The latest data for 1978 suggests that the situa-tion may, in fact, be deteriorating.... we maybe losing the war on air pollution."

3. For examples see House Subcommittee on theEnvironment and the Atmosphere, The Environ-mental Protection Agency's Research Programwith Primary Emphasis on the CommunityHealth and Environmental Surveillance System(CHESS): An Investigative Report (GovernmentPrinting Office, Washington, D.C., 1976), espe-cially chapters 4 to 6.

4. Without trying to be entirely rigorous, we willuse an NSF definition: "Basic research is thattype of research which is directed toward in-crease of knowledge in science. It is researchwhere the primary aim of the investigator is afuller knowledge or understanding of the subjectunder study, rather than a practical applicationthereof." This was given by A. T. Waterman,then director of NSF, in Symposium on BasicResearch, D. Wolfie, Ed. (American Associ-ation for the Advancement of Science, Washing-ton, D.C., 1959), p. 20.

5. For example, the EPA administrator, D. Costle,in a letter dated 12 June 1978 to Senator WilliamProxmire, chairman of the HUD-IndependentAgencies Subcommittee of the Senate Appropri-ations Committee, said concerning environmen-tal research, "I've had to make too many billiondollar decisions over the last year without thecritical information this sort of investment,made five years ago, would have provided."

6. U.S. Congress, Office of Technology Assess-ment, A Review of the U.S. EnvironmentalProtection Agency Environmental ResearchOutlook FY 1976 through 1980 (GovernmentPrinting Office, Washington, D.C., 1976).

7. National Academy of Sciences, Commission onNatural Resources, Analytical Studies for theU.S. Environmental Protection Agency, vol. 3,Research and Development in the Environmen-tal Protection Agency (National Academy ofSciences, Washington, D.C., 1977).

8. National Advisory Committee on Oceans andAtmosphere, A Report to the President and theCongress, fifth annual report (GovernmentPrinting Office, Washington, D.C., 1976).

9. ORD Program Guide (EPA-600/-79-038, Envi-ronmental Protection Agency, Washington,D.C., 1979).

10. Research Outlook, 1980 (EPA-600/9-80-006, En-vironmental Protection Agency, Washington,D.C., 1980). This presents the agency's 5-yearenvironmental research plan in response to stat-utory requirement. The plan is updated and anew report issued annually.

11. Many examples of the environmental problemsEPA faces are reported in Environmental Out-look 1980 (EPA 600/8-80-003, EnvironmentalProtection Agency, Washington, D.C., 1980).

12. At the beginning of the 94th Congress (Janu-

ary 1975) the Committee on Science and Tech-nology received jurisdiction over "environ-mental research" as a result of several changesin the rules of the House of Representatives.The Subcommittee on the Environment and theAtmosphere was formed to handle this juris-diction and for 4 years (two Congresses), withCongressman Brown as chairman, had respon-sibility for ORD. In January 1979, as a re-sult of reorganization within the Committee onScience and Technology, Congressman Brownmoved to the chair of the Subcommittee onScience, Research, and Technology. The Sub-committee on the Environment and Atmospherewas renamed Subcommittee on Natural Re-sources and Environment and given some addi-tional jurisdiction.

13. Environmental Protection Agency Research andDevelopment Issues: 1978, hearings before theHouse Subcommittee on the Environment andthe Atmosphere, 19 July and 13 and 14 Septem-ber 1978 (Government Printing Office, Washing-ton, D.C., 1979).

14. In making funding decisions, the agency uses azero-base budgeting (ZBB) process in whichprograms are approved by a consensus of theadministrator and the six assistant administra-tors. In the ZBB process, the ORD has onlyabout one of six votes, and thus research pro-grams are vulnerable to a great deal of influencefrom the program offices. Because they playsuch a substantial role in defining the program ofresearch ultimately conducted by ORD, theadministrator and all assistant administratorswere asked to testify on what they expect fromthat office.

15. Special Urban Air Pollution Problems: Denverand Houston, hearings before the House Sub-committee on the Environment and the Atmo-sphere, 19 and 21 November 1977 (GovernmentPrinting Office, Washington, D.C., 1978).

16. Long-Term Environmental Research in the En-vironmental Protection Agency, hearings beforethe House Subcommittee on the Environmentand the Atmosphere, 30 June 1977 (GovernmentPrinting Office, Washington, D.C., 1978). Seetfie testimony of R. L. Sansom, especially hissupplemental statement, p. 52.

17. H. Kissinger, The Reporter, 5 March 1959, p.30.

18. For example, the agency has instituted a newsystem of research grants putatively aimed atbringing new work of high quality into its pro-gram. Despite this aim the published solicitationfor grant proposals does not explicitly andunambiguously state that funding decisions willbe based on scientific quality. Instead the fol-lowing appears: "Scientific merit and relevanceof proposals will be significant and balancedfactors in the evaluation procedures since allprojects must be in concert with the Agency's

budget appropriations." In other words, itseems that work on highly relevant mattersmight be funded even if of poor quality. [SeeEPA and the Academic Community (EPA-600/8-80-010, Environmental Protection Agency, Cin-cinnati, Ohio, 1980), p. 2.]

19. National Academy of Sciences, Materials Advi-sory Board, Report ofthe Ad Hoc Committee onPrinciples of Research-Engineering Interaction(National Academy of Sciences, Washington,D.C., 1966), p. 16. - -

20. W. 0. Baker, in House Committee on Scienceand Technology, Seminar on Research, Produc-tivity, and the National Economy, 18 June 1980(Government Printing Office, Washington,D.C., 1980).

21. Testimony of J. N. Pitts, in 1980 Authorizationfor the Office of Research and Development,Environmental Protection Agency, hearings be-fore the House Subcommittee on Science andTechnology, 13 and 15 February 1979 (Govern-ment Printing Office, Washington, D.C., 1979).

22. H. W. Bode, in Basic Research and NationalGoals, a report to the House Committee onScience and Astronautics (National Academy ofSciences, Washington, D.C., 1965), p. 74.

23. At present the program offices guide EPA'sresearch not only through the ZBB process butalso through the mechanism of 13 research com-mittees. These committees translate programoffice needs into "research strategy docu-ments" which guide all EPA research (10).

24. This provision is contained in section 6 of PublicLaw 95-155, the FY 1978 authorization act forORD. For explanation of congressional intentsee Conference Report to Accompany H.R.5101, 95th Congress, Report No. 95-722 (Gov-ernment Printing Office, Washington, D.C.,1977).

25. This provision is contained in section 11 ofPublic Law 95-155. For explanation see thereport cited in (10), and also Report to Accom-pany H.R. 5101, 95th Congress, Report No. 95-157 (Government Printing Office, Washington,D.C., 1977).

26. This was contained in section 4(a) of H.R. 7099,the House version of the FY 1981 authorizationbill. The provision was deleted from the finalversion of the bill at least in part because theagency strenuously (if informally) opposed itand succeeded in having it removed from theSenate-passed version of the bill. For explana-tion of intent, see Report to Accompany H.R.7099, 96th Congress, Report No. 96-959 (Gov-ernment Printing Office, Washington, D.C.,1980).

27. J. Bronowski, The Common Sense of Science(Harvard Univ. Press, Cambridge, Mass., 19:8,p. 143.

28. We thank A. V. Applegate for substantial a%sis'-ance in the preparation of this paper.

The Evolution of CooperationRobert Axelrod and William D. Hamilton

The theory of evolution is based on thestruggle for life and the survival of thefittest. Yet cooperation is common be-tween members of the same species andeven between members of different spe-cies. Before about 1960, accounts of theevolutionary process largely dismissedcooperative phenomena as not requiringspecial attention. This position followedfrom a misreading of theory that as-signed most adaptation to selection at

the level of populations or whole spe-cies. As a result of such misreading,cooperation was always consideredadaptive. Recent reviews of the evolu-tionary process, however, have shownno sound basis for a pervasive group-benefit view of selection; at the level of aspecies or a population, the processes ofselection are weak. The original individ-ualistic emphasis of Darwin's theory ismore valid (1, 2).

0036-8075/81/0327-1390$01.50/0 Copyright 1981 AAAS

To account for the manifest existenceof cooperation and related group behav-ior, such as altruism and restraint incompetition, evolutionary theory has re-cently acquired two kinds of extension.These extensions are, broadly, geneticalkinship theory (3) and reciprocation the-ory (4, 5). Most of the recent activity,both in field work and in further develop-ments of theory, has been on the side ofkinship. Formal approaches have varied,but kinship theory has increasingly takena gene's-eye view of natural selection(6). A gene, in effect, looks beyond itsmortal bearer to interests of the poten-tially immortal set of its replicas existingin other related individuals. If interac-tants are sufficiently closely related, al-

Dr. Axelrod is a professor of political science andresearch scientist at the Institute of Public PolicyStudies, University of Michigan, Ann Arbor 48109.Dr. Hamilton is a professor of evolutionary biologyin the Museum of Zoology and the Division ofBiological Sciences, University of Michigan.

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truism can benefit reproduction of theset, despite losses to the individual altru-ist. In accord with this theory's predic-tions, apart from the human species,almost all clear cases of altruism, andmost observed cooperation, occur incontexts of high relatedness, usually be-tween immediate family members. Theevolution of the suicidal barbed sting ofthe honeybee worker could be taken asparadigm for this line of theory (7).Conspicuous examples of cooperation

(although almost never of ultimate self-sacrifice) also occur where relatedness islow or absent. Mutualistic symbiosesoffer striking examples such as these: thefungus and alga that compose a lichen;the ants and ant-acacias, where the treeshouse and feed the ants which, in turn,protect the trees (8); and the fig waspsand fig tree, where wasps, which areobligate parasites of fig flowers, serve asthe tree's sole means of pollination andseed set (9). Usually the course of coop-eration in such symbioses is smooth, butsometimes the partners show signs ofantagonism, either spontaneous or elicit-ed by particular treatments (10). Al-though kinship may be involved, as willbe discussed later, symbioses mainly il-lustrate the other recent extension ofevolutionary theory, the theory of recip-rocation.Cooperation per se has received com-

paratively little attention from biologistssince the pioneer account of Trivers (5);but an associated issue, concerning re-straint in conflict situations, has beendeveloped theoretically. In this connec-tion, a new concept, that of an evolution-aiily stable strategy, has been formallydeveloped (6, 11). Cooperadion in themore normal sense has remained cloud-ed by certain difficulties, particularlythose concerning initiation of cooper-ation from a previously asocial state (12)and its stable maintenance once estab-lished. A formal theory of cooperation isincreasingly needed. The renewed em-phasis on individualism has focused onthe frequent ease of cheating in recipro-catory arrangements. This makes thestability of even mutualistic symbiosesappear more questionable than under theold view of adaptation for species bene-fit. At the same time other cases thatonce appeared firmly in the domain ofkinship theory now begin to reveal rela-tednesses of interactants that are too lowfor much nepotistic altruism to be ex-pected. This applies both to cooperativebreeding in birds (13) and to cooperativeacts more generally in primate groups(14). Here either the appearances of co-operation are deceptive-they are casesof part-kin altruism and part cheat-27 MARCH 1981

ing-or a larger part of the behavior isattributable to stable reciprocity. Pre-vious accounts that already invoke reci-procity, however, underemphasize thestringency of its conditions (15).Our contribution in this area is new in

three ways.1) In a biological context, our model is

novel in its probabilistic treatment of thepossibility that two individuals may in-teract again. This allows us to shed new

Prisoner's Dilemma game in particular,allow a formalization of the strategicpossibilities inherent in such situations.The Prisoner's Dilemma game is an

elegant embodiment of the problem ofachieving mutual cooperation (16), andtherefore provides the basis for our anal-ysis. To keep the analysis tractable, wefocus on the two-player version of thegame, which describes situations thatinvolve interactions between pairs of

Summary. Cooperation in organisms, whether bacteria or primates, has been adifficulty for evolutionary theory since Darwin. On the assumption that interactionsbetween pairs of individuals occur on a probabilistic basis, a model is developedbased on the concept of an evolutionarily stable strategy in the context of thePrisoner's Dilemma game. Deductions from the model, and the results of a computertournament show how cooperation based on reciprocity can get started in an asocialworld, can thrive while interacting with a wide range of other strategies, and can resistinvasion once fully established. Potential applications include specific aspects ofterritoriality, mating, and disease.

light on certain specific biological pro-cesses such as aging and territoriality.

2) Our analysis of the evolution ofcooperation considers not just the finalstability of a given strategy, but also theinitial viability of a strategy in an envi-ronment dominated by noncooperatingindividuals, as well as the robustness of astrategy in a variegated environmentcomposed of other individuals using avariety of more or less sophisticatedstrategies. This allows a richer under-standing of the full chronology of theevolution of cooperation than has pre-viously been possible.

3) Our applications include behavioralinteraction at the microbial level. Thisleads us to some speculative suggestionsof rationales able to account for theexistence of both chronic and acutephases in many diseases, and for a cer-tain class of chromosomal nondisjunc-tion, exemplified by Down's syndrome.

Strategies in the Prisoner's Dilemma

Many of the benefits sought by livingthings are disproportionally available tocooperating groups. While there are con-siderable differences in what is meant bythe terms "benefits" and "sought," thisstatement, insofar as it is true, lays downa fundamental basis for all social life.The problem is that while an individualcan benefit from mutual cooperation,each one can also do even better byexploiting the cooperative efforts of oth-ers. Over a period of time, the sameindividuals may interact again, allowingfor complex patterns of strategic interac-tions. Game theory in general, and the

individuals. In the Prisoner's Dilemmagame, two individuals can each eithercooperate or defect. The payoff to aplayer is in terms of the effect on itsfitness (survival and fecundity). No mat-ter what the other does, the selfishchoice of defection yields a higher payoffthan cooperation. But if both defect,both do worse than if both had cooperat-ed.

Figure 1 shows the payoff matrix ofthe Prisoner's Dilemma. If the otherplayer cooperates, there is a choice be-tween cooperation which yields R (thereward for mutual cooperation) or defec-tion which yields T (the temptation todefect). By assumption, T > R, so that itpays to defect if the other player cooper-ates. On the other hand, if the otherplayer defects, there is a choice betweencooperation which yields S (the sucker'spayoff) or defection which yields P (thepunishment for mutual defection). Byassumption P > S, so it pays to defect ifthe other player defects. Thus, no matterwhat the other player does, it pays todefect. But, if both defect, both get Prather than the larger value ofR that theyboth could have gotten had both cooper-ated. Hence the dilemma (17).With two individuals destined never to

meet again, the only strategy that can becalled a solution to the game is to defectalways despite the seemingly paradox-ical outcome that both do worse thanthey could have had they cooperated.

Apart from being the solution in gametheory, defection is also the solution inbiological evolution (18). It is the out-come of inevitable evolutionary trendsthrough mutation and natural selection:if the payoffs are in terms of fitness, and

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Player B

Player A

C

Cooperation

DDefection

C

Cooperation

the interactions between pairs of individ-uals are random and not repeated, thenany population with a mixture of herita-ble strategies evolves to a state where allindividuals are defectors. Moreover, no

single differing mutant strategy can dobetter than others when the population isusing this strategy. In these respects thestrategy of defection is stable.

This concept of stability is essential tothe discussion of what follows and it isuseful to state it more formally. A strate-gy is evolutionarily stable if a populationof individuals using that strategy cannotbe invaded by a rare mutant adopting a

different strategy (11). In the case of thePrisoner's Dilemma played only once,

no strategy can invade the strategy ofpure defection. This is because no otherstrategy can do better with the defectingindividuals than the P achieved by thedefecting players who interact with eachother. So in the single-shot Prisoner'sDilemma, to defect always is an evolu-tionarily stable strategy.

In many biological settings, the same

two individuals may meet more thanonce. If an individual can recognize a

previous interactant and remember some

aspects of the prior outcomes, then thestrategic situation becomes an iteratedPrisoner's Dilemma with a much richerset of possibilities. A strategy would takethe form of a decision rule which deter-mined the probability of cooperation ordefection as a function of the history ofthe interaction so far. But if there is a

known number of interactions between a

pair of individuals, to defect always isstill evolutionarily stable and is still theonly strategy which is. The reason is thatdefection on the last interaction wouldbe optimal for both sides, and conse-

quently so would defection on the next-to-last interaction, and so on back to thefirst interaction.Our model is based on the more realis-

tic assumption that the number of inter-actions is not fixed in advance. Instead,there is some probability, w, that afterthe current interaction the same two

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DDefection

Fig. 1. The Prisoner's Dilem-ma game. The payoff to playerA is shown with illustrativenumerical values. The game isdefined by T>R>P>Sand R > (S + 7)/2.

individuals will meet again. Factors thataffect the magnitude of this probability ofmeeting again include the average life-span, relative mobility, and health of theindividuals. For any value of w, thestrategy of unconditional defection(ALL D) is evolutionarily stable; if ev-

eryone is using this strategy, no mutantstrategy can invade the population. Butother strategies may be evolutionarilystable as well. In fact, when w is suffi-ciently great, there is no single beststrategy regardless of the behavior of theothers in the population (19). Just be-cause there is no single best strategy, itdoes not follow that analysis is hopeless.On the contrary, we demonstrate notonly the stability of a given strategy, butalso its robustness and initial viability.

Before turning to the development ofthe theory, let us consider the range ofbiological reality that is encompassed bythe game theoretic approach. To startwith, an organism does not need a brainto employ a strategy. Bacteria, for exam-ple, have a basic capacity to play gamesin that (i) bacteria are highly responsiveto selected aspects of their environment,especially their chemical environment;(ii) this implies that they can responddifferentially to what other organismsaround them are doing; (iii) these condi-tional strategies of behavior can certain-ly be inherited; and (iv) the behavior of abacterium can affect the fitness of otherorganisms around it, just as the behaviorof other organisms can affect the fitnessof a bacterium.While the strategies can easily include

differential responsiveness to recentchanges in the environment or to cumu-

lative averages over time, in other waystheir range of responsiveness is limited.Bacteria cannot "remember" or "inter-pret" a complex past sequence ofchanges, and they probably cannot dis-tinguish alternative origins of adverse or

beneficial changes. Some bacteria, forexample, produce their own antibiotics,bacteriocins; those are harmless to bac-teria of the producing strain, but destruc-

tive to others. A bacterium might easilyhave production of its own bacteriocindependent on the perceived presence oflike hostile products in its environment,but it could not aim the toxin producedtoward an offending initiator. From ex-

isting evidence, so far from an individuallevel, discrimination seems to be by spe-

cies rather even than variety. For exam-

ple, a Rhizobium strain may occur innodules which it causes on the roots ofmany species of leguminous plants, but itmay fix nitrogen for the benefit of theplant in only a few of these species (20).Thus, in many legumes the Rhizobiumseems to be a pure parasite. In the lightof theory to follow, it would be interest-ing to know whether these parasitizedlegumes are perhaps less beneficial tofree living Rhizobium in the surroundingsoil than are those in which the fullsymbiosis is established. But the mainpoint of concern here is that such dis-crimination by a Rhizobium seems not tobe known even at the level of varietieswithin a species.As one moves up the evolutionary

ladder in neural complexity, game-play-ing behavior becomes richer. The intelli-gence of primates, including humans,allows a number of relevant improve-ments: a more complex memory, more

complex processing of information todetermine the next action as a functionof the interaction so far, a better estimateof the probability of future interactionwith the same individual, and a betterability to distinguish between differentindividuals. The discrimination of othersmay be among the most important ofabilities because it allows one to handleinteractions with many individuals with-out having to treat them all the same,thus making possible the rewarding ofcooperation from one individual and thepunishing of defection from another.The model of the iterated Prisoner's

Dilemma is much less restricted than itmay at first appear. Not only can it applyto interactions between two bacteria or

interactions between two primates, but itcan also apply to the interactions be-tween a colony of bacteria and, say, a

primate serving as a host. There is no

assumption of commensurability ofpayoffs between the two sides. Providedthat the payoffs to each side satisfy theinequalities that define the Prisoner'sDilemma (Fig. 1), the results of the anal-ysis will be applicable.The model does assume that the

choices are made simultaneously andwith discrete time intervals. For mostanalytic purposes, this is equivalent to a

continuous interaction over time, with

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the time period of the model correspond-ing to the minimum time between achange in behavior by one side and aresponse by the other. And while themodel treats the choices as simulta-neous, it would make little difference ifthey were treated as sequential (21).Turning to the development of the

theory, the evolution of cooperation canbe conceptualized in terms of three sepa-rate questions:

1) Robustness. What type of strategycan thrive in a variegated environmentcomposed of others using a wide varietyof more or less sophisticated strategies?

2) Stability. Under what conditionscan such a strategy, once fully estab-lished, resist invasion by mutant strate-gies?

3) Initial viability. Even if a strategy isrobust and stable, how can it ever get afoothold in an environment which is pre-dominantly noncooperative?

Robustness

To see what type of strategy can thrivein a variegated environment of more orless sophisticated strategies, one of us(R.A.) conducted a computer tourna-ment for the Prisoner's Dilemma. Thestrategies were submitted by game theo-rists in economics, sociology, politicalscience, and mathematics (22). The rulesimplied the payoff matrix shown in Fig. 1and a game length of 200 moves. The 14entries and a totally random strategywere paired with each other in a roundrobin tournament. Some of the strategieswere quite intricate. An example is onewhich on each move models the behav-ior of the other player as a Markovprocess, and then uses Bayesian infer-ence to select what seems the bestchoice for the long run. However, theresult of the tournament was that thehighest average score was attained bythe simplest of all strategies submitted:TIT FOR TAT. This strategy is simplyone of cooperating on the first move andthen doing whatever the other player didon the preceding move. Thus TIT FORTAT is a strategy of cooperation basedon reciprocity.The results of the first round were then

circulated and entries for a second roundwere solicited. This time there were 62entries from six countries (23). Most ofthe contestants were computer hob-byists, but there were also professors ofevolutionary biology, physics, and com-puter science, as well as the five disci-plines represented in the first round. TITFOR TAT was again submitted by the27 MARCH 1981

winner of the first round, Professor Ana-tol Rapoport of the Institute for Ad-vanced Study (Vienna). It won again. Ananalysis of the 3 million choices whichwere made in the second round identifiedthe impressive robustness of TIT FORTAT as dependent on three features: itwas never the first to defect, it wasprovocable into retaliation by a defectionof the other, and it was forgiving afterjust one act of retaliation (24).The robustness of TIT FOR TAT was

also manifest in an ecological analysis ofa whole series of future tournaments.The ecological approach takes as giventhe varieties which are present and in-vestigates how they do over time wheninteracting with each other. This analysiswas based on what would happen if eachof the strategies in the second roundwere submitted to a hypothetical nextround in proportion to its success in theprevious round. The process was thenrepeated to generate the time path of thedistribution of strategies. The resultsshowed that, as the less successful ruleswere displaced, TIT FOR TAT contin-ued to do well with the rules whichinitially scored near the top. In the longrun, TIT FOR TAT displaced all theother rules and went to fixation (24).This provides further evidence that TITFOR TAT's cooperation based on reci-procity is a robust strategy that canthrive in a variegated environment.

Stability

Once a strategy has gone to fixation,the question of evolutionary stabilitydeals with whether it can resist invasionby a mutant strategy. In fact, we willnow show that once TIT FOR TAT isestablished, it can resist invasion by anypossible mutant strategy provided thatthe individuals who interact have a suffi-ciently large probability, w, of meetingagain. The proof is described in the nexttwo paragraphs.As a first step in the proof we note that

since TIT FOR TAT "remembers" onlyone move back, one C by the otherplayer in any round is sufficient to resetthe situation as it was at the beginning ofthe game. Likewise, one D sets the situa-tion to what it was at the second roundafter a D was played in the first. Sincethere is a fixed chance, w, of the interac-tion not ending at any given move, astrategy cannot be maximal in playingwith TIT FOR TAT unless it does thesame thing both at the first occurrence ofa given state and at each resetting to thatstate. Thus, if a rule is maximal and

begins with C, the second round has thesame state as the first, and thus a maxi-mal rule will continue with C and hencealways cooperate with TIT FOR TAT.But such a rule will not do better thanTIT FOR TAT does with another TITFOR TAT, and hence it cannot invade.If, on the other hand, a rule begins withD, then this first D induces a switch inthe state of TIT FOR TAT and there aretwo possibilities for continuation thatcould be maximal. If D follows the firstD, then this being maximal at the startimplies that it is everywhere maximal tofollow D with D, making the strategyequivalent to ALL D. If C follows theinitial D, the game is then reset as for thefirst move; so it must be maximal torepeat the sequence of DC indefinitely.These points show that the task ofsearching a seemingly infinite array ofrules of behavior for one potentiallycapable of invading TIT FOR TAT isreally easier than it seemed: if neitherALL D nor alternation of D and C caninvade TIT FOR TAT, then no strategycan.To see when these strategies can in-

vade, we note that the probability thatthe nth interaction actually occurs isw" . Therefore, the expression for thetotal payoff is easily found by applyingthe weights 1, w, w2 . .. to the payoffsequence and summing the resultant se-ries. When TIT FOR TAT plays anotherTIT FOR TAT, it gets a payoff ofR eachmove for a total of R + wR + w2R... , which is R/(1 - w). ALL D play-ing with TIT FOR TAT gets T on the firstmove and P thereafter, so it cannot in-vade TIT FOR TAT if

R/(l - w) > T + wPI(1 - w)

Similarly when alternation of D and Cplays TIT FOR TAT, it gets a payoff of

T = wS + w2T + s3S ...- (T + wS)/(l - w2)

Alternation of D and C thus cannot in-vade TIT FOR TAT if

R/(1 - w) : (T + wS)/(l - w2)

Hence, with reference to the magnitudeof w, we find that neither of these twostrategies (and hence no strategy at all)can invade TIT FOR TAT if and only- ifboth

w -(T - R)/(T - P) andw . (T - R)/(R - S) (1)

This demonstrates that TIT FOR TAT isevolutionarily stable if and only if theinteractions between the individualshave a sufficiently large probability ofcontinuing (19).

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Initial Viability

TIT FOR TAT is not the only strategythat can be evolutionarily stable. In fact,ALL D is evolutionarily stable no matterwhat is the probability of interactioncontinuing. This raises the problem ofhow an evolutionary trend to coopera-

tive behavior could ever have started inthe first place.

Genetic kinship theory suggests a

plausible escape from the equilibrium ofALL D. Close relatedness of interac-tants permits true altruism-sacrifice offitness by one individual for the benefitof another. True altruism can evolvewhen the conditions of cost, benefit, andrelatedness yield net gains for the altru-ism-causing genes that are resident in therelated individuals (25). Not defecting ina single-move Prisoner's Dilemma is al-truism of a kind (the individual is forego-ing proceeds that might have been taken)and so can evolve if the two interactantsare sufficiently related (18). In effect,recalculation of the payoff matrix in sucha way that an individual has a part inter-est in the partner's gain (that is, reckon-ing payoffs in terms of inclusive fitness)can often eliminate the inequalitiesT > R and P > S, in which case cooper-

ation becomes unconditionally favored(18, 26). Thus it is possible to imaginethat the benefits of cooperation in Pris-oner's Dilemma-like situations can beginto be harvested by groups of closelyrelated individuals. Obviously, as re-

gards pairs, a parent and its offspring or a

pair of siblings would be especiallypromising, and in fact many examples ofcooperation or restraint of selfishness insuch pairs are known.Once the genes for cooperation exist,

selection will promote strategies thatbase cooperative behavior on cues in theenvironment (4). Such factors as promis-cuous fatherhood (27) and events at ill-defined group margins will always leadto uncertain relatedness among potentialinteractants. The recognition of any im-proved correlates of relatedness and use

of these cues to determine cooperativebehavior will always permit advance ininclusive fitness (4). When a cooperativechoice has been made, one cue to relat-edness is simply the fact of reciprocationof the cooperation. Thus modifiers formore selfish behavior after a negativeresponse from the other are advanta-geous whenever the degree of related-ness is low or in doubt. As such, condi-tionality is acquired, and cooperationcan spread into circumstances of lessand less relatedness. Finally, when theprobability of two individuals meetingeach other again is sufficiently high,

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cooperation based on reciprocity canthrive and be evolutionarily stable in apopulation with no relatedness at all.A case of cooperation that fits this

scenario, at least on first evidence, hasbeen discovered in the spawning rela-tionships in a sea bass (28). The fish,which are hermaphroditic, form pairsand roughly may be said to take turns atbeing the high investment partner (layingeggs) and low investment partner (pro-viding sperm to fertilize eggs). Up to tenspawnings occur in a day and only a feweggs are provided each time. Pairs tendto break up if sex roles are not dividedevenly. The system appears to allow theevolution of much economy in the size oftestes, but Fischer (28) has suggestedthat the testis condition may haveevolved when the species was moresparse and inclined to inbreed. Inbreed-ing would imply relatedness in the pairsand this initially may have transferredthe system to attractance of tit-for-tatcooperation-that is, to cooperation un-needful of relatedness.Another mechanism that can get coop-

eration started when virtually everyoneis using ALL D is clustering. Supposethat a small group of individuals is usinga strategy such as TIT FOR TAT andthat a certain proportion, p, of the inter-actions of members of this cluster arewith other members of the cluster. Thenthe average score attained by the mem-bers of the cluster in playing the TITFOR TAT strategy is

p[RM(1 - w)] +(1 - p)[S + wP/(l - w)]

If the members of the cluster provide anegligible proportion of the interactionsfor the other individuals, then the scoreattained by those using ALL D is still PI(1 - w). When p and w are largeenough, a cluster of TIT FOR TAT indi-viduals can then become initially viablein an environment composed over-whelmingly of ALL D (19).

Clustering is often associated with kin-ship, and the two mechanisms can rein-force each other in promoting the initialviability of reciprocal cooperation. How-ever, it is possible for clustering to beeffective without kinship (3).We have seen that TIT FOR TAT can

intrude in a cluster on a population ofALL D, even though ALL D is evolu-tionarily stable. This is possible becausea cluster of TIT FOR TAT's gives eachmember a nontrivial probability of meet-ing another individual who will recipro-cate the cooperation. While this suggestsa mechanism for the initiation of cooper-ation, it also raises the question aboutwhether the reverse could happen once a

strategy like TIT FOR TAT became es-tablished itself. Actually, there is an in-teresting asymmetry here. Let us definea nice strategy as one, such as TIT FORTAT, which will never be the first todefect. Obviously, when two nice strate-gies interact, they both receive R eachmove, which is the highest average scorean individual can get when interactingwith another individual using the samestrategy. Therefore, if a strategy is niceand is evolutionarily stable, it cannot beintruded upon by a cluster. This is be-cause the score achieved by the strategythat comes in a cluster is a weightedaverage of how it does with others of itskind and with the predominant strategy.Each of these components is less than orequal to the score achieved by the pre-dominant, nice, evolutionarily stablestrategy, and therefore the strategy ar-riving in a cluster cannot intrude on thenice, evolutionarily stable strategy (19).This means that when w is large enoughto make TIT FOR TAT an evolutionarilystable strategy it can resist intrusion byany cluster of any other strategy. Thegear wheels of social evolution have aratchet.The chronological story that emerges

from this analysis is the following. ALLD is the primeval state and is evolution-arily stable. This means that it can resistthe invasion of any strategy that hasvirtually all of its interactions with ALLD. But cooperation based on reciprocitycan gain a foothold through two differentmechanisms. First, there can be kinshipbetween mutant strategies, giving thegenes of the mutants some stake in eachother's success, thereby altering theeffective payoff matrix of the interactionwhen viewed from the perspective of thegene rather than the individual. A secondmechanism to overcome total defectionis for the mutant strategies to arrive in acluster so that they provide a nontrivialproportion of the interactions each has,even if they are so few as to provide anegligible proportion of the interactionswhich the ALL D individuals have. Thenthe tournament approach demonstratesthat once a variety of strategies is pres-ent, TIT FOR TAT is an extremely ro-bust one. It does well in a wide range ofcircumstances and gradually displacesall other strategies in a simulation of agreat variety of more or less sophisticat-ed decision rules. And if the probabilitythat interaction between two individualswill continue is great enough, then TITFOR TAT is itself evolutionarily stable.Moreover, its stability is especially se-cure because it can resist the intrusion ofwhole clusters of mutant strategies. Thuscooperation based on reciprocity can get

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started in a predominantly noncoopera-tive world, can thrive in a variegatedenvironment, and can defend itself oncefully established.

Applications

A variety of specific biological appli-cations of our approach follows from twoof the requirements for the evolution ofcooperation. The basic idea is that anindividual must not be able to get awaywith defecting without the other individ-uals being able to retaliate effectively(29). The response requires that the de-fecting individual not be lost in an anony-mous sea of others. Higher organismsavoid this problem by their well-devel-oped ability to recognize many differentindividuals of their species, but lowerorganisms must rely on mechanisms thatdrastically limit the number of differentindividuals or colonies with which theycan interact effectively. The other impor-tant requirement to make retaliationeffective is that the probability, w, of thesame two individuals' meeting againmust be sufficiently high.When an organism is not able to recog-

nize the individual with which it had aprior interaction, a substitute mechanismis to make sure that all of one's interac-tions are with the same interactant. Thiscan be done by maintaining continuouscontact with the other. This method isapplied in most interspecies mutualism,whether a hermit crab and his sea-anem-one partner, a cicada and the variedmicroorganismic colonies housed in itsbody, or a tree and its mycorrhizal fungi.The ability of such partners to respond

specifically to defection is not known butseems posible. A host insect that carriessymbionts often carries several kinds(for example, yeasts and bacteria). Dif-ferences in the roles of these are almostwholly obscure (30). Perhaps roles areactually the same, and being host tomore than one increases the security ofretaliation against a particular exploita-tive colony. Where host and colony arenot permanently paired, a method forimmediate drastic retaliation is some-times apparent instead. This is so withfig wasps. By nature of their remarkablerole in pollination, female fig waspsserve the fig tree as a motile aerial malegamete. Through the extreme protogynyand simultaneity in flowering, fig waspscannot remain with a single tree. It turnsout in many cases that if a fig waspentering a young fig does not pollinateenough flowers for seeds and insteadlays eggs in almost all, the tree cutsoff the developing fig at an early stage.27 MARCH 1981

All progeny of the wasp then perish.Another mechanism to avoid the need

for recognition is to guarantee theuniqueness of the pairing of interactantsby employing a fixed place of meeting.Consider, for example, cleaner mutual-isms in which a small fish or a crustaceanremoves and eats ectoparasites from thebody (or even from the inside of themouth) of a larger fish which is its poten-tial predator. These aquatic cleaner mu-tualisms occur in coastal and reef situa-tions where animals live in fixed homeranges or territories (4, 5). They seem tobe unknown in the free-mixing circum-stances of the open sea.Other mutualisms are also characteris-

tic of situations where continued associ-ation is likely, and normally they involvequasi-permanent pairing of individuals orof endogamous or asexual stocks, or ofindividuals with such stocks (7, 31). Con-versely, conditions of free-mixing andtransitory pairing conditions where rec-ognition is impossible are much morelikely to result in exploitation-parasit-ism, disease, and the like. Thus, whereasant colonies participate in many sym-bioses and are sometimes largely depen-dent on them, honeybee colonies, whichare much less permanent in place ofabode, have no known symbionts butmany parasites (32). The small fresh-water animal Chlorohydra viridissimahas a permanent stable association withgreen algae that are always naturallyfound in its tissues and are very difficultto remove. In this species the alga istransmitted to new generations by wayof the egg. Hydra vulgaris and H. atten-uata also associate with algae but do nothave egg transmission. In these species itis said that "infection is preceded byenfeeblement of the animals and is ac-companied by pathological symptoms in-dicating a definite parasitism by theplant" (33). Again, it is seen that imper-manence of association tends to destabi-lize symbiosis.

In species with a limited ability todiscriminate between other members ofthe same species, reciprocal cooperationcan be stable with the aid of a mecha-nism that reduces the amount of dis-crimination necessary. Philopatry in gen-eral and territoriality in particular canserve this purpose. The phrase stableterritories means that there are two quitedifferent kinds of interaction: those inneighboring territories where the prob-ability of interaction is high, and strang-ers whose probability of future interac-tion is low. In the case of male territorialbirds, songs are used to allow neighborsto recognize each other. Consistent withour theory, such male territorial birds

show much more aggressive reactionswhen the song of an unfamiliar malerather than a neighbor is reproducednearby (34).

Reciprocal cooperation can be stablewith a larger range of individuals if dis-crimination can cover a wide variety ofothers with less reliance on supplemen-tary cues such as location. In humansthis ability is well developed, and islargely based on the recognition offaces.The extent to which this function hasbecome specialized is revealed by abrain disorder called prosopagnosia. Anormal person can name someone fromfacial features alone, even if the featureshave changed substantially over theyears. People with prosopagnosia are notable to make this association, but havefew other neurological symptoms otherthan a loss of some part of the visualfield. The lesions responsible for proso-pagnosia occur in an identifiable part ofthe brain: the underside of both occipitallobes, extending forward to the innersurface of the temporal lobes. This local-ization of cause, and specificity of effect,indicates that the recognition of individ-ual faces has been an important enoughtask for a significant portion of thebrain's resources to be devoted to it (35).

Just as the ability to recognize theother interactant is invaluable in extend-ing the range of stable cooperation, theability to monitor cues for the likelihoodof continued interaction is helpful as anindication of when reciprocal cooper-ation is or is not stable. In particular,when the value of w falls below thethreshold for stability given in condition(1), it will no longer pay to reciprocatethe other's cooperation. Illness in onepartner leading to reduced viabilitywould be one detectable sign of decliningw. Both animals in a partnership wouldthen be expected to become less cooper-ative. Aging of a partner would be verylike disease in this respect, resulting inan incentive to defect so as to take a one-time gain when the probability of futureinteraction becomes small enough.These mechanisms could operate even

at the microbial level. Any symbiont thatstill has a transmission "horizontally"(that is, infective) as well as vertically(that is, transovarial, or more rarelythrough sperm, or both) would be ex-pected to shift from mutualism to para-sitism when the probability of continuedinteraction with the host lessened. In themore parasitic phase it could exploit thehost more severely by producing moreinfective propagules. This phase wouldbe expected when the host is severelyinjured, contracted some other whollyparasitic infection that threatened death,

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or when it manifested signs of age. Infact, bacteria that are normal and seem-ingly harmless or even beneficial in thegut can be found contributing to sepsis inthe body when the gut is perforated(implying a severe wound) (36). Andnormal inhabitants of the body surface(like Candida albicans) can become in-vasive and dangerous in either sick orelderly persons.

It is possible also that this argumenthas some bearing on the etiology ofcancer, insofar as it turns out to be dueto viruses potentially latent in thegenome (37). Cancers do tend to havetheir onset at ages when the chances ofvertical transmission are rapidly declin-ing (38). One oncogenic virus, that ofBurkitt's lymphoma, does not have ver-tical transmission but may have alterna-tives of slow or fast production of infec-tious propagules. The slow form appearsas a chronic mononucleosis, the fast asan acute mononucleosis or as a lym-phoma (39). The point of interest is that,as some evidence suggests, lymphomacan be triggered by the host's contract-ing malaria. The lymphoma grows ex-tremely fast and so can probably com-pete with malaria for transmission (pos-sibly by mosquitoes) before death re-sults. Considering other cases ofsimultaneous infection by two or morespecies of pathogen, or by two strains ofthe same one, our theory may have rel-evance more generally to whether a dis-ease will follow a slow, joint-optimalexploitation course ("chronic" for thehost) or a rapid severe exploitation("acute" for the host). With single infec-tion the slow course would be expected.With double infection, crash exploitationmight, as dictated by implied payofffunctions, begin immediately, or haveonset later at an appropriate stage ofsenescence (40).Our model (with symmetry of the two

parties) could also be tentatively appliedto the increase with maternal age ofchromosomal nondisjunction duringovum formation (oogenesis) (41). Thiseffect leads to various conditions of se-verely handicapped offspring, Down'ssyndrome (caused by an extra copy ofchromosome 21) being the most familiarexample. It depends almost entirely onfailure of the normal separation of thepaired chromosomes in the mother, andthis suggests the possible connectionwith our story. Cell divisions of oogene-sis, but not usually of spermatogenesis,are characteristically unsymmetrical,with rejection (as a so-called polar body)of chromosomes that go to the unluckypole of the cell. It seems possible that,while homologous chromosomes gener-

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ally stand to gain by steadily cooperatingin a diploid organism, the situation inoogenesis is a Prisoner's Dilemma: achromosome which can be "first to de-fect" can get itself into the egg nucleusrather than the polar body. We mayhypothesize that such an action triggerssimilar attempts by the homolog in sub-sequent meioses, and when both mem-bers of a homologous pair try it at once,an extra chromosome in the offspringcould be the occasional result. The fit-ness of the bearers of extra chromo-somes is generally extremely low, but achromosome which lets itself be sent tothe polar body makes a fitness contribu-tion of zero. Thus P > S holds. For themodel to work, an incident of "defec-tion" in one developing egg would haveto be perceptible by others still waiting.That this would occur is pure specula-tion, as is the feasibility of self-promot-ing behavior by chromosomes during agametic cell division. But the effects donot seem inconceivable: a bacterium,after all, with its single chromosome, cando complex conditional things. Givensuch effects, our model would explainthe much greater incidence of abnormalchromosome increase in eggs (and notsperm) with parental age.

Conclusion

Darwin's emphasis on individual ad-vantage has been formalized in terms ofgame theory. This establishes conditionsunder which cooperation based on reci-procity can evolve.

References and Notes1. G. C. Williams, Adaptations and Natural Selec-

tion (Princeton Univ. Press, Princeton, 1966);W. D. Hamilton, in Bisocial Anthropology, R.Fox, Ed. (Malaby, London, 1975), p. 133.

2. For the best recent case for effective selection atgroup levels and for altruism based on geneticcorrection of non-kin interactants see D. S.Wilson, Natural Selection of Populations andCommunities (Benjamin/Cummings, MenloPark, Calif., 1979).

3. W. D. Hamilton, J. Theoret. Biol. 7, 1 (1964).4. R. Trivers, Q. Rev. Biol. 46, 35 (1971).5. For additions to the theory of biological cooper-

ation see I. D. Chase [Am. Nat. 115, 827 (1980)],R. M. Fagen [ibid., p. 858 (1980)], and S. A.Boorman and P. R. Levitt [The Genetics ofAltruism (Academic Press, New York, 1980)].

6. R. Dawkins, The Sefish Gene (Oxford Univ.Press, Oxford, 1976).

7. W. D. Hamilton, Annu. Rev. Ecol. Syst. 3, 193(1972).

8. D. H. Janzen, Evolution 20, 249 (1966).9. J. T. Wiebes, Gard. Bull. (Singapore) 29, 207

(1976); D. H. Janzen, Annu. Rev. Ecol. Syst. 10,31 (1979).

10. M. Caullery, Parasitism and Symbiosis (Sidg-wick and Jackson, London, 1952). This givesexamples of antagonism in orchid-fungus andlichen symbioses. For the example of wasp-antsymbiosis, see (7).

11. J. Maynard Smith and G. R. Price, Nature(Londqn) 246, 15 (1973); J. Maynard Smith andG. A. Parker, Anim. Behav. 24, 159 (1976); G.A. Parker, Nature (London) 274, 849 (1978).

12. J. Elster, Ulysses and the Sirens (CambridgeUniv. Press, London, 1979).

13. S. T. Emlen, in Behavioral Ecology: An Evolu-

tionary Approach, J. Krebs and N. Davies, Eds.(Blackwell, Oxford, 1978), p. 245; P. B. Stacey,Behav. Ecol. Sociobiol. 6, 53 (1979).

14. A. H. Harcourt, Z. Tierpsychol. 48, 401 (1978);C. Packer, Anim. Behav. 27, 1 (1979); R. W.Wrangham, Soc. Sci. Info. 18, 335 (1979).

15. J. D. Ligon and S. H. Ligon, Nature (London)276, 496 (1978).

16. A. Rapoport and A. M. Chammah, Prisoner'sDilemma (Univ. of Michigan Press, Ann Arbor,1965). There are many other patterns of interac-tion which allow gains for cooperation. See forexample the model of intraspecific combat in J.Maynard Smith and G. R. Price, in (11).

17. The condition that R > (S + 7)/2 is also part ofthe definition to rule out the possibility thatalternating exploitation could be better for boththan mutual cooperation.

18. W. D. Hamilton, in Man and Beast: Compara-tive Social Behavior (Smithsonian Press, Wash-ington, 1971), p. 57. R. M. Fagen [in (5)] showssome conditions for single encounters wheredefection is not the solution.

19. For a formal proof, see R. Axelrod, Am. Politi-cal Sci. Rev., in press. For related results on thepotential stability of cooperative behavior see R.D. Luce and H. Raiffa, Games and Decisions(Wiley, New York, 1957), p. 102; M. Taylor,Anarchy and Cooperation (Wiley, New York,1976); M. Kurz, in Economic Progress, PrivateValues and Public Policy, B. Balassa and R.Nelson, Eds. (North-Holland, Amsterdam,1977), p. 177.

20. M. Alexander, Microbial Ecology (Wiley, NewYork, 1971).

21. In either case, cooperation on a tit-for-tat basisis evolutionarily stable if and only if w is suffi-ciently high. In the case of sequential moves,suppose there is a fixed chance, p, that a giveninteractant of the pair will be the next one toneed help. The critical value of w can be shownto be the minimum of the two side's value of A/p(A + B) where A is the cost of giving assist-ance, and B is the benefit of assistance whenreceived. See also P. R. Thompson, Soc. Sci.Info. 19, 341 (1980).

22. R. Axelrod, J. Conflict Resolution 24, 3 (1980).23. In the second round, the length of the games was

uncertain, with an expected probability of 200moves. This was achieved by setting the prob-ability that a given move would not be the last atw = .99654. As in the first round, each pair wasmatched in five games (24).

24. R. Axelrod, J. Conflict Resolution 24, 379(1980).

25. R. A. Fisher, The Genetical Theory of NaturalSelection (Oxford Univ. Press, Oxford, 1930); J.B. S. Haldane, Nature (London) New Biol. 18,34 (1955); W. D. Hamilton, Am. Nat. 97, 354(1963).

26. M. J. Wade and F. Breden, Behav. Ecol. Socio-biol, in press.

27. R. D. Alexander, Annu. Rev. Ecol. Syst. 5, 325(1974).

28. E. Fischer, Anim. Behav. 28, 620 (1980); E. G.Leigh, Jr., Proc. Natl. Acad. Sci. U.S.A. 74,4542 (1977).

29. For economic theory on this point see G. Aker-lof, Q. J. Econ. 84, 488 (1970); M. R. Darby andE. Karni, J. Law Econ. 16, 67 (1973); 0. E.Williamson, Markets and Hierarchies (FreePress, New York, 1975).

30. P. Buchner, Endosymbiosis of Animals withPlant Microorganisms (Interscience, NewYork, 1965).

31. W. D. Hamilton, in Diversity of Insect Faunas,L. A. Mound and N. Waloff, Eds. (Blackwell,Oxford, 1978).

32. E. 0. Wilson, The Insect Societies (Bellknap,Cambridge, Mass., 1971); M. Treisman, Anim.Behav. 28, 311 (1980).

33. C. M. Yonge [Nature (London) 134, 12 (1979)]gives other examples of invertebrates with uni-cellular algae.

34. E. 0. Wilson, Sociobiology (Harvard Univ.Press, Cambridge, Mass., 1975), p. 273.

35. N. Geschwind, Sci. Am. 241, (No. 3), 180(1979).

36. D. C. Savage, in Microbial Ecology of the Gut,R. T. J. Clarke and T. Bauchop, Eds. (AcademicPress, New York, 1977), p. 300.

37. J. T. Manning, J. Theoret. Biol. 55, 397 (1975);M. J. Orlove, ibid. 65, 605 (1977).

38. W. D. Hamilton, ibid. 12, 12 (1966).39. W. Henle, G. Henle, E. T. Lenette, Sci. Am.

241 (No. 1), 48 (1979).40. See also I. Eshel, Theoret. Pop. Biol. 11, 410

(1977) for a related possible implication of multi-clonal infection.

41. C. Stern, Principles of Human Genetics (Free-man, San Francisco, 1973).

42. For helpful suggestions we thank Robert Boyd,Michael Cohen, and David Sloan Wilson.

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The evolution of cooperationR Axelrod and WD Hamilton

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