the evolution of strong reciprocity:cooperation in ...€¦ · shunning, and those punished in this...

Theoretical Population Biology 65 (2004) 17–28

ARTICLE IN PRESS

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The evolution of strong reciprocity: cooperation inheterogeneous populations

Samuel Bowlesa,b and Herbert Gintisa,c,�

a Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USAb University of Siena, Siena, Italy

c University of Massachusetts, Amherst, MA 01003, USA

Received 5 August 2002

Abstract

How do human groups maintain a high level of cooperation despite a low level of genetic relatedness among group members? We

suggest that many humans have a predisposition to punish those who violate group-beneficial norms, even when this imposes a

fitness cost on the punisher. Such altruistic punishment is widely observed to sustain high levels of cooperation in behavioral

experiments and in natural settings.

We offer a model of cooperation and punishment that we call strong reciprocity: where members of a group benefit from mutual

adherence to a social norm, strong reciprocators obey the norm and punish its violators, even though as a result they receive lower

payoffs than other group members, such as selfish agents who violate the norm and do not punish, and pure cooperators who adhere

to the norm but free-ride by never punishing. Our agent-based simulations show that, under assumptions approximating likely

human environments over the 100,000 years prior to the domestication of animals and plants, the proliferation of strong

reciprocators when initially rare is highly likely, and that substantial frequencies of all three behavioral types can be sustained in a

population. As a result, high levels of cooperation are sustained. Our results do not require that group members be related or that

group extinctions occur.

r 2003 Published by Elsevier Inc.

Keywords: Multi-level selection; Strong reciprocity; Human cooperation; Altruistic punishment

1. Introduction

How do human groups maintain a high level ofcooperation despite a low level of genetic relatednessamong group members? The hypothesis we explore isthat cooperation is maintained because many humanshave a predisposition to punish those who violategroup-beneficial norms, even when this reduces theirfitness relative to other group members. Compellingevidence for the existence and importance of suchaltruistic punishment comes from controlled laboratoryexperiments, particularly the study of public goods,

ing author. University of Massachusetts, 15 Forbes

ampton, MA 01060-2843, USA. Fax: +1-413-586-

esses: [email protected] (S. Bowles),

st.net (H. Gintis).

://www.santafe.edu/~bowles,

x.oit.umass.edu/~gintis.

e front matter r 2003 Published by Elsevier Inc.

b.2003.07.001

common pool resource, ultimatum, and other games(Yamagishi, 1986; Ostrom et al., 1992; Fehr andGachter, 2002), from ethnographic studies of simplesocieties (Knauft, 1991; Boehm, 1984, 1993), fromhistorical accounts of collective action (Moore, 1978;Scott, 1976; Wood, 2003), as well as from everydayobservation.

Several plausible resolutions to the evolutionarilypuzzle posed by altruistic punishment have been offered.If group extinctions are sufficiently common, altruisticpunishment may evolve through the contribution ofnorm adherence to group survival (Boyd et al., 2003).Also, those engaging in punishment of norm violatorsmay reap fitness benefits if their punishment is treated asa costly signal of some underlying but unobservablequality as a mate, coalition partner, or opponent (Gintiset al., 2001). Here we explore a different mechanism inwhich neither signaling nor group extinctions plays arole. Rather, punishment takes the form of ostracism or

ARTICLE IN PRESSS. Bowles, H. Gintis / Theoretical Population Biology 65 (2004) 17–2818

shunning, and those punished in this manner sufferfitness costs.

We hypothesize that where members of a groupbenefit from mutual adherence to a norm, individualsmay obey the norm and punish its violators, even whenthis behavior incurs fitness costs by comparison to othergroup members who either do not obey the norm or donot punish norm violators, or both. We call this strong

reciprocity. Strong reciprocity is altruistic, conferringgroup benefits by promoting cooperation, while impos-ing upon the reciprocator the cost of punishing shirkers.

It might be thought that Cooperators, who uncondi-tionally cooperate but never punish would outcompeteReciprocators, who bear the cost of punishing normviolators. But as Cooperators replace Reciprocators in agroup, the fraction of Selfish agents increases, and withReciprocators less frequent in the group, the Selfishagents increasingly shirk, thereby attaining higher fitnessthan the Cooperators, and eventually replacing them.We model this dynamic below (see Fig. 1). For thisreason, Cooperators do not displace Reciprocators inthe population as a whole. Moreover, in groups in whicha low level of shirking is established, the expected costsof punishing others become quite low, so the within-group selection pressures operating against Reciproca-tors is weak.

We base our model on the structure of interactionamong members of the mobile hunter-gatherer bands inthe late Pleistocene. Modern accounts of these societiesrecord considerable variety in social organization andlivelihood (Kelly, 1995; Binford, 2001). But widespreadparticipation in joint projects such as hunting andcommon defense as well as the sharing of food, valuableinformation, and other sources of survival among many

Fig. 1. Within group dynamics with ostracism but no migration. This

diagram is based on s42c (the cost of being ostracized is greater than

twice the cost of working for one period). The value of fr for which’fr ¼ 0 and the value of fr for which ’fc ¼ 0 are based on the cost of

effort function (6) below.

of these societies in the modern world is well established.A good case can be made that these cooperative projectswere at least as important among our Late Pleistoceneancestors as they are among modern mobile foragingbands (Boehm, 2002).

Our model therefore reflects the following empiricalconsiderations. First, groups are sufficiently small thatmembers directly observe and interact with one another,yet sufficiently large that the problem of shirking incontributing to public goods is present. Second, there isno centralized structure of governance (state, judicialsystem, Big Man, or other) so the enforcement of normsdepends on the participation of peers. Third, there aremany unrelated individuals, so altruism cannot beexplained by inclusive fitness. Fourth, status differencesare quite limited, especially by comparison to agricul-tural and later industrial societies, which justifies ourtreatment of individuals as homogeneous other than bybehavioral type and by the group to which they belong.Fifth, the sharing on which our model is based—eitherof food individually acquired or of the common work ofacquiring food, for example—is characteristic of thesesocieties. Sixth, the individuals in our model do not storefood or accumulate resources. This, too, is a character-istic of at least those hunter-gather bands based on whatWoodburn (1982) calls an ‘‘immediate return’’ system ofproduction.

Seventh, we take the major form of punishment to beostracism and we treat the cost of being ostracized asendogenously determined by the amount of punishmentand the evolving demographic structure of the popula-tion. This manner of treating punishment reflects acentral aspect of hunter-gatherer life: since individualscan often leave the group to avoid punishment, the costof being ostracized is among the more serious penaltiesthat can be levied upon an individual group member.1

Finally, behavioral heterogeneity is an emergent prop-erty of populations in our model, one that correspondsto what we know from the ethnographic record offoraging bands, as well as from the experimentalevidence on both hunter gatherers (Henrich et al.,2003) and modern market based societies (Loewensteinet al., 1989; Andreoni and Miller, 2002).

2. Working, shirking and punishing within a group

Consider a population in which agents can live andwork alone, in which case each has fitness foo0: Weassume reproduction is haploid. By the fitness of an

1 There being relatively little individually held property, individuals

cannot be severely punished by having their wealth confiscated; there

being no fixed residence, individuals cannot be jailed or otherwise

confined; extreme physical harm can be meted out against norm

violators, but such measures are generally reserved for such serious

crimes as adultery and murder.

ARTICLE IN PRESS

2 Either of two informational assumptions justify our model. The

first is that the type of an agent is unknown, but the fraction of

Reciprocators is known to Selfish agents. The second is that the

identity of Reciprocators is known to Selfish agents, but this cannot

affect the probability of being caught shirking. It does not matter for

our model whether or not Reciprocators can distinguish between

Cooperators and Selfish agents, or whether they know the expected

cost of ostracism used by a Selfish agent to determine the agent’s

shirking level. All of these informational assumptions can be

weakened, at the cost of increased model complexity, but none is

crucial to its operation.3 We obtain the second term by assuming each Reciprocator

randomly chooses one agent to monitor in each period. Then the

probability of being ostracized is

ss½1 � ð1 � 1=ðn � 1ÞÞfrn�:We approximate this by ssfr; for simplicity. The approximation is very

good for fro0:4; but for higher fr; ours is an overestimate. For

instance, when fr ¼ 1; the actual cost is 0:66sss; but our estimate is sss:

This is a harmless but useful approximation, since when fr40:4; there

is always universal cooperation in our simulations, so Selfish agents

rarely pay the cost of being ostracized.

S. Bowles, H. Gintis / Theoretical Population Biology 65 (2004) 17–28 19

agent, we mean the expected number offspring producedby the agent in one period minus the probability theagent dies in that period. Agents can also workcooperatively in a group, each producing an amount b

at cost c (all benefits and costs are in fitness units). Weassume that output of the group is shared equally by theagents, so if all group members work, each has a netgroup fitness benefit b � c40:

The group consists of three type of actors. The firsttype, whom we call Reciprocators, work unconditionallyand punish shirkers. The second type, whom we callSelfish, maximize fitness. They never punish shirkers,and work only to the extent that the expected fitness costof working exceeds the expected fitness cost of beingpunished. The third type, whom we call Cooperators

work unconditionally but never punish shirkers.Parents pass on their type to their offspring with

probability 1 � e; and with probability e=2; an offspringtakes on each of the other two types. We call e the rate of

mutation. Also, with probability 1 � e; Selfish agentsinherit the estimate of s40 (the cost of being ostracized)from their parents. With probability e an offspring is amutant whose s is drawn from a uniform distribution on[0,1]. Thus, s is an endogenous variable. Selfish agentswith an s that is different from the objective fitness costs� of being ostracized may shirk too little or too much,leading to suboptimal fitness, a selective pressure for amodification of s:

We assume an ostracized agent works alone for aperiod of time before being readmitted to a group. Theobjective cost of ostracism therefore depends on thelength of a spell of solitary living that occurs afterleaving the group, and this changes over time as thedistribution of the population between those in groupsand those living alone changes. So s� is also endogenous.In our model, Selfish agents with very high values of s

behave exactly like Cooperators, except that if there arezero Reciprocators in the group, they do not work.

Suppose a Selfish agent shirks (that is, does not work)a fraction ss of the time, so the average rate of shirkingis given by s ¼ ð1 � fr � fcÞss; where fr is the fraction ofthe group who are Reciprocators, and fc is the fractionwho are Cooperators. The fitness value of group outputis nð1 � sÞb; where n is the size of the group. Sinceoutput is shared equally, each member receives ð1 � sÞb:The loss to the group from a Selfish agent shirking isbss: The fitness cost of working function, which can bewritten as lðosÞ; where os � 1 � ss; is increasing andconvex in its argument (i.e., l0; l0040; with lð1Þ ¼ c andlð0Þ ¼ 0). Expending effort always benefits the groupmore than it costs the workers, so osb4lðosÞ forssAð0; 1�: Thus, at every level of effort, os; workinghelps the group more than it hurts the worker.

Further, we assume that the cost of effort function issuch that in the absence of punishment of normviolators, the members face a public goods problem

(i.e., an n-player prisoner’s dilemma), in which thedominant strategy is to contribute very little or nothing.

We model punishment as follows. The fitness cost to aReciprocator of punishing a shirker is cp40: A membershirking at rate ss will be punished with probability frss:Punishment consists of being ostracized from the group.

Selfish agents, given their individual assessment s ofthe cost of being ostracized, and with the knowledgethat there is a fraction fr of Reciprocators in their group,choose a level of shirking, ss; to maximize expectedfitness.2

Writing the expected fitness cost of working, gðssÞ; asthe cost of effort plus the expected cost of beingostracized, plus the agent’s share in the loss of outputassociated with one’s own shirking, we have3

gðssÞ ¼ lð1 � ssÞ þ sfrss þ ssb=n: ð1Þ

Then, Selfish agents select s�s ; namely, that whichminimizes the cost of working (1). Assuming an interiorsolution, this is given by

g0ðs�s Þ ¼ l0ð1 � s�s Þ þ frs þ b=n ¼ 0; ð2Þ

requiring the shirker to equate the marginal fitnessbenefits of expending less effort on work (the first andthird terms) with the marginal costs of greater shirking,namely the increased likelihood of bearing the fitnesscost of ostracism (the second term). Since l00ðosÞ40;there is at most one solution to this equation, and it is aminimum. This first-order condition (2) shows thatSelfish agents who inherit a large s (i.e., who believe thecost of ostracism is very high) will shirk less, as also willthose in groups with a larger fraction of Reciprocators.

The expected contribution of each group member tothe group’s population in the next period is equal to themember’s fitness minus (for the Selfish agents) the


likelihood of ostracism. This gives

ps ¼ ð1 � sÞb � lð1 � ssÞ � frss; ð3Þ

pc ¼ ð1 � sÞb � c; ð4Þ

pr ¼ ð1 � sÞb � c � cpð1 � fr � fcÞss; ð5Þwhere the subscripts s; c; and r refer to Selfish agents,Cooperators, and Reciprocators. The final term in theexpression for pr follows because each Reciprocatorchooses a random agent to monitor; this agent is Selfishwith probability ð1 � fr � fcÞ and this agent shirks withprobability ss:

We assume that at the end of each period, groupsadmit a number of new members equal to a fraction m oftheir existing numbers. Candidates for immigration intogroups are the pool of solitary individuals, plus afraction g of current group members who want toemigrate for exogenous reasons (e.g., to find a mate, orto end a personal dispute with another group member).If the number of candidates exceeds the number ofplaces, a random sample of these candidates emigrate togroups. We assume that group members that desired toemigrate but did not find a receptive group remain intheir current group.

The number of groups and the total population isfixed. A simulation starts with all groups of the samesize, which we call the initial group size. Individual groupsize will, of course, change from period to period. It isplausible that there is an optimal group size, excessivedeviation from which leads to efficiency losses. Ratherthan explicitly building such losses into our model, weassume that if a group falls below some nmin in size, itdisbands, the remaining members migrating to the pool.We further assume that the vacated site is repopulatedby migrants randomly chosen from the most populousremaining groups, restoring the initial group size. Thesetwo procedures ensure that extremes in group size areavoided (details of the simulation structure are pre-sented in the appendix).

We can gain more insight into the dynamics of thissystem by choosing a specific function lð1 � sÞ satisfy-ing the conditions lð1Þ ¼ c; lð0Þ ¼ 0; l0ð1 � sÞo0; andl00ð1 � sÞ40: Extensive simulations suggest that theexact form of this function is unimportant, and thesimplest function satisfying these conditions is

lð1 � sÞ ¼ cð1 � sÞ2: ð6ÞUsing (6) and (2), it is easy to check that Selfish agentsthen shirk according to the function

ssð frÞ ¼1 � frsn � b

2cnfor frpf max

r ¼ 2c þ b=n

s;

0 for fr4f maxr :

8<: ð7Þ

A phase diagram of within-group dynamics, abstract-ing from ostracism and group dissolution, appears inFig. 1. In this figure, each point in the simplex is a

distribution of behavioral types in the population. Thevertex S refers to the all-shirking group compositionð fr ¼ fc ¼ 0Þ; vertex R refers to the all-Reciprocatorcomposition ð fr ¼ 1Þ; and C refers to the all-Cooperatorcase ð fc ¼ 1Þ: For the parameter values illustrated in thefigure, there is some fraction of Reciprocators f max

r ¼ð2c þ b=nÞ=s (the line BD) at and above which Selfishagents do not shirk at all, but below which they shirk ata strictly positive rate. Thus in the triangle RBD allthree types have equal payoffs, equal to b � c: Along thewhole CR segment, Reciprocators and Cooperators doequally well, since there are no Selfish agents to punish(the payoffs are again b � c). Along the CS segment,Reciprocators are absent, so Selfish agents do betterthan Cooperators. On the segment DS, Selfish agents dobetter than Reciprocators. Selfish agents optimize, sowhen ssAð0; 1Þ; we know from (2) that an increase in fr

holding the frequency of Selfish agents constant, mustentail a decline in ss: This, along with Eq. (7), meansthat lowering the fraction of Selfish agents increases thepayoff to Reciprocators relative to Selfish agents in thearea CBDS. Moreover, Cooperators always have higherpayoffs than Reciprocators in the interior of this area.We conclude that the only asymptotically stableequilibrium of the system is the all-Selfish point S, andits basin of attraction consists of all interior pointsbelow the line BD in Fig. 1.

Clearly, then, if cooperation is to be sustained, it mustbe because Cooperators, who undermine the coopera-tive equilibrium by driving out Reciprocators, mustthemselves be harmed by shirking Selfish agents whenReciprocators are rare. Fig. 1 illustrates exactly thisprocess, with Selfish agents proliferating at the expenseof both Cooperators and Reciprocators once thefrequency of Reciprocators falls below the line AE inthe figure. We shall show by simulation that this isindeed the case for a wide range of plausible parametervalues.

Fig. 2 shows the group average payoffs as a functionof the distribution of types within a group. The curvedlines are iso-group-average-fitness loci, showing clearlythat average group fitness increases as we move awayfrom the unique stable equilibrium S.

In the next section we consider the evolution of anumber of groups, each occupying a site allowingcooperative production as described above. The result-ing model is too complex to admit an analyticalsolution, so we provide a series of simulations thatillustrate its characteristics over an appropriate range ofparameter values.

3. Simulating strong reciprocity

For our baseline simulation, we set up 20 groups, eachstarting out with 20 members, and an empty pool. We

ARTICLE IN PRESS

Fig. 2. Average payoffs and group composition. This diagram is based

on b ¼ 0:2; c ¼ cp ¼ 0:1; and s ¼ 0:3: The arrows point towards

increasing payoffs. For all frequencies in BDR, p ¼ 0:1:

Period0 500 1000 1500 2000 2500 3000

Perc

ent

0

10

20

30

40

50

60

70

80

90

100

Selfish

Reciprocator

Cooperator

Shirking Rate

Fig. 3. Initial periods of a single simulation run. As is clear from the

figure, and as in all our simulations, the initial population consisted of

Selfish agents alone. The baseline parameters are as in Table 1.

Table 1

Baseline parameters

Value Description

0.2 Output per agent, no shirking ðbÞ0.1 Cost of working, no shirking ðcÞ0.1 Cost of punishing ðcpÞ0.05 Emigration rate ðgÞ0.03 Immigration rate ðmÞ20 Initial group size ðnÞ20 Number of groups

�0:1 Fitness in pool ðf0Þ6 Minimum group size

[0,1] Initially seeded expected cost of ostracism ðsÞUniformly distributed on this interval

0.01 Mutation rate ðeÞ

These parameters are used in all simulations, unless otherwise noted.

All simulations start with a homogeneous population of Selfish agents.

Table 2

Long run simulation statistics

Long-run Values

Value Description

37.2% Fraction of Reciprocators

24.6% Fraction of Cooperators

38.2% Fraction of Selfish agents

11.1% Average shirking rate

4% Fraction of population in pool

0.38% Fraction of Reciprocators in pool

0.48% Fraction of Cooperators in pool

10% Fraction of Selfish agents in pool

4% Fraction of pool who are Reciprocators

3% Fraction of pool who are Cooperators

93% Fraction of pool who are Selfish

1.21 Ratio of Cooperators to Reciprocators in disbanded groups

3.4 Ratio of Selfish agents to Reciprocators in disbanded groups

The baseline parameters are as in Table 1. The statistics represent the

average of the last 1000 periods of a 50,000 period simulation,

averaged over 25 simulations.


set the initial frequency of Selfish agents at 100%, andwe assigned each Selfish agent a cost of being ostracizedðsÞ; using a random number drawn from a uniformdistribution on the interval [0,1]. We assume thatimmigration into a group occurs at a rate of 12% pergeneration, which we take to be four simulation periods.Therefore the immigration rate is m ¼ 0:03:

We assume a desired emigration rate of g ¼ 0:05 perperiod, so more agents would like to emigrate fromgroups than are admitted into groups. We set the fitnesscost of being in the pool to be equal to the cost ofworking (as Fig. 6 shows, this figure is not at all critical).We also set individual productivity, net of the cost ofworking, equal to the cost of punishing a shirker.Simulations show that it matters little how large thisparameter is, and we set it to 0.1 in our baselinesimulations. Since we assume the cost of working is c ¼0:1; the cost of punishing becomes cp ¼ 0:1 andindividual productivity is b ¼ 0:2: The reason absoluteproductivity does not matter is that we cull or augmentthe population randomly at the end of each period tomaintain a constant population size. Effectively, fitnessfigures are therefore relative. The baseline parametersare listed in Table 1.

Using these parameters, Fig. 3 shows the evolution ofthe distribution of agent types and the average shirkingrate for the whole population in the initial 3000 periodsof a typical run. The results shown are backward-moving averages over 100 periods. To determine thetypical behavior of the model, we ran the simulation 25times with the baseline parameters for 30,000 periods,and calculated the average fraction of each type and theaverage shirking rate, averaged over the last 1000periods. These averages are reported in Table 2. Therewas remarkably little variation across the runs—in all


cases the standard error of the frequencies reported isless than 1.14% points.

Why does the long-run behavior of the system involveroughly equal numbers of the three types of agents?Table 2 shows that over this period, Cooperators wereslightly more likely (0.48%) than Reciprocators (0.38%)to find themselves in the pool of solitary agents, whileSelfish agents were more than an order of magnitudemore likely to be in this position (10%). This is in partbecause Cooperators are more likely than Reciprocators

Number of Reciprocators

Round320 340 360 380

Num

ber

of R

ecip

roca

tors

0

2

4

6

8

Round

320 340 360 380

Num

ber

of C

oope

rato

rs

0

2

4

6

8

10

12

14

16

Round320 340 360 380

Num

ber

of S

hirk

ers

0

2

4

6

8

10

12

14

16

18

Number of Shirkers

in Group

Number of Cooperators

Fig. 4. Snapshot of the life history of a single group, from repopulation of a

baseline parameters are as in Table 1.

to be in disbanded groups (by a ratio of 1.21 to 1), andthe Selfish agents are more likely than Reciprocators tobe in disbanded groups (by a ratio of 3.4 to 1). Butostracism, not disbanding, is overwhelmingly importantin populating the pool with Selfish agents. Indeed, wehave found that even when groups are not disbandeduntil a single agent is left in the group (at whichtime it is no better than solitary production), similarlong-run values of the major variables obtain. Thus, thedispersion of members of very small groups, while

Round320 340 360 380

Shir

king

Rat

e

0.0

0.2

0.4

0.6

0.8

1.0

Aggregate Shirking Rate

Round

320 340 360 380

Gro

up S

ize

5

10

15

20

25 Group Size

site to disbanding: membership composition, size and efficiency. The

ARTICLE IN PRESS

Period20000 21000 22000 23000 24000 25000

-0.004

-0.002

0.000

0.002

0.004

Within-Group Termin Price Equation

Between-Group Termin Price Equation

Sum of Within-Groupand Between-Group

Terms

1000 Period Running Average of Sum of Within-Group

and Between-GroupTerms

Fig. 5. Price’s equation applied to a dynamic simulation. The baseline

parameters are as in Table 1. This figure shows a 5000 period segment

of a 30,000 period run. Measurements were taken every 100 periods.

The within-group term measures the tendency of Cooperators to enjoy

a fitness advantage within groups due to the fact that they do not

punish, while the between-group term measures the fitness disadvan-

tage of Cooperators across groups due to the fact that members of

groups with a large fraction of Cooperators have low mean fitness. The

sum of the two terms is highly variable over a small number of periods,

but average to zero, since the fraction of Cooperators is stable in the

long run. Over the 5000 period segment depicted, the Fraction of

Cooperators rose slightly, which accounts for the small positive bias in

the long-run average of within- and between-group terms.


empirically realistic, is not crucial to the model’sworkings.

To illustrate that the dynamics depicted in Figs. 1 and2 are operative, in Fig. 4 we trace a bit of the history of asingle group, from ‘‘birth’’ in period 320 (repopulationof a site after another group had disbanded) to ‘‘death’’in period 390 (disbanding because group size fell belowthe minimum sustainable group size). This group beganwith roughly equal numbers of the three agent types, butearly on, Selfish agents were driven out by theReciprocators and were replaced by Cooperators.Starting in period 330, Cooperators began displacingReciprocators until, about period 340, the groupconsisted of many Cooperators and a few Selfish agents(i.e., near the C vertex in Fig. 1). With few Reciproca-tors present, the expected cost of shirking fell dramati-cally, shirking rose, and the Selfish thereforeoutperformed the Cooperators. The numbers of Selfishtherefore grew rapidly from period 340 to 350, displa-cing Cooperators. This process reproduces the dynamicillustrated by the curved arrow QS in Fig. 1. From thispoint, average group fitness was low (the groupcomposition placed it close to the S vertex in Fig. 2)and hence, despite a small chance infusion of immigrantReciprocators, the group loses members until it dis-bands in period 390. Fig. 4 also shows the effect of thesedemographic movements on the shirking rate and groupsize. We see that the shirking rate remains very low untilperiod 340, and then climbs steadily until just prior tothe end of the group’s life. Near the end there is anincrease in group fitness because a couple of Recipro-cators migrate into the group and the Selfish respond byshirking less, but the high level of shirking combinedwith the high cost of deterring it through ostracismreduces group size below the minimum before it canrecover.

Our interpretation of this group’s life course anddemise illustrates the population-level forces preventingCooperators from driving out Reciprocators. We canformalize this reasoning considerably, and subject it toan empirical test. Cooperators in our model are negative

altruists, who have a fitness advantage within groups,offset by the lower average fitness of groups with a highfrequency of Cooperators. If the group effect issufficiently strong. Cooperators do not drive outReciprocators in the population, even though theyeliminate Reciprocators from the groups in which theycoexist. We can use Price’s equation (Price, 1970) for theanalysis of multi-level selection processes to demon-strate this.

Suppose there are groups i ¼ 1;y; m; and let qi bethe fraction of the total population in group i: Supposepi average fitness of members of group i; and let f i

c ; f ir ; f i

s

be the fraction of Cooperators, Reciprocators, andSelfish in group i: Price’s equation for the change in thefraction of the entire population who are Cooperators,

Dfc; can then be written as

%pD %fc ¼X

qiðpi � %pÞf ic þ

Xqipif

icp

ic; ð8Þ

where pi ¼ f icp

ic þ f i

rpir þ f i

spis and %p ¼

Pqipi:

The first summation in (8) is the covariance betweenaverage group fitness and the share of Cooperators inthe group. The interpretation offered above and thegroup history depicted in Fig. 4 suggests this term willbe negative, since groups with a high frequency ofCooperators are also likely to have a high frequency ofSelfish agents who engage in high levels of shirking.These groups thus will have lower than average meanfitness. The second summation is the expected change inwithin-group Cooperator fitness, which we expect to bepositive since, unless Selfish agents are entirely absent,Cooperators free-ride on the altruistic punishment ofshirkers by Reciprocators. Our model is too complex tosolve Price’s equation analytically, but we can show thatour description of Cooperator fitness is accurate, sincewhen we use values from the simulation in (8), the twosummations have the expected signs, and approximatelyoffset each other, over many thousands of rounds ofsimulation, thereby explaining why fc oscillates around astationary long-term average (as illustrated in Fig. 3).

Fig. 5 show the movement of the terms of the Priceequation (8) for this simulation. As predicted, thecovariance between average group fitness and the shareof Cooperators is negative, the expected change inwithin-group Cooperator fitness is positive, and the two


are approximately offsetting over many thousands ofperiods.

4. Variations and extensions

In further simulations, we explore a large parameterspace with two objectives. First, we will check that thesimulation results respond in plausible ways to para-meter shifts, thus illuminating the causal structure of themodel. Second, we will confirm that the model works forvalues approximating human ancestral environments.

The first three panels of Fig. 6 show that the modelresponds in the expected way to changes in parametervalues, and that high levels of cooperation are sustainedfor a quite large parameter space. These panels show theaverage shirking value, plotted against the fitness ofagents per period in the pool of solitary agents, the costto Reciprocators of punishing shirkers, and initial groupsize. These figures are the average of the last 1000periods of ten runs of 30,000 periods. In each case, wesee that the shirking rate, which is the best aggregatemeasure of group cooperation, is small or moderate in

Fig. 6. The effect on shirking of the assumed values of fitness in pool, cost of

are otherwise as in Table 1. For average group size larger than about 120, R

rate panel shows, for a population of 50 groups, the average over 25 runs of

1000 periods, first fell below 10%.

size over a large range of parameters, and moves in theexpected direction with parameter changes. Our resultsare quite insensitive to variations in other parameters,including the immigration rate, the emigration rate, andminimum group size. In each case, we find cooperationto be robust over a wide range of parameters.

Our simulations show that the ostracism mechanismpromotes high levels of cooperation in groups and that asubstantial fraction of the population are Reciprocatorsin the long-term steady state of this model under a widerange of parameter values. But how could Reciprocatorscome into existence de novo? We speculate that it couldhave emerged through a rather trivial modification offitness-enhancing behaviors. For example, a good casecould be made that strong reciprocity among kin couldemerge and proliferate through as a form of kin-basedaltruism, and then be generalized to unrelated indivi-duals. Another possibility is that strong reciprocityarose through a modification of the individual fitnessenhancing strategy of reciprocal altruism. In this casethe modification is trivial: simply ignore the futurepayoffs to current behavior. Like the extension of kin-based strong reciprocity to non-kin, the mutation or

punishing, group size, and the mutation rate. The baseline parameters

eciprocators rarely invade an initially Selfish population. The mutation

the number of periods until the shirking rate, averaged over previous

ARTICLE IN PRESS

Exogamy Fraction (%)

0 20 40 60 80 100

Perc

ent (

%)

0

10

20

30

40

50

60

% Selfish

% Reciprocator

Shirking Rate

% Cooperator

Fitness

Fig. 7. Degree of exogamy and degree of cooperation. The baseline

parameters are as in Table 1.


mutations to convert reciprocal altruist strategy to astrong reciprocal one involves a reduction in complexdiscrimination rather than an increase in complexity.These strategy conversions thus might occur with highprobability.

As we have seen (Fig. 3), the model supports theemergence of strong reciprocity after as few as 500periods. This occurs because at the rate of mutationassumed, it does not take many periods before at leastone group will have enough Reciprocators to implementa high level of cooperation. When this occurs, thecooperative groups grows in size, and as a result it seedsother groups by migration and repopulates the sites ofdisbanded groups. The rate at which this process takesplace obviously depends on the number of groups in thepopulation. In the fourth panel of Fig. 6 we present datain a population with 50 groups. A high level ofcooperation is achieved (on the average) after about1500 periods, for mutation rates as low as e ¼ 0:002:Simulations with just 20 groups, by contrast, show thatfor mutation rates lower than 0.002, it takes on theaverage 30,000 periods before the shirking rate first fallsbelow 10%. We think that our simulations with 50groups probably overstate the obstacles to the emer-gence of strong reciprocity for the simple reason that inorder to proliferate the behavior need only becomecommon in a single group, and there were far more than50 bands of early foraging humans.

Since offspring of group members remain in the groupuntil they either migrate, die, or are ostracized, ourmodel is also likely to have some kin selection involvedin both strengthening the altruism of Reciprocators anddamping the free-riding of Cooperators. In a haploidmodel, the relatedness of two agents is either unity ifthey are in the same clonal group, and zero otherwise.Thus, the within-group relatedness of a single groupmember is equal to the number of other agents in thegroup who are in the same clonal family, divided bygroup size minus one. Average within-group relatednessis the mean of this statistic over all agents in groups. Inour baseline simulation, we find the degree of related-ness of group member to be about 10%, varying from7% to 14% at different times within a single simulation.These figures move in the expected direction whenmigration and mutation rates are varied.

To assess quantitatively the contribution of kinselection to the maintenance of cooperation in themodel, we allowed the fraction of offspring whose firstperiod of life is within the parental group to vary from0% to 100%, the remaining offspring being randomlydistributed among all groups. A major reason foroffspring to migrate to other groups is exogamy, whichin small groups may be necessary to avoid inbreeding.So we define the degree of exogamy to be the fraction x

of offspring who leave the group for random reassign-ment to other groups, with the remaining fraction 1 � x

staying in the parental group unless reassigned throughostracism or migration (those leaving for ‘exogamyreasons’ were simply added to the migration flowsmentioned above).

Fig. 7 shows that the propensity of offspring toremain in the parental group is an important factor inpromoting cooperation and reciprocity. When all off-spring stay in the parental group, the average shirkinglevel, using the same parameters as in Table 1, isapproximately 11%, whereas when all offspring arerandomly located to groups, the average shirking raterises to 24%. In a plausible intermediate case, that of50% exogamy, the average shirking rate is about 18%.This variation occurs, as is clear from the figure, becausethe long-run fraction of Reciprocators depends upon thedegree of exogamy: with zero exogamy, this rate is about37%, whereas with 100% exogamy, there are only 22%Reciprocators in the long run. However, while showingthat within-group relatedness has the predicted effectson the population frequencies, Fig. 7 also makes it clearthat within group relatedness is not necessary to sustainhigh levels of cooperation in groups.

5. Discussion

Explanations of the evolution of cooperation amongunrelated humans sometimes fail to explain why similarbehaviors are seldom observed in other animals. Ourmodel, however, relies on cognitive, linguistic, and othercapacities unique to our species. The moralistic aggres-

sion (Robert Trivers’ apt term) that arguably providesthe motivational underpinnings of altruistic punishmentrequires uniquely human cognitive and linguistic abil-ities in the formulation of behavioral norms, theachievement of group consensus that the norms oughtto be followed, the communication of their violations,and the coordination of the often collective nature of the

ARTICLE IN PRESS

4 Even though our stage game is a one-shot, it may in fact involve

behaviors that take place over several, or even many years (e.g., a

hunting season, of which one period in our model may comprise

several). Our treatment of being ‘‘detected shirking’’ is compatible with

individuals’ building reputations during the course of the game that at

some point trigger punishment. Our ‘‘probability of being detected

shirking’’ is a summary description of this process, which may occur

over time even in a one-shot game.

S. Bowles, H. Gintis / Theoretical Population Biology 65 (2004) 17–2826

punishment of miscreants. Additionally, uniquely hu-man capacities to inflict punishment at a distance,through projectile weapons, reduce the cost of ostraciz-ing a norm violator.

Our proposed explanation of human cooperationcontrasts with the more standard interpretation stressingreciprocal altruism (Trivers, 1971; Axelrod and Hamil-ton, 1981). The canonical status of this view notwith-standing, there is little evidence that cooperation inprisoners’ dilemma type situations among non-humananimals is explained by the opportunities for inflictingcosts on non-cooperators offered by repeated interac-tions (Stephens et al., 2002). Thus, if our speculationthat strong reciprocity emerged through a modificationof reciprocal altruist behaviors is correct, this providesanother reason why strong reciprocity might be uniquelyhuman, given that reciprocal altruism appears to be veryrare in other species.

Among humans however, we do not doubt theimportance of repeated interactions and other structuresthat reward cooperators with higher fitness or otherpayoffs, rendering seemingly selfish acts a form ofmutualism. While an important part of the explanationof human cooperation, there are several reasons fordoubting the adequacy of this explanation. First,reciprocal altruism fails when a social group isthreatened with dissolution, since members who sacrificenow on behalf of group members do not have a highprobability of being repaid in the future (Gintis, 2000).

Second, many human interactions in the relevantevolutionary context took the form of n-person publicgoods games—food sharing and other co-insurance, aswell as common defense—rather than dyadic interac-tions. Even if repeated with high probability, n-personpublic goods (or common pool resource) interactionsmake cooperation difficult to sustain by means of thestandard tit-for-tat and other reciprocal behaviors, assuggested by Joshi (1987), Boyd and Richerson (1988),and Choi (2003). Alexander (1987) has proposed a moregeneral ‘‘indirect reciprocity’’ mechanism more amen-able to large group interactions, and this has beenformalized by Nowak and Sigmund (1998). Accordingto this model, agents reward and punish other agentswho have defected in pairwise interaction with thirdparties. While indirect reciprocity may well be animportant source of cooperation in humans, for reasonsgiven by Leimar and Hammerstein (2001), we doubtthat indirect reciprocity can be sustained in a populationof self-interested agents. Indirect reciprocity is morelikely promoted, as in our model, by strong reciproca-tors who reward prosocial behavior and punish anti-social behavior even when this behavior reduces within-group fitness. For an empirical study supporting thisidea, see Urs Fischbacher and Engleman (2002).

Third, the contemporary study of human behaviorhas documented a large class of prosocial behaviors

inexplicable in terms of reciprocal altruism. Forinstance, there is extensive support for income redis-tribution in advanced industrial economies, even amongthose who cannot expect to be net beneficiaries (Fonget al., 2002). Group incentives for large work teams areoften effective motivators even when the opportunity forreciprocation is absent and the benefits of cooperationare so widely shared that a self-interested group memberwould gain from free-riding on the effort of others(Ghemawat, 1995; Hansen, 1997; Knez and Simester,2001). Finally, laboratory and field experiments showthat non-selfish motives are frequently robust predictorsof behavior, even in one-shot, anonymous setting. Thisresearch has been summarized in Ostrom (1998) andFehr and Gachter (2000) for industrial societies, andHenrich et al. (2001) for hunter-gatherer and other smallscale societies.

Our model differs from other explanations ofcooperation among unrelated individuals in severalways. Most models of reciprocity treat interactionsamong pairs of agents (Boorman and Levitt, 1980;Axelrod and Hamilton, 1981; Kreps et al., 1982;Axelrod, 1984). Since strong reciprocity is exhibited insuch collective situations as group food-sharing anddefense, these models are not suited to explaining thisphenomenon. By contrast, we model n-agent groups(where n is on the order of ten to 100) in a series ofproduction periods that are effectively one-shot, sincethe only inter-period influences are those involving thebiological and cultural reproduction of new agents.Moreover, in contrast to other models of cooperation ingroups (Robson, 1990; Nowak et al., 2000; Wedekindand Milinski, 2000), we assume Reciprocators cannotgain from being phenotypically identified as such, or byestablishing a reputation for reciprocation acrossproduction periods.4

Nor in our model can Reciprocators use theiraltruistic behavior as a costly signal of superior fitness(Zahavi, 1975; Bliege Bird et al., 2001; Gintis et al.,2001). Finally, while most models of strong reciprocitydepend on group extinctions (Gintis, 2000; Boyd et al.,2003; Bowles et al., 2003), ours does not.

Our approach is related to the model of Aviles et al.(2002), as applied to tree-killing bark beetles (Raffa andBerryman, 1987) and other species in which there arestrong fitness benefits associated with social living. Theyposit a minimum group size and positive fitnesseffects of group size for smaller groups. While these

ARTICLE IN PRESSS. Bowles, H. Gintis / Theoretical Population Biology 65 (2004) 17–28 27

conventional Allee effects play no role in our model,they are approximated by our assumption that living incooperative groups confers fitness benefits and thatsolitary individuals bear fitness costs. Like Trivers(1971), Hirshleifer and Rasmusen (1989), Boyd andRicherson (1992), Sethi and Somanathan (1996), andFriedman and Singh (2001), we stress the importance ofaltruistic punishment. Hirshleifer and Rasmusen (1989)and Friedman and Singh (2001) develop models of teamproduction in which the threat of ostracism detersshirking. But, because they assume that ostracizing isnot costly to the individual ostracizer, their models,unlike ours, do not explain the persistence of altruisticbehaviors. Our paper is most closely related to Sethi andSomanathan (1996). But, in Sethi and Somanathan’smodel the equilibrium frequency of Reciprocators iszero and cooperation is complete. By contrast, ourmodel supports a positive (indeed, quite high) fractionof Reciprocators and a significant level of non-coopera-tion in the long run.

We think that our model, suitably extended, cancapture the environments that may have supported highlevels of cooperation among our ancestors living inmobile foraging bands during the late Pleistocene. Wedo not know that a human predisposition to strongreciprocity evolved as we have described. But oursimulations suggest that it could have.

Acknowledgments

We would like to thank Christopher Boehm, RobertBoyd, Jung-Kyoo Choi, Leda Cosmides, Marcus Feld-man, Steven Frank, Alan Grafen, Kristin Hawkes,Hillard Kaplan, Olof Leimar, Peter Richerson, RajivSethi, Eric Alden Smith, E. Somanathan, Leigh Tesfat-sion, Polly Wiessner, and Peyton Young for their helpwith this paper, the John D. and Catherine T.MacArthur Foundation and the Santa Fe Institute forfinancial support.

Appendix. Simulation details

Initialization specifies the following parameters (base-line values in parenthesis): initial number of agents pergroup (20), number of groups (20), initial fraction rr ofpopulation who are Reciprocators (0), initial fraction rc

of population who are Cooperators (0), cost c ofcooperating (0.1), cost cp of punishing (0.1), gain b

from cooperation (0.2), fraction g of members of groupsseeking to emigrate to another group (0.05), fraction mof groups size allowed as immigrants (0.03), fitness inpool f0 ð�0:01Þ; mutation rate (0.01), fraction r0

c ofReciprocators in seeded groups (0.8), minimum groupsize (6), total number of rounds (30,000), range of

uniform distribution for subjective cost s of beingostracized ([0,1]).

The initial agents are then created, and assigned arandom value of s: These agents are then randomlyassigned to groups, with a fraction rr being Reciproca-tors and a fraction rc begin Cooperators.

A period of play consists of (a) the frequency of eachtype of agent in each group determines the shirkingchoice of each Selfish agent, and from this the averageshirking level for each group; (b) within-group fitnesspayoffs are assigned, using (3); (c) agents reproduce anddie according to these fitnesses; offspring are copies oftheir single parent with probability 1 � e; and arerandom mutants with probability e (a mutant has equalprobability of being either type different from hisparent, and has a random draw from the uniformdistribution of subjective cost of being ostracized; (d)shirkers are ostracized with the appropriate probabil-ities; (e) immigration to groups from the pool and othergroups takes place; a maximum number of immigrantsequal to a fraction m of current group members isdetermined, and set of potential emigrants, consisting ofall pool members, plus a fraction g of group members, isspecified; if this set of candidates for immigration issmaller than the maximum number of immigrants, allare randomly assigned to groups in proportion to theirsize; more likely, this set will be considerably larger thanthe maximum number of immigrants, in which case arandomly chosen subset is specified, and this subset issimilarly distributed among groups; (f) if the totalpopulation has grown, agents are randomly killed torestore the simulation total population size; given thebaseline parameters, this usually involved killing 5–8%of the population per period; (g) groups that are lessthan minimum group size are disbanded, and theirmembers are sent to the pool; the site is repopulated bymigration of members randomly drawn from the largestgroup, until the source group reaches initial group size,and so on for all groups larger than initial group size; ifthe site is still not fully populated, agents are randomlyassigned to the site from the pool.

References

Alexander, R.D., 1987. The Biology of Moral Systems. Aldine, New

York.

Andreoni, J., Miller, J.H., 2002. Giving according to GARP: an

experimental test of the consistency of preferences for altruism.

Econometrica 70 (2), 737–753.

Aviles, L., Abbot, P., Cutter, A.D., 2002. Propulation ecology,

nonlinear dynamics, and social evolution. I. associations among

nonrelatives. Am. Nat. 159 (2), 115–128.

Axelrod, R., 1984. The Evolution of Cooperation. Basic Books, New

York.

Axelrod, R., Hamilton, W.D., 1981. The evolution of cooperation.

Science 211, 1390–1396.


Binford, L., 2001. Constructing Frames of Reference: An Analytical

Method for Archeological Theory Using Hunter-Gatherer and

Environmental Data Sets. University of California Press, Berkeley,

CA.

Bliege Bird, Rebecca, L., Smith, E.A., Bird, D.W., 2001. The hunting

handicap: costly signaling in human foraging strategies. Behav.

Ecol. Sociobiol. 50, 9–19.

Boehm, C., 1984. Blood Revenge: The Enactment and Management of

Conflict in Montenegro and Other Tribal Societies. University of

Pennsylvania Press, Philadelphia, PA.

Boehm, C., 1993. Egalitarian behaviour and reverse dominance

hierarchy. Curr. Anthropol. 34 (3), 227–254.

Boehm, C., 2002. Variance reduction and the evolution of social

control. Department of Anthropology, University of Southern

California.

Boorman, S.A., Levitt, P., 1980. The Genetics of Altruism. Academic

Press, New York.

Bowles, S., Choi, J.-k., Hopfensitz, A., 2003. The co-evolution of

individual behaviors and social institutions. J. Theor. Biol. 223,

135–147.

Boyd, R., Richerson, P.J., 1988. The evolution of reciprocity in sizable

groups. J. Theor. Biol. 132, 337–356.

Boyd, R., Richerson, P.J., 1992. Punishment allows the evolution of

cooperation (or anything else) in sizeable groups. Ethol. Sociobiol.

113, 171–195.

Boyd, R., Gintis, H., Bowles, S., Richerson, P.J., 2003. Evolution of

altruistic punishment. Proc. Natl. Acad. Sci. 100 (6), 3531–3535.

Choi, J.-K., 2003. Is Repetition Sufficient to Support Retaliation?

Santa Fe Institute.

Fehr, E., Gachter, S., 2000. Cooperation and punishment. Am. Econ.

Rev. 90 (4), 980–994.

Fehr, E., Gachter, S., 2002. Altruistic punishment in humans. Nature

415, 137–140.

Fong, C.M., Bowles, S., Gintis, H., 2002. Reciprocity and the welfare

state. In: Mercier-Ythier, J., Kolm, S., Gerard-Varet, L.-A. (Eds.),

Handbook on the Economics of Giving, Reciprocity and Altruism.

Elsevier, Amsterdam.

Friedman, D., Singh, N., 2001. Evolution and negative reciprocity. In:

Aruka, Y. (Ed.), Evolutionary Controversies in Economics.

Springer, New York.

Ghemawat, P., 1995. Competitive advantage and internal organiza-

tion: nucor revised. J. Econ. Management Strategy 3 (4), 685–717.

Gintis, H., 2000. Strong reciprocity and human sociality. J. Theor.

Biol. 206, 169–171.

Gintis, H., Smith, E.A., Bowles, S., 2001. Costly signaling and

cooperation. J. Theor. Biol. 213, 103–119.

Hansen, D.G., 1997. Individual responses to a group incentive. Ind.

Labor Relations Rev. 51 (1), 37–49.

Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H.,

McElreath, R., 2001. Cooperation, reciprocity and punishment in

fifteen small-scale societies. Am. Econ. Rev. 91, 73–78.

Henrich, J., Boyd, R., Bowles, S., Camerer, C., Fehr, E., Gintis, H.,

2003. Foundations of Human Sociality: Ethnography and Experi-

ments in Fifteen Small-scale Societies. Oxford University Press,

Oxford.

Hirshleifer, D., Rasmusen, E., 1989. Cooperation in a repeated

prisoner’s dilemma with ostracism. J. Econ. Behav. Organization

12, 87–106.

Joshi, N.V., 1987. Evolution of cooperation by reciprocation within

structured demes. J. Genet. 66 (1), 69–84.

Kelly, R.L., 1995. The Foraging Spectrum: Diversity in Hunter-

Gatherer Lifeways. The Smithsonian Institution, Washington, DC.

Knauft, B., 1991. Violence and sociality in human evolution. Curr.

Anthropol. 32 (4), 391–428.

Knez, M., Simester, D., 2001. Firm-wide incentives and mutual

monitoring at continental airlines. J. Labor Econ. 19 (4),

743–772.

Kreps, D.M., Milgrom, P., Roberts, J., Wilson, R., 1982. Rational co-

operation in the finitely repeated prisoner’s dilemma. J. Econ.

Theory 27, 245–252.

Leimar, O., Hammerstein, P., 2001. Evolution of cooperation through

indirect reciprocity. Proc. R. Soc. Lond. B 268, 745–753.

Loewenstein, G.F., Thompson, L., Bazerman, M.H., 1989. Social

utility and decision making in interpersonal contexts. J. Personality

Social Psychol. 57 (3), 426–441.

Moore Jr., B., 1978. Injustice: The Social Bases of Obedience and

Revolt. M. E. Sharpe, White Plains.

Nowak, M.A., Sigmund, K., 1998. Evolution of indirect reciprocity by

image scoring. Nature 393, 573–577.

Nowak, M.A., Page, K.M., Sigmund, K., 2000. Fairness versus reason

in the ultimatum game. Science 289, 1773–1775.

Ostrom, E., 1998. A behavioral approach to the rational choice theory

of collective action. Am. Political Sci. Rev. 92 (1), 1–21.

Ostrom, E., Walker, J., Gardner, R., 1992. Covenants with and

without a sword: self-governance is possible. Am. Political Sci.

Rev. 86 (2), 404–417.

Price, G.R., 1970. Selection and covariance. Nature 227, 520–521.

Raffa, K.F., Berryman, A.A., 1987. Interacting selective pressures in

conifer-bark beetle systems: a basis for reciprocal adaptations? Am.

Nat. 129, 234–262.

Robson, A.J., 1990. Efficiency in evolutionary games: Darwin, Nash,

and the secret handshake. J. Theor. Biol. 144, 379–396.

Scott, J.C., 1976. The Moral Economy of the Peasant: Rebellion and

Subsistence in Southeast Asia. Yale University Press, New Haven,

CT.

Sethi, R., Somanathan, E., 1996. The evolution of social norms

in common property resource use. Am. Econ. Rev. 86 (4),

766–788.

Stephens, W., McLinn, C.M., Stevens, J.R., 2002. Discounting and

reciprocity in an iterated prisoner’s dilemma. Science 298,

2216–2218.

Trivers, R.L., 1971. The evolution of reciprocal altruism. Quart. Rev.

Biol. 46, 35–57.

Urs Fischbacher, Engleman, D., 2002. Indirect reciprocity and

strategic reputation building in an experimental helping

game, Institute for Empirical Research in Economics Working

Paper.

Wedekind, C., Milinski, M., 2000. Cooperation through image scoring

in humans. Science 289, 850–852.

Wood, E.J., 2003. Insurgent Collective Action and Civil War in El

Salvador. Cambridge University Press, Cambridge.

Woodburn, J., 1982. Egalitarian societies. Man 17 (3), 431–451.

Yamagishi, T., 1986. The Provision of a Sanctioning System as a

Public Good. J. Personality Social Psychol. 51, 110–116.

Zahavi, A., 1975. Mate Selection—A Selection for Handicap. J. Theor.

Biol. 53, 205–214.

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