(1 2 x) Rearranging terms one nds this expressionequivalent to p(x) 5 m 1 x (1 2 m)


Proposition 3 In a haystack model in which the game played among foundersis an N-player linear public goods game where a( x) is the index of assorta-tivity a population of cooperators will be stable if and only if a(1)b 2 c 0and a population of defectors will be stable if and only if a(0)b 2 c 0where c 5 c 2 bN

The proof of Proposition 3 is sketched as follows Recall that where x is thefraction of cooperators in the population the index of assortativity a(x) is thedifference between the expected fraction of cooperators encountered by cooper-ators and that encountered by defectors Therefore the expected difference be-tween the total bene ts experienced by cooperators and by defectors is just a(x)band since c is the net cost of cooperating the reproduction rate of cooperators willexceed that of defectors if a(x)b 2 c 0 A large population of cooperators isstable if a mutant defector in this population will reproduce less rapidly thancooperators This happens if a(1)b 2 c 0 A large population of defectors isstable if a mutant cooperator in a population of defectors will reproduce lessrapidly than defectors This will happen if a(0)b 2 c 0

Bergstrom (1995 2002) generalizes Proposition 3 from the special class oflinear public goods games to games in which payoffs are not linear in the numberof cooperators For the case of pairwise matching with a constant index of assor-tativity a the equilibrium behavior can be described as follows Take the actionthat you would choose if you believed that with probability a your partner willmimic your action and with probability 1 2 a your partner will mimic a randomdraw from the population at large Bergstrom calls this the semi-Kantian rule sinceit can be viewed as a probabilistic version of Kantrsquos categorical imperative

Family Groups and Assortative MatchingFamilies are conspicuous examples of nonrandomly formed groups William

Hamilton (1964) developed kin selection theory which predicts the willingness ofindividuals to make sacri ces to bene t their relatives according to a bene t-costprinciple known as Hamiltonrsquos rule Hamiltonrsquos rule states that individuals are willingto reduce their own expected number of offspring by c in order to add b to that ofa relative if and only if br c where r is the coefcient of relatedness between the tworelatives Biologists de ne the coef cient of relatedness between two individuals asthe probability that a rare gene found in one of them also appears in the other Ina population without inbreeding the coef cient of relatedness is one-half for fullsiblings one-fourth for half siblings and one-eighth for rst cousins

Hamilton (1964) obtained his result for a simpli ed genetic model known assexual haploidy In sexual haploids an inherited trait is determined by a single genethat is inherited from a random draw of the heirrsquos two parents10 The sexualhaploid model seems appropriate for studying cultural transmission where behav-

10 See Boorman and Levitt (1980) and Bergstrom (1995) for similar results applying to sexual diploids


ior is passed from parents to children by imitation Bergstrom (2002) and Berg-strom and Stark (1993) show that if mating between parents is not assortative andif inheritance follows the sexual haploid model then the index of assortativitybetween two relatives is equal to their coef cient of relatedness For example twofull siblings inherit their behavior from the same parent with probability 12 andfrom different parents with probability 12 The difference between the probabilitythat a cooperator has a cooperative sibling and the probability that a defector hasa cooperative sibling is a( x) 5 1 2 which is also their degree of relatedness SinceHamiltonrsquos model of interactions is equivalent to a two-player linear public goodsgame11 Hamiltonrsquos rule is a special case of Proposition 3

Bergstrom (2002) shows that the index of assortativity can be calculated undera variety of alternative assumptions about cultural or genetic inheritance Theseinclude cases where parents mate assortatively where children may copy a ran-domly chosen stranger rather than one of their parents where children preferen-tially copy mother or father and where marriage is polygamous

Assortative Matching with Partner ChoiceIn a multiplayer prisonersrsquo dilemma game everyone prefers being matched

with cooperators rather than defectors Thus if groups could restrict entry andplayersrsquo types were observable cooperators would not admit defectors to theirgroups two types would be strictly segregated and cooperators would reproducemore rapidly than would defectors In more realistic environments type detectionis imperfect and the index of assortativity falls between zero and one

Bergstrom (2002) studies players who are labeled with an imperfect indicatorof their type Everyone sees the same labels and so when players choose partnersthere are only two distinguishable types players who are labeled cooperator andplayers who are labeled defector Although everyone realizes that the indicators areimperfect everyone prefers to match with an apparent cooperator rather than withan apparent defector Therefore with voluntary matching all individuals arematched with others of the same label The expected proportion of true cooper-ators encountered by true cooperators will exceed that encountered by true defec-tors The index of assortativity a(x) is shown to vary with the proportion ofcooperators in such a way that a(0) 5 a(1) 5 0 while a(x) is positive forintermediate values Where groups play a linear public goods game there turns outto be a unique stable polymorphic equilibrium that includes positive fractions ofboth types Frank (1987) presents an alternative model with two types who emitpartially informative type indicators and also nds a unique polymorphicequilibrium

Skyrms and Pemantle (2000) study dynamic formation of groups by reinforce-ment learning Individuals initially meet at random and play a game The payoffsdetermine which interactions are reinforced and a social network emerges The

11 In Hamiltonrsquos formulation the bene t b accrues only to onersquos relative and not to oneself This modelis equivalent to a linear public goods game with c 5 c


networks that tend to form in their model consist of small interaction groups withinwhich there is partial coordination of strategies and which can support cooperativeoutcomes

Assortative Matching Induced by Spatial StructureEvolutionary biologists have stressed the importance of spatial structure on the

spread of mutations genetic variation and the formation of species Wright (1943)studied the degree of inbreeding in a population distributed over a large areawhere individuals are more likely to mate with those who live nearby Kimura andWeiss (1964) studied genetic correlations in a one-dimensional ldquostepping stonemodelrdquo with colonies arrayed along a line and where ldquoin each generation anindividual can migrate at most lsquoone steprsquo in either directionrdquo Nowak and May(1993) ran computer simulations with agents located on a two-dimensional gridplaying the prisonersrsquo dilemma with their neighbors After each round of play eachsite is occupied by its original owner or by one of its neighbors depending on whohad the highest score in the previous round This process generates chaoticallychanging spatial patterns in which the proportions of cooperators and defectors uctuate about long-term averages

Bergstrom and Stark (1993) considered a population of farmers located on aroad that loops around a lake Each farmer plays the prisonersrsquo dilemma with histwo neighbors The farmersrsquo sons observe the strategies and payoffs of their fathersand their immediate neighbors and imitate the most successful In this case it turnsout that an arrangement is stable if cooperators appear in clusters of three or moreand defectors in clusters of two or more With slightly different rules they show thatspatial patterns of behavior ldquomove in a circlerdquo around the lake Thus a long-livedchronicler who observed behavior at a single farm would see cyclic behavior inwhich spells of cooperation are interrupted by defection according to a regulartemporal pattern

Eshel Samuelson and Shaked (1998) studied a similar circular setup butallowed the possibility of random mutations They discovered that in the limit as themutation rate becomes small the only stationary states that have positive probabil-ity are those in which at least 60 percent of the population are cooperators As theauthors explain ldquoAltruists can thus invade a world of Egoists with only a local burstof mutation that creates a small string of Altruists which will then subsequentlygrow to a large number of Altruists Mutations can create small pockets of egoismbut these pockets destroy one another if they are placed too close together placingan upper bound on the number of Egoists that can appearrdquo

Eshel Sansone and Shaked (1999) constructed another circular model inwhich each individual plays the prisonersrsquo dilemma with her k nearest neighborsand observes the payoffs realized by her n nearest neighbors They showed that thepopulation dynamics can be determined from an explicitly calculated index ofassortativity r(k n) for critical players who are located on the frontier between astring of cooperators and a string of defectors Where the game played between


neighbors is a linear public goods game cooperation will prevail if r(k n) b cand defection will prevail if r(k n)b c

Cooperation without the Prisonersrsquo Dilemma

Ken Binmore (1994b) has observed ldquoIf our Game of Life were the one-shotPrisonersrsquo Dilemma we should never have evolved as social animalsrdquo Binmoreargues that the ldquoGame of Liferdquo is best modeled as an inde nitely repeated game inwhich reciprocal rewards and punishments can be practiced As Binmore pointsout this idea is not new In the seventh century before Christ Hesiod (1929) statedthe maxim ldquoGive to him who gives and do not give to him who does notrdquo DavidHume (1739 [1978] p 521) used language that is suggestive of modern gametheory ldquoI learn to do service to another without bearing him any real kindnessbecause I foresee that he will return my service in expectation of another of thesame kind and in order to maintain the same correspondence of good of ces withme and others And accordingly after I have servrsquod him he is induced to do hispart as foreseeing the consequences of his refusalrdquo

The Equilibrium Selection ProblemSeveral game theorists in the 1950s nearly simultaneously discovered a result

known as the folk theorem which tells us that in inde nitely repeated games almostany pattern of individual behavior can be sustained as a Nash equilibria by a stableself-policing norm Such a norm prescribes a course of action to each player andincludes instructions to punish anyone who violates his prescribed course of actionFor game theorists this is discouraging news since it means that the usual tools ofgame theory have little predictive power Those who want further guidance fromtheory must seek some way to distinguish ldquoplausiblerdquo Nash equilibria from implau-sible ones Game theorists call this the ldquoequilibrium selection problemrdquo

The repeated prisonersrsquo dilemma like other repeated games has many Nashequilibria some of which are Pareto superior to others Group selection can play apowerful role here as suggested by Boyd and Richerson (1990 1992 2002) andBinmore (1992 1994a b) A mechanism that allows groups with higher totalpayoffs to ldquoreproducerdquo more rapidly will not be directly opposed by individualselection within groups As Boyd and Richerson (1990) explain ldquoViewed from thewithin-group perspective behavior will seem egoistic but the egoistically enforcedequilibria with the greatest group bene t will prevailrdquo

Since norms and the amount of cooperation differ greatly across societies itseems that the attainment of ef cient cooperation by group selection is neitherswift nor inevitable Soltis Boyd and Richerson (1995) propose a model of groupselection that requires that there is variation in norms among groups that extinc-tion of groups is fairly common and that new groups are formed by ssion ofexisting groups Using data on group extinction rates of New Guinea tribes theauthors estimate that the amount of time needed for a rare advantageous cultural


attribute to replace a common cultural attribute is of the order of 500 to 1000 yearsHowever Boyd and Richerson (2002) show that the spread of socially bene cialnorms will be much faster if individuals occasionally imitate strategies of inhabitantsof successful neighboring groups

The Punishment ProblemAlthough we know from the folk theorem that punishment norms can main-

tain cooperation as Nash equilibria it is not obvious that evolutionary processes willsustain the willingness to punish As Henrich and Boyd (2001) put it ldquoManystudents of human behavior believe that large-scale human cooperation is main-tained by threat of punishment However explaining cooperation in this wayleads to a new problem why do people punish noncooperators Individualswho punish defectors provide a public good and thus can be exploited by non-punishing cooperators if punishment is costlyrdquo

The standard game theoretic answer is that equilibrium strategies includeinstructions to punish others who are ldquosupposed to punishrdquo and fail to do so Theseinstructions for punishing include instructions to punish those who wonrsquot punishothers when obliged to and so on ad in nitum From an evolutionary point of viewthis resolution seems unsatisfactory It does not seem reasonable to expect individ-uals to be able to keep track of higher order failures to punish deviations frompunishment norms Moreover if a society is in an equilibrium where all attempt toobey the norm direct violations would be suf ciently infrequent that selection forpunishing violators would be weak

ldquoThe Viability of Vengeancerdquo by Friedman and Singh (1999) has a nicediscussion of the evolutionary stability of costly punishment They suggest thatwithin groups onersquos actions are observed and remembered A reputation for beingwilling to avenge harmful actions may be suf cient compensation for the costs ofretribution In dealing with outsiders however one is remembered not as anindividual but as a representative of her group Accordingly a willingness to avengeharm done by outsiders is a public good for onersquos group since it deters outsidersfrom uncooperative behavior to group members They propose that failure toavenge wrongs from outsiders is punished (costlessly) by onersquos own group throughloss of status

Henrich and Boyd (2001) propose an interesting explanation for the viabilityof vengeance They argue that ldquothe evolution of cooperation and punishment area side effect of a tendency to adopt common behaviors during enculturationrdquo Sinceit is not possible for humans to analyze and to ldquosolverdquo the complex social games thatthey play imitation becomes important It is often easier to observe a playerrsquosactions than to observe both actions and consequences Thus Henrich and Boydsuggest that imitation may take the form of ldquocopy-the-majorityrdquo rather than ldquocopy-the-most-successfulrdquo

Henrich and Boyd (2001) show that it takes only a slight tendency towardconformity to maintain an equilibrium that supports punishment strategies In asimpli ed version of their model community members engage in a two-stage game


The rst stage is a linear public goods game where players decide to cooperate ordefect but with a small probability a player who intends to cooperate inadvertentlydefects In the second stage individuals decide whether to punish rst-stage defec-tors Punishing is costly both to the punisher and the punished Consider apopulation in which initially everyone intends to cooperate at the rst stage andwhere in the second stage everyone intends to punish those who defected in the rst stage Since everyone intends to cooperate the only defections observed aremistakes Since everyone intends to punish those who defect in the rst stage thepayoff to those who defect in the rst stage is lower than the payoff to those whocooperate Individuals who fail in the second stage to punish rst-stage defectorsget higher payoffs than those who cooperate by punishing rst-stage defectors butonly slightly higher since there are very few rst-stage defections Since mostindividuals conform to the norm the expected cost of punishing observed defec-tions is low and thus even a very small weight on the conformity measure issuf cient to overcome the payoff loss from punishing Henrich and Boyd show thatwhen higher levels of punishment are accounted for an even smaller weight onconformity suf ces to maintain cooperation at all stages

Fehr and Gachter (2000) nd interesting experimental evidence of the viabil-ity of vengeance In their experiment subjects play a linear public goods gamerepeatedly with anonymous partners who are reshuf ed after each play The gamealso has a punishment stage in which at a cost to themselves players can imposepunishments on those who have defected Fehr and Gachter nd that althoughsubjects are unlikely to reencounter those whom they punish they frequentlypunish defectors In consequence in later rounds of play most subjects cooperatefully

Cultural versus Genetic TransmissionThere is room to question whether the visceral seemingly irrational anger that

people feel when they are cheated or otherwise violated can be explained bycultural transmission rather than as genetic hard-wiring Cosmides and Tooby(1989) offer experimental evidence indicating that people are much better atsolving logical problems that are framed as ldquocheater detectionrdquo problems than atsolving equivalent problems in other frameworks In their view this is evidence thathumans have evolved special mental modules for solving such problems

There is however evidence that culture in uences readiness to anger Exper-iments by Nisbett and Cohen (1996) subjected male college students to rude andinsulting behavior in the laboratory Using questionnaires behavioral responsesand checks of testosterone levels they found that students raised in the AmericanSouth become much angrier and more ready to ght than those raised in theNorth The authors attribute this difference to the existence of a ldquoculture of honorrdquoin the South that is not present in the North

Economists and anthropologists have conducted a remarkable cross-culturalseries of experiments in which subjects play the ultimatum game In the ultimatumgame two players are matched to divide a xed sum of money The rst player ldquothe


proposerrdquo offers a portion of the total to the second player ldquothe responderrdquo If theresponder accepts the offer the money is divided as proposed If the responderrejects both players receive nothing If this game is played by rational players whocare only about their own monetary payoffs then in equilibrium the proposeroffers a very small share and the responder accepts In laboratory experimentsproposers typically offer a share of about one half and this is accepted Whenproposers attempt to capture a signi cantly larger share responders usually rejectthe proposal in effect foregoing a small gain in order to ldquopunishrdquo a greedyproposer A study conducted in the United States Israel Japan and Slovenia foundsimilar results across these countries (Roth Prasnikar Okuno-Fujiwara and Zamir1991) But very different results were found when the ultimatum game was con-ducted with the Machiguenga a hunter-gatherer group who live in small extendedfamily hamlets scattered through the tropical forests of the Amazon Henrich(2000) found that the modal share offered by the Machiguenga was only15 percent Despite the fact that responders were offered a small share theyaccepted these offers about 95 percent of the time Henrich reports that in ordinaryMachiguenga life ldquocooperation above the family level is almost unknownrdquo A recentstudy reports on ultimatum game experiments conducted in a total of 15 ldquosmall-scale societiesrdquo including hunter-gathers pastoralists farmers and villagers (Hen-rich et al 2001) The studies found wide divergence among these societies

The great diversity of norms across societies indicates that the details ofprescribed behavior must be transmitted culturally rather than genetically On theother hand it appears that the emotional and intellectual prerequisites for thesupport of cultural norms are part of the common genetic endowment of humansBy analogy humans raised in different environments grow up to speak differentlanguages but all normal humans appear to be genetically endowed with an innateability to learn language and manage grammar and syntax It would be interestingto know more about just which abilities and instincts are genetically transferred andwhich are culturally transmitted While the qualitative character of evolutionarydynamics may be roughly the same for either transmission mechanism the rates ofmutation and of selection for traits transmitted culturally are likely to be muchfaster than for genetically transmitted traits

Final Remarks

Further ReadingThe literature on social evolution is large diverse and multidisciplinary and I

have con ned my attention to a small portion of this work For those who want toread further in this area here are a few works that I have found especiallystimulating

Cavalli-Sforza and Feldmanrsquos Cultural Transmission and Evolution (1981) pio-neered formal modeling of this subject Their introductory chapter presents aclear-headed formulation of the implications of mutation transmission and natural


selection for culturally transmitted characteristics There is also an empirical studyof the transmission from parents to children of such cultural behavior as religiousbeliefs political af liation listening to classical music reading horoscopes andhigh salt usage

Rajiv Sethi and R Somanathanrsquos ldquoUnderstanding Reciprocityrdquo (2002) lucidlypresents much interesting work not discussed here Sober and Wilsonrsquos (1999)book Unto Others contains an extensive history of theoretical controversies betweengroup and individual selectionists They also offer a fascinating survey of eldobservations of group norms in a sample of 25 cultures selected from anthropo-logical studies

H Peyton Youngrsquos (1998) Individual Strategy and Social Structure An EvolutionaryTheory of Social Institutions contains a remarkably accessible introduction to themathematical theory of stochastic dynamics and to its applications in the study ofthe evolution of social institutions Young maintains that a proper treatment of thevery long run must directly incorporate the stochastic process into the laws ofmotion and he shows that in models with multiple equilibria ldquolong run averagebehavior can be predicted much more sharply than that of the correspondingdeterminate dynamicsrdquo

Skyrmsrsquos (1996) Evolution of the Social Contract is a beautifully written applica-tion of evolutionary dynamics to the study of bargaining games and the evolutionof notions of fairness and social contracts

Finally my own thinking about the evolutionary foundations of social behaviorhas been much in uenced by Ken Binmorersquos (1994a b) two-volume work GameTheory and the Social Contract These books combines social philosophy politicaltheory evolutionary theory anthropology and modern game theory with greatdepth and subtlety

ConclusionI have attempted to map the territory between the opposing poles of individual

and group selection theory The former predicts outcomes that are Nash equilibriain games played by sel sh individuals while the latter predicts outcomes in whichindividuals act so as to maximize the total reproductive success of their own groups

Haystack models occupy interesting intermediate terrain In this setting vari-ations in reproductive success depend both on individualsrsquo own actions and on thecomposition of the groups to which they are assigned In haystack models if groupsare assembled nonassortatively and if the reproductive success of founding groupmembers is determined by a multiperson prisonersrsquo dilemma then cooperationcannot be sustained in equilibrium But the assumptions that ensure the defeat ofcooperation are not always satis ed and there are many important social situationsin which at least some cooperation is sustained

Stable groups of moderate size are likely to foster social interactions whereunlike in prisonersrsquo dilemmas individual self-interest is consistent with behaviorthat maximizes group success Interaction in such groups is best modeled as arepeated game In repeated games where onersquos actions can be observed and


remembered by others almost any pattern of individual behavior includingbehavior that maximizes group payoff can be sustained by social norms that includeobligations to punish norm violations by others Where many equilibria are possi-ble group selection is likely to play a major role in determining which equilibriumwill obtain In a population where different groups maintain different internallystable equilibria each supported by a different norm those groups following normsthat lead to higher group success may be expected to reproduce more rapidly inwhich case the behavior predicted by group selection models may predominate

Evolutionary theory laboratory experiments and eld observations indicatethat humans are ldquosocial animalsrdquo who take a strong interest in the effects of theiractions on others and whose behavior is not always explained by simple models ofsel sh behavior Does this mean that our familiar analytic tool sel sh old homoeconomicus is an endangered species I donrsquot think his admirers have reason toworry Among modern humans and probably among our distant ancestors match-ing is far from perfectly assortative While reciprocity and the presence of normscan support a great deal of cooperation much human activity and most humanmotivation is impossible for others to observe and hence lies beyond the reach ofpunishment or reward If you seek empirical evidence that homo economicus survivesyou need only venture onto a congested freeway where you will observe his closerelatives piloting their gargantuan sports utility vehicles

y I thank Carl Bergstrom Jack Hirschleifer and the JEP referees for encouragement anduseful advice

References

Bergstrom Theodore C 1995 ldquoOn the Evo-lution of Altruistic Ethical Rules for SiblingsrdquoAmerican Economic Review 851 pp 58ndash81

Bergstrom Theodore C 2002 ldquoThe Algebraof Assortative Encounters and the Evolution ofCooperationrdquo International Game Theory ReviewForthcoming

Bergstrom Theodore and Oded Stark 1993ldquoHow Altruism Can Prevail in an EvolutionaryEnvironmentrdquo American Economic Review 832pp 149ndash55

Binmore Ken 1992 Fun and Games Lexing-ton Mass DC Heath

Binmore Ken 1994a Game Theory and the So-cial Contract I Playing Fair Cambridge MassMIT Press

Binmore Ken 1994b Game Theory and the So-

cial Contract II Just Playing Cambridge MassMIT Press

Boorman SA and PR Levitt 1980 The Ge-netics of Altruism New York Academic Press

Boyd Robert and Peter Richerson 1990ldquoGroup Selection among Alternative Evolution-arily Stable Strategiesrdquo Journal of Theoretical Biol-ogy August 145 pp 331ndash42

Boyd Robert and Peter Richerson 1992ldquoPunishment Allows the Evolution of Coopera-tion (or Anything Else) in Sizable Groupsrdquo Ethol-ogy and Sociobiology May 13 pp 171ndash95

Boyd Robert and Peter Richerson 2002ldquoGroup Bene cial Norms can Spread Rapidly inStructured Populationsrdquo Journal of Theoretical Bi-ology Forthcoming

Carr-Saunders AM 1922 The Population Prob-


lem A Study in Human Evolution Oxford Claren-don Press

Cavalli-Sforza LL and MW Feldman 1981Cultural Transmission and Evolution A Quantita-tive Approach Princeton NJ Princeton Univer-sity Press

Cohen D and I Eshel 1976 ldquoOn theFounder Effect and the Evolution of AltruisticTraitsrdquo Theoretical Population Biology December10 pp 276ndash302

Cosmides Leda 1989 ldquoThe Logic of SocialExchange Has Natural Selection Shaped HowHumans Reasonrdquo Cognition April 313 pp187ndash276

Cosmides Leda and John Tooby 1989 ldquoEvo-lutionary Psychology and the Generation of Cul-ture Part II A Computational Theory of Ex-changerdquo Ethology and Sociobiology January 10pp 51ndash97

Dawkins Richard 1976 The Selsh Gene Ox-ford Oxford University Press

Edwards VC Wynne 1962 Animal Dispersionin Relation to Social Behaviour Edinburgh andLondon Oliver and Boyd

Eshel Ilan 1972 ldquoOn the Neighbor Effectand the Evolution of Altruistic Traitsrdquo TheoreticalPopulation Biology September 3 pp 258ndash77

Eshel Ilan Larry Samuelson and AvnerShaked 1998 ldquoAltruists Egoists and Hooligansin a Local Interaction Modelrdquo American EconomicReview March 881 pp 157ndash79

Eshel Ilan Emilia Sansone and Avner Shaked1999 ldquoThe Emergence of Kinship Behavior inStructured Populations of Unrelated Individu-alsrdquo International Journal of Game Theory Novem-ber 284 pp 447ndash63

Fehr Ernst and Simon Gachter 2000 ldquoCoop-eration and Punishment in Public Goods Exper-imentsrdquo American Economic Review September904 pp 980ndash94

Frank Robert H 1987 ldquoIf Homo EconomicusCould Choose His Own Utility Function WouldHe Want One with a Consciencerdquo American Eco-nomic Review September 774 pp 593ndash604

Friedman Daniel and Nirvikar Singh 1999ldquoThe Viability of Vengeancerdquo Technical ReportUniversity of California at Santa Cruz

Grafen Alan 1984 ldquoNatural Selection GroupSelection and Kin Selectionrdquo in Behavioural Ecol-ogy Second Edition JR Kreb and NB Davieseds London Blackwell chapter 3 pp 62ndash80

Haldane JBS 1932 The Causes of EvolutionNew York and London Harper amp Brothers

Hamilton William D 1964 ldquoThe GeneticalEvolution of Social Behavior Parts I and IIrdquoJournal of Theoretical Biology July 7 pp 1ndash52

Henrich Joseph 2000 ldquoDoes Culture Matter

in Economic Behavior Ultimatum Game Bar-gaining among the Machiguenga of the Peru-vian Amazonrdquo American Economic Review Sep-tember 904 pp 973ndash79

Henrich Joseph and Robert Boyd 2001 ldquoWhyPeople Punish Defectorsrdquo Journal of TheoreticalBiology 2081 pp 79ndash89

Henrich Joseph et al 2001 ldquoIn Search ofHomo Economicus Behavioral Experiments in15 Small-Scale Societiesrdquo American Economic Re-view May 912 pp 73ndash78

Hesiod 1929 H Evelyn Waugh ed HesiodThe Homeric Hymns and Homerica LondonHeineman

Hume David 1739 A Treatise of Human Na-ture Second Edition Oxford Clarendon PressLA Selby-Bigge ed Revised by P Nidditch1978

Kimura Motoo and George H Weiss 1964ldquoThe Stepping Stone Model of Population Struc-ture and the Decrease of Genetic Correlationwith Distancerdquo Genetics April 49 pp 561ndash76

Ledyard John O 1995 ldquoPublic Goods A Sur-vey of Experimental Researchrdquo in The Handbookof Experimental Economics John Kagel and AlvinRoth eds Princeton NJ Princeton UniversityPress chapter 2 pp 111ndash81

Levin BR and WL Kilmer 1974 ldquoInter-demic Selection and the Evolution of AltruismrdquoEvolution December 284 pp 527ndash45

Levins R 1970 ldquoExtinctionrdquo in Some Mathe-matical Problems in Biology M Gerstenhaber edProvidence American Mathematical Society pp77ndash107

Maynard Smith John 1964 ldquoGroup Selectionand Kin Selectionrdquo Nature March 14 201 pp1145ndash147

Nachbar John 1990 ldquolsquoEvolutionaryrsquo Selec-tion Dynamics in Games Convergence andLimit Propertiesrdquo International Journal of GameTheory 191 pp 59 ndash89

Nisbett Richard E and Dov Cohen 1996Culture of Honor The Psychology of Violence in theSouth Boulder Colo Westview Press

Nowak Martin A and Robert M May 1993ldquoEvolutionary Games and Spatial Chaosrdquo NatureOctober 29 359 pp 826ndash29

Roth Alvin E Vesna Prasnikar MasahiroOkuno-Fujiwara and Shmuel Zamir 1991 ldquoBar-gaining and Market Behavior in JerusalemLjubljana Pittsburgh and Tokyo An Experi-mental Studyrdquo American Economic Review Decem-ber 815 pp 1068ndash095

Rousseau Jean Jacques 1755 [1950] Dis-course on the Origin and Foundation of InequalityAmong Men (Second Discourse) Everymanrsquos Li-brary NY Dutton


Sethi Rajiv and E Somanathan 2002ldquoUnderstanding Reciprocityrdquo Journal of EconomicBehavior and Organization Forthcoming

Skyrms Brian 1996 Evolution of the Social Con-tract Cambridge Cambridge University Press

Skyrms Brian Forthcoming ldquoThe StagHuntrdquo Proceedings and Addresses of the AmericanPhilosophical Association

Skyrms Brian and Robin Pemantle 2000 ldquoADynamic Model of Social Network FormationrdquoProceedings of the National Academy of Science Au-gust 9716 pp 9340ndash346

Sober Eliot and David Sloan Wilson 1999Unto Others Cambridge Mass Harvard Univer-sity Press

Soltis Joseph Robert Boyd and Peter Richer-son 1995 ldquoCan Group-Functional BehaviorsEvolve by Cultural Group Selection An EmpiricalTestrdquo Current Anthropology June 363 pp 473ndash83

Weibull Jorgen 1995 Evolutionary Game The-ory Cambridge Mass MIT Press

Williams George C 1966 Adaptation and Nat-ural Selection A Critique of Some Current Evolution-ary Thought Princeton NJ Princeton Univer-sity Press

Wilson David Sloan 1975 ldquoA Theory ofGroup Selectionrdquo Proceedings of the National Acad-emy of Sciences January 721 pp 143ndash46

Wilson David Sloan 1979 ldquoStructured Demesand Trait-Group Variationrdquo American NaturalistJanuary 113 pp 157ndash85

Wright Sewall 1921 ldquoSystems of Matingrdquo Ge-netics March 62 pp 111ndash78

Wright Sewall 1943 ldquoIsolation by DistancerdquoGenetics January 28 pp 114ndash38

Wright Sewall 1945 ldquoTempo and Mode inEvolution A Critical Reviewrdquo Ecology October26 pp 415ndash19

Young H Peyton 1998 Individual Strategyand Social Structure An Evolutionary Theory ofInstitutions Princeton NJ Princeton Univer-sity Press


was infrequent These groups usually managed to avoid overpopulation and theattendant scourges of war famine and disease Population densities remainedroughly constant and close to the levels that maximized per capita food consump-tion To support these claims Carr-Saunders offered evidence that in existingprimitive societies fertility is deliberately restrained by means of abortion infanti-cide and long-term sexual abstinence He argued that such reproductive restraintis inconsistent with sel sh maximization of individual fertility and must somehowbe explained by ldquogroup selectionrdquo

In an encyclopedic study of the spatial dispersion of animal populations VCWynne-Edwards (1962) proposed that this principle has far more ancient roots Hebelieved that in much of the animal kingdom species maintain population densi-ties at an ldquooptimal level for each habitat that they occupyrdquo Wynne-Edwards arguedthat group selection is possible because ldquoanimal (and plant) species tend to groupinto more or less isolated populationsrdquo who depend on food resources of aldquolocalized immobilerdquo character and that ldquothe local stock conserves its resources andthereby safeguards the future survival of its descendantsrdquo

Some biologists viewed Wynne-Edwardsrsquo book as academic heresy George CWilliams (1966) argued that the behavior that Wynne-Edwards cites as evidence forgroup selection is consistent with individuals maximizing their own long-run re-productive interests or those of close relatives For example individuals may nd itin their own reproductive interests to vary their birth rates inversely with populationdensity It also may be in an individualrsquos sel sh interest to defend territories thatexceed minimum requirements in normal years because the extra territory will becritically important in bad years Other biologists have attempted to provide formalunderpinnings for Wynne-Edwardsrsquos rather loosely argued proposition A detailedand interesting account of this controversy can be found in Sober and Wilson(1999)

The polar theories of individual and group selection make dramatically dif-ferent predictions about social interactions Individual selection theory suggests aworld populated by resolutely sel sh homo economicus and his zoological (andbotanical) counterparts By contrast a world shaped by group selection would likelybe inhabited by natural socialists with an instinctive ldquoKantianrdquo morality towardother members of their group Of course the localism that leads to group selectionwould also tend to produce unsavory impulses toward xenophobia and intertribalwarfare

Games and Social Interactions

Prisonersrsquo Dilemma GamesEvolutionary biologists game theorists and anthropologists have frequently

used the prisonersrsquo dilemma game as a research vehicle to explore the polarregions of individual and group selection theory and the interesting terrain that liesbetween A multiplayer prisonersrsquo dilemma is a game in which individuals may take



















Defect 3 3


























Defect r r2














































































Final Remarks


















References















































































Defect 3 3


























Defect r r2














































































Final Remarks


















References






















































































Defect r r2














































































Final Remarks


















References










































































































































Final Remarks


















References











































































References






























































evolution of social behavior: individual and group...

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