The Evolution of Cooperation Author(s): Robert Axelrod and William D. Hamilton Source: Science, New Series, Vol. 211, No. 4489 (Mar. 27, 1981), pp. 1390-1396 Published by: American Association for the Advancement of Science Stable URL: http://www.jstor.org/stable/1685895 Accessed: 11/02/2010 09:56

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http://www.jstor.org The latest data for 1978 suggests that the situa- ary 1975)the Committeeon Science and Tech- budget appropriations."In other words, it tion may, in fact, be deteriorating..... we may nology received jurisdiction over "environ- seems that work on highly relevant matters be losing the war on air pollution." mentalresearch" as a result of several changes might be funded even if of poor quality. [See 3. For examples see House Subcommitteeon the in the rules of the House of Representatives. EPAand the AcademicCommunity (EPA-600/8- Environmentand the Atmosphere,The Environ- The Subcommitteeon the Environmentand the 80-010,Environmental Protection Agency, Cin- mentalProtection Agency's Research Program Atmospherewas formed to handle this juris- cinnati,Ohio, 1980),p. 2.] with Primary Emphasis on the Community diction and for 4 years (two Congresses),with 19. NationalAcademy of Sciences, MaterialsAdvi- Health and EnvironmentalSurveillance System CongressmanBrown as chairman,had respon- sory Board,Report of theAd Hoc Committeeon (CHESS):An InvestigativeReport (Government sibility for ORD. In January 1979, as a re- Principlesof Research-EngineeringInteraction PrintingOffice, Washington,D.C., 1976),espe- sult of reorganizationwithin the Committeeon (National Academy of Sciences, Washington, cially chapters4 to 6. Science and Technology, CongressmanBrown D.C., 1966),p. 16. 4. Withouttrying to be entirely rigorous, we will moved to the chair of the Subcommitteeon 20. W. O. Baker, in House Committeeon Science use an NSF definition:"Basic researchis that Science, Research, and Technology. The Sub- andTechnology, Seminar on Research,Produc- type of research which is directed toward in- committeeon the Environmentand Atmosphere tivity,and the National Economy, 18 June 1980 crease of knowledge in science. It is research was renamed Subcommittee on Natural Re- (Government Printing Office, Washington, where the primaryaim of the investigatoris a sources and Environmentand given some addi- D.C., 1980). fullerknowledge or understandingof the subject tionaljurisdiction. 21. Testimonyof J. N. Pitts, in 1980Authorization under study, ratherthan a practicalapplication 13. EnvironmentalProtection Agency Research and for the Office of Research and Development, thereof." This was given by A. T. Waterman, DevelopmentIssues: 1978, hearingsbefore the EnvironmentalProtection Agency, hearingsbe- then directorof NSF, in Symposiumon Basic House Subcommitteeon the Environmentand fore the House Subcommitteeon Science and Research, D. Wolfle, Ed. (American Associ- the Atmosphere,19 July and 13 and 14 Septem- Technology, 13 and 15 February1979 (Govern- ationfor the Advancementof Science, Washing- ber 1978(Government Printing Office, Washing- ment PrintingOffice, Washington, D.C., 1979). ton, D.C., 1959),p. 20. ton, D.C., 1979). 22. H. W. Bode, in Basic Research and National 5. For example,the EPA administrator,D. Costle, 14. In makingfunding decisions, the agency uses a Goals, a report to the House Committee on in a letter dated 12 June 1978to SenatorWilliam zero-base budgeting (ZBB) process in which Science and Astronautics(National Academy of Proxmire, chairmanof the HUD-Independent programsare approvedby a consensus of the Sciences, Washington,D.C., 1965),p. 74. AgenciesSubcommittee of the SenateAppropri- administratorand the six assistant administra- 23. At present the program offices guide EPA's ations Committee,said concerningenvironmen- tors. In the ZBB process, the ORD has only researchnot only throughthe ZBB process but tal research,"I've had to maketoo manybillion about one of six votes, and thus researchpro- also throughthe mechanismof 13 researchcom- dollar decisions over the last year without the gramsare vulnerableto a greatdeal of influence mittees. These committees translate program critical information this sort of investment, from the programoffices. Because they play office needs into "research strategy docu- made five years ago, would have provided." such a substantialrole in definingthe programof ments" which guide all EPA research(10). 6. U.S. Congress, Office of Technology Assess- research ultimately conducted by ORD, the 24. Thisprovision is containedin section6 of Public ment, A Review of the U.S. Environmental administratorand all assistant administrators Law 95-155, the FY 1978 authorizationact for Protection Agency Environmental Research were asked to testify on what they expect from ORD. For explanationof congressionalintent Outlook FY 1976 through 1980 (Government that office. see Conference Report to Accompany H.R. PrintingOffice, Washington,D.C., 1976). 15. Special UrbanAir Pollution Problems:Denver 5101, 95th Congress, Report No. 95-722 (Gov- 7. NationalAcademy of Sciences, Commissionon and Houston, hearingsbefore the House Sub- ernment Printing Office, Washington, D.C., Natural Resources, Analytical Studies for the committeeon the Environmentand the Atmo- 1977). U.S. EnvironmentalProtection Agency, vol. 3, sphere, 19 and 21 November 1977(Government 25. This provision is contained in section 11 of Research and Developmentin the Environmen- PrintingOffice, Washington, D.C., 1978). Public Law .95-155. For explanation see the tal Protection Agency (National Academy of 16. Long-TermEnvironmental Research in the En- reportcited in (10), and also Report to Accom- Sciences, Washington,D.C., 1977). vironmentalProtection Agency, hearingsbefore pany H.R. 5101, 95th Congress,Report No. 95- 8. National Advisory Committee on Oceans and the House Subcommitteeon the Environment 157 (GovernmentPrinting Office, Washington, Atmosphere,A Report to the Presidentand the andthe Atmosphere,30 June 1977(Government D.C., 1977). Congress, fifth annual report (Government PrintingOffice, Washington,D.C., 1978). See 26. This was containedin section 4(a) of H.R. 7099, PrintingOffice, Washington,D.C., 1976). the testimony of R. L. Sansom, especially his the House version of the FY 1981authorization 9. ORD ProgramGuide (EPA-600/9-79-038,Envi- supplementalstatement, p. 52. bill. The provision was deleted from the final ronmental Protection Agency, Washington, 17. H. Kissinger, The Reporter, 5 March 1959, p. version of the bill at least in part because the D.C., 1979). 30. agency strenuously (if informally)opposed it 10. ResearchOutlook, 1980 (EPA-600/9-80-006, En- 18. For example, the agency has instituteda new and succeeded in having it removed from the vironmentalProtection Agency, Washington, system of research grants putatively aimed at Senate-passedversion of the bill. For explana- D.C., 1980).This presents the agency's 5-year bringingnew work of high quality into its pro- tion of intent, see Report to AccompanyH.R. environmentalresearch plan in responseto stat- gram.Despite this aim the publishedsolicitation 7099, 96th Congress, Report No. 96-959 (Gov- utory requirement.The plan is updated and a for grant proposals does not explicitly and ernment Printing Office, Washington, D.C., new reportissued annually. unambiguouslystate that fundingdecisions will 1980). 11. Many examples of the environmentalproblems be based on scientific quality. Instead the fol- 27. J. Bronowski, The CommonSense of Science EPA faces are reportedin EnvironmentalOut- lowing appears:"Scientific merit and relevance (HarvardUniv. Press, Cambridge,Mass., 1978), look 1980 (EPA 600/8-80-003,Environmental of proposals will be significantand balanced p. 143. ProtectionAgency, Washington,D.C., 1980). factors in the evaluation procedures since all 28. We thankA. V. Applegatefor substantialassist- 12. At the beginningof the 94th Congress (Janu- projects must be in concert with the Agency's ance in the preparationof this paper.

To account for the manifest existence of cooperationand related group behav- ior, such as altruism and restraint in competition,evolutionary theory has re- cently acquiredtwo kinds of extension. The Evolution of These extensions are, broadly, genetical Cooperation kinshiptheory (3) and reciprocationthe- ory (4, 5). Most of the recent activity, Robert Axelrod and D. Hamilton William both in field work and in furtherdevelop- ments of theory, has been on the side of kinship.Formal approaches have varied, but kinshiptheory has increasinglytaken The theory of evolution is based on the the level of populations or whole spe- a gene's-eye view of natural selection struggle for life and the survival of the cies. As a result of such misreading, (6). A gene, in effect, looks beyond its fittest. Yet cooperation is common be- cooperation was always considered mortal bearer to interests of the poten- tween membersof the same species and adaptive. Recent reviews of the evolu- tially immortalset of its replicas existing even between membersof differentspe- tionary process, however, have shown in other related individuals. If interac- cies. Before about 1960, accounts of the no sound basis for a pervasive group- tants are sufficientlyclosely related, al- evolutionary process largely dismissed benefitview of selection; at the level of a cooperativephenomena as not requiring species or a the of Dr. Axelrodis a professorof politicalscience and population, processes research scientist at the Institute of Public Policy special attention. This position followed selection are weak. The originalindivid- Studies, Universityof Michigan,Ann Arbor48109. from a of that as- ualistic emphasis of Darwin's is Dr. Hamiltonis a professorof evolutionarybiology misreading theory theory in the Museum of Zoology and the Division of signed most adaptation to selection at more valid (1, 2). BiologicalSciences, Universityof Michigan. 1390 0036-8075/81/0327-1390$01.50/0Copyright ? 1981AAAS SCIENCE,VOL. 211, 27 MARCH 1981 truism can benefit reproduction of the ing-or a larger part of the behavior is Prisoner's Dilemma game in particular, set, despite losses to the individualaltru- attributable to stable reciprocity. Pre- allow a formalization of the strategic ist. In accord with this theory's predic- vious accounts that already invoke reci- possibilities inherent in such situations. tions, apart from the human species, procity, however, underemphasize the The Prisoner's Dilemma game is an almost all clear cases of altruism, and stringencyof its conditions (15). elegant embodiment of the problem of most observed cooperation, occur in Our contributionin this area is new in achieving mutual cooperation (16), and contexts of high relatedness, usually be- three ways. thereforeprovides the basis for our anal- tween immediate family members. The 1) In a biological context, our model is ysis. To keep the analysis tractable, we evolution of the suicidal barbed sting of novel in its probabilistictreatment of the focus on the two-player version of the the honeybee worker could be taken as possibility that two individuals may in- game, which describes situations that paradigmfor this line of theory (7). teract again. This allows us to shed new involve interactions between pairs of Conspicuousexamples of cooperation (althoughalmost never of ultimate self- sacrifice)also occur where relatednessis Summary.Cooperation in organisms, whether bacteria or primates, has been a low or absent. Mutualistic symbioses difficultyfor evolutionarytheory since Darwin.On the assumption that interactions offerstriking examples such as these: the between pairs of individualsoccur on a probabilisticbasis, a model is developed fungus and alga that compose a lichen; based on the concept of an evolutionarilystable strategy in the context of the the ants and ant-acacias,where the trees Prisoner'sDilemma game. Deductionsfrom the model, and the results of a computer house and feed the ants which, in turn, tournamentshow how cooperationbased on reciprocitycan get started in an asocial protect the trees (8); and the fig wasps world,can thrivewhile interactingwith a wide range of other strategies, and can resist and fig tree, where wasps, which are invasion once fully established. Potential applications include specific aspects of obligateparasites of fig flowers, serve as territoriality,mating, and disease. the tree's sole means of pollination and seed set (9). Usually the course of coop- erationin such symbioses is smooth, but light on certain specific biological pro- individuals. In the Prisoner's Dilemma sometimes the partners show signs of cesses such as aging and territoriality. game, two individuals can each either antagonism,either spontaneousor elicit- 2) Our analysis of the evolution of cooperate or defect. The payoff to a ed by particular treatments (10). Al- cooperation considers not just the final player is in terms of the effect on its though kinship may be involved, as will stabilityof a given strategy, but also the fitness (survivaland fecundity). No mat- be discussed later, symbioses mainly il- initial viability of a strategy in an envi- ter what the other does, the selfish lustrate the other recent extension of ronment dominated by noncooperating choice of defection yields a higherpayoff evolutionarytheory, the theory of recip- individuals,as well as the robustnessof a than cooperation. But if both defect, rocation. strategy in a variegated environment both do worse than if both had cooperat- Cooperationper se has received com- composed of other individuals using a ed. parativelylittle attention from biologists variety of more or less sophisticated Figure 1 shows the payoff matrix of since the pioneer account of Trivers (5); strategies. This allows a richer under- the Prisoner's Dilemma. If the other but an associated issue, concerning re- standing of the full chronology of the player cooperates, there is a choice be- straint in conflict situations, has been evolution of cooperation than has pre- tween cooperation which yields R (the developed theoretically. In this connec- viously been possible. rewardfor mutualcooperation) or defec- tion, a new concept, that of an evolution- 3) Our applicationsinclude behavioral tion which yields T (the temptation to arily stable strategy, has been formally interaction at the microbial level. This defect). By assumption, T > R, so that it developed (6, 11). Cooperation in the leads us to some speculative suggestions pays to defect if the other player cooper- more normal sense has remainedcloud- of rationales able to account for the ates. On the other hand, if the other ed by certain difficulties, particularly existence of both chronic and acute player defects, there is a choice between those concerning initiation of cooper- phases in many diseases, and for a cer- cooperationwhich yields S (the sucker's ation from a previously asocial state (12) tain class of chromosomal nondisjunc- payoff) or defection which yields P (the and its stable maintenance once estab- tion, exemplifiedby Down's syndrome. punishment for mutual defection). By lished. A formaltheory of cooperationis assumptionP > S, so it pays to defect if increasingly needed. The renewed em- the other player defects. Thus, no matter phasis on individualismhas focused on Strategies in the Prisoner's Dilemma what the other player does, it pays to the frequent ease of cheating in recipro- defect. But, if both defect, both get P catory arrangements. This makes the Many of the benefits sought by living ratherthan the largervalue of R that they stability of even mutualistic symbioses things are disproportionallyavailable to both could have gotten had both cooper- appearmore questionablethan underthe cooperatinggroups. While there are con- ated. Hence the dilemma (17). old view of adaptationfor species bene- siderabledifferences in what is meant by Withtwo individualsdestined never to fit. At the same time other cases that the terms "benefits" and "sought," this meet again, the only strategythat can be once appeared firmly in the domain of statement,insofar as it is true, lays down called a solution to the game is to defect kinshiptheory now begin to reveal rela- a fundamental basis for all social life. always despite the seemingly paradox- tednesses of interactantsthat are too low The problem is that while an individual ical outcome that both do worse than for much nepotistic altruism to be ex- can benefit from mutual cooperation, they could have had they cooperated. pected. This applies both to cooperative each one can also do even better by Apart from being the solution in game breedingin birds (13) and to cooperative exploitingthe cooperative efforts of oth- theory, defection is also the solution in acts more generally in primate groups ers. Over a period of time, the same biological evolution (18). It is the out- (14). Here either the appearancesof co- individualsmay interact again, allowing come of inevitable evolutionary trends operationare deceptive-they are cases for complex patternsof strategicinterac- throughmutation and natural selection: of part-kin altruism and part cheat- tions. Game theory in general, and the if the payoffs are in terms of fitness, and 27 MARCH 1981 1391 Player B tive to others. A bacteriummight easily C D have production of its own bacteriocin Cooperation Defection Player A dependenton the perceived presence of in R=3 S=O Fig. 1. The Prisoner's Dilem- like hostile products its environment, C Reward for ma game. The payoffto player but it could not aim the toxin produced A is shown with illustrative Cooperation mutual cooperation Sucker's payoff toward an offending initiator. From ex- numericalvalues. The game is isting evidence, so far from an individual ------? ?-- - defined T> R> P > S by discriminationseems to be T=5 P=1 and R > (S + 7)/2. level, by spe- cies rathereven than For exam- D Temptation to Punishment for variety. Defection defect mutual defection ple, a Rhizobium strain may occur in nodules which it causes on the roots of --~ ~~~~....- manyspecies of leguminousplants, but it may fix nitrogen for the benefit of the plant in only a few of these species (20). the interactionsbetween pairs of individ- individualswill meet again. Factors that Thus, in many legumes the Rhizobium uals are randomand not repeated, then affectthe magnitudeof this probabilityof seems to be a pure parasite. In the light any populationwith a mixture of herita- meeting again include the average life- of theory to follow, it would be interest- ble strategiesevolves to a state where all span, relative mobility, and health of the ing to know whether these parasitized individualsare defectors. Moreover, no individuals. For any value of w, the legumes are perhaps less beneficial to single differing mutant strategy can do strategy of unconditional defection free living Rhizobiumin the surrounding betterthan others when the populationis (ALL D) is evolutionarily stable; if ev- soil than are those in which the full using this strategy. In these respects the eryone is using this strategy, no mutant symbiosis is established. But the main strategy of defection is stable. strategy can invade the population. But point of concern here is that such dis- This concept of stabilityis essential to other strategies may be evolutionarily criminationby a Rhizobiumseems not to the discussion of what follows and it is stable as well. In fact, when w is suffi- be known even at the level of varieties useful to state it more formally.A strate- ciently great, there is no single best within a species. gy is evolutionarilystable if a population strategyregardless of the behaviorof the As one moves up the evolutionary of individualsusing that strategy cannot others in the population (19). Just be- ladder in neural complexity, game-play- be invaded by a rare mutant adopting a cause there is no single best strategy, it ing behaviorbecomes richer. The intelli- different strategy (11). In the case of the does not follow that analysis is hopeless. gence of primates, including humans, Prisoner's Dilemma played only once, On the contrary, we demonstrate not allows a number of relevant improve- no strategy can invade the strategy of only the stabilityof a given strategy, but ments: a more complex memory, more pure defection. This is because no other also its robustness and initial viability. complex processing of information to strategycan do better with the defecting Before turningto the development of determinethe next action as a function individualsthan the P achieved by the the theory, let us consider the range of of the interactionso far, a better estimate defectingplayers who interactwith each biologicalreality that is encompassedby of the probability of future interaction other. So in the single-shot Prisoner's the game theoretic approach. To start with the same individual, and a better Dilemma, to defect always is an evolu- with, an organismdoes not need a brain ability to distinguish between different tionarilystable strategy. to employ a strategy. Bacteria,for exam- individuals.The discriminationof others In many biological settings, the same ple, have a basic capacity to play games may be among the most important of two individuals may meet more than in that (i) bacteria are highly responsive abilities because it allows one to handle once. If an individual can recognize a to selected aspects of their environment, interactionswith many individualswith- previousinteractant and remembersome especially their chemical environment; out having to treat them all the same, aspects of the prior outcomes, then the (ii) this implies that they can respond thus making possible the rewarding of strategic situation becomes an iterated differentially to what other organisms cooperationfrom one individualand the Prisoner's Dilemma with a much richer aroundthem are doing; (iii) these condi- punishingof defection from another. set of possibilities. A strategywould take tional strategies of behavior can certain- The model of the iterated Prisoner's the form of a decision rule which deter- ly be inherited;and (iv) the behaviorof a Dilemma is much less restricted than it mined the probabilityof cooperation or bacteriumcan affect the fitness of other may at firstappear. Not only can it apply defection as a function of the history of organismsaround it, just as the behavior to interactionsbetween two bacteria or the interaction so far. But if there is a of other organismscan affect the fitness interactionsbetween two primates,but it known numberof interactionsbetween a of a bacterium. can also apply to the interactions be- pair of individuals, to defect always is While the strategiescan easily include tween a colony of bacteria and, say, a still evolutionarilystable and is still the differential responsiveness to recent primate serving as a host. There is no only strategywhich is. The reason is that changes in the environmentor to cumu- assumption of commensurability of defection on the last interaction would lative averages over time, in other ways payoffsbetween the two sides. Provided be optimal for both sides, and conse- their range of responsiveness is limited. that the payoffs to each side satisfy the quently so would defection on the next- Bacteria cannot "remember"or "inter- inequalities that define the Prisoner's to-last interaction,and so on back to the pret" a complex past sequence of Dilemma(Fig. 1), the results of the anal- first interaction. changes, and they probably cannot dis- ysis will be applicable. Ourmodel is based on the more realis- tinguishalternative origins of adverse or The model does assume that the tic assumptionthat the numberof inter- beneficial changes. Some bacteria, for choices are made simultaneously and actions is not fixed in advance. Instead, example, produce their own antibiotics, with discrete time intervals. For most there is some probability, w, that after bacteriocins;those are harmless to bac- analyticpurposes, this is equivalentto a the current interaction the same two teriaof the producingstrain, but destruc- continuous interaction over time, with 1392 SCIENCE, VOL. 211 the time period of the model correspond- winnerof the first round, Professor Ana- begins with C, the second round has the ing to the minimum time between a tol Rapoport of the Institute for Ad- same state as the first, and thus a maxi- change in behavior by one side and a vanced Study (Vienna). It won again. An mal rule will continue with C and hence response by the other. And while the analysis of the 3 million choices which always cooperate with TIT FOR TAT. model treats the choices as simulta- were made in the second roundidentified But such a rule will not do better than neous, it would make little difference if the impressive robustness of TIT FOR TIT FOR TAT does with another TIT they were treated as sequential (21). TAT as dependent on three features: it FOR TAT, and hence it cannot invade. Turning to the development of the was never the first to defect, it was If, on the other hand, a rule begins with theory, the evolution of cooperationcan provocableinto retaliationby a defection D, then this first D induces a switch in be conceptualizedin terms of three sepa- of the other, and it was forgiving after the state of TIT FOR TAT and there are rate questions: just one act of retaliation(24). two possibilities for continuation that 1) Robustness. What type of strategy The robustness of TIT FOR TAT was could be maximal. If D follows the first can thrive in a variegated environment also manifestin an ecological analysis of D, then this being maximal at the start composed of others using a wide variety a whole series of future tournaments. implies that it is everywhere maximalto of more or less sophisticated strategies? The ecological approach takes as given follow D with D, making the strategy 2) Stability. Under what conditions the varieties which are present and in- equivalent to ALL D. If C follows the can such a strategy, once fully estab- vestigates how they do over time when initialD, the game is then reset as for the lished, resist invasion by mutant strate- interactingwith each other. This analysis first move; so it must be maximal to gies? was based on what would happenif each repeat the sequence of DC indefinitely. 3) Initial viability.Even if a strategyis of the strategies in the second round These points show that the task of robust and stable, how can it ever get a were submitted to a hypothetical next searching a seemingly infinite array of foothold in an environmentwhich is pre- round in proportionto its success in the rules of behavior for one potentially dominantlynoncooperative? previous round. The process was then capable of invading TIT FOR TAT is repeatedto generate the time path of the really easier than it seemed: if neither distribution of strategies. The results ALL D nor alternationof D and C can Robustness showed that, as the less successful rules invade TIT FOR TAT, then no strategy were displaced, TIT FOR TAT contin- can. To see what type of strategycan thrive ued to do well with the rules which To see when these strategies can in- in a variegatedenvironment of more or initially scored near the top. In the long vade, we note that the probability that less sophisticated strategies, one of us run, TIT FOR TAT displaced all the the nth interaction actually occurs is (R.A.) conducted a computer tourna- other rules and went to fixation (24). wn- . Therefore, the expression for the ment for the Prisoner's Dilemma. The This provides furtherevidence that TIT total payoff is easily found by applying strategieswere submittedby game theo- FOR TAT's cooperation based on reci- the weights 1, w, w2... to the payoff rists in economics, sociology, political procity is a robust strategy that can sequence and summingthe resultant se- science, and mathematics(22). The rules thrive in a variegatedenvironment. ries. When TIT FOR TAT plays another impliedthe payoff matrixshown in Fig. 1 TIT FOR TAT, it gets a payoff of R each and a game length of 200 moves. The 14 move for a total of R + wR + w2R entries and a totally random strategy Stability ..., which is Rl(1 - w). ALL D play- were paired with each other in a round ing with TIT FOR TAT gets T on the first robintournament. Some of the strategies Once a strategy has gone to fixation, move and P thereafter, so it cannot in- were quite intricate. An example is one the question of evolutionary stability vade TIT FOR TAT if which on each move models the behav- deals with whether it can resist invasion R/(1 - w) - T + wP/(1 - w) ior of the other player as a Markov by a mutant strategy. In fact, we will process, and then uses Bayesian infer- now show that once TIT FOR TAT is Similarly when alternation of D and C ence to select what seems the best established,it can resist invasion by any plays TIT FOR TAT, it gets a payoff of choice for the run. the mutant that long However, possible strategy provided T = + w2T + result of the tournament was that the the individualswho interacthave a suffi- wS s3S... = (T + wS)/(1 - w2) highest average score was attained by ciently large probability, w, of meeting the simplest of all strategies submitted: again. The proof is described in the next Alternation of D and C thus cannot in- TIT FOR TAT. This strategy is simply two paragraphs. vade TIT FOR TAT if one of cooperatingon the first move and As a first step in the proof we note that Rl(1 - w) - (T + wS)/(1 - w2) then doing whateverthe other player did since TIT FOR TAT "remembers"only on the preceding move. Thus TIT FOR one move back, one C by the other Hence, with reference to the magnitude TAT is a strategy of cooperation based player in any round is sufficientto reset of w, we find that neither of these two on reciprocity. the situationas it was at the beginningof strategies (and hence no strategy at all) The results of the firstround were then the game. Likewise, one D sets the situa- can invade TIT FOR TAT if and only if circulatedand entries for a second round tion to what it was at the second round both were solicited. This time there were 62 after a D was played in the first. Since w > (T - R)/(T - P) and entries from six countries (23). Most of there is a fixed chance, w, of the interac- w - (T - R)/(R - S) the contestants were computer hob- tion not ending at any given move, a (1) byists, but there were also professors of strategy cannot be maximal in playing This demonstratesthat TIT FOR TAT is evolutionarybiology, physics, and com- with TIT FOR TAT unless it does the evolutionarily stable if and only if the puter science, as well as the five disci- same thingboth at the first occurrenceof interactions between the individuals plines representedin the first round. TIT a given state and at each resettingto that have a sufficiently large probability of FOR TAT was again submitted by the state. Thus, if a rule is maximal and continuing(19). 27 MARCH 1981 1393 Initial Viability cooperation based on reciprocity can strategy like TIT FOR TAT became es- thrive and be evolutionarily stable in a tablished itself. Actually, there is an in- TIT FOR TAT is not the only strategy populationwith no relatedness at all. teresting asymmetry here. Let us define that can be evolutionarilystable. In fact, A case of cooperation that fits this a nice strategy as one, such as TIT FOR ALL D is evolutionarilystable no matter scenario, at least on first evidence, has TAT, which will never be the first to what is the probability of interaction been discovered in the spawning rela- defect. Obviously, when two nice strate- continuing. This raises the problem of tionships in a sea bass (28). The fish, gies interact, they both receive R each how an evolutionary trend to coopera- which are hermaphroditic,form pairs move, which is the highest average score tive behavior could ever have started in and roughlymay be said to take turns at an individual can get when interacting the first place. being the high investmentpartner (laying with another individual using the same Genetic kinship theory suggests a eggs) and low investment partner (pro- strategy. Therefore, if a strategy is nice plausibleescape from the equilibriumof viding sperm to fertilize eggs). Up to ten and is evolutionarily stable, it cannot be ALL D. Close relatedness of interac- spawningsoccur in a day and only a few intruded upon by a cluster. This is be- tants permits true altruism-sacrifice of eggs are provided each time. Pairs tend cause the score achieved by the strategy fitness by one individualfor the benefit to break up if sex roles are not divided that comes in a cluster is a weighted of another. True altruism can evolve evenly. The system appearsto allow the average of how it does with others of its when the conditions of cost, benefit, and evolutionof much economy in the size of kind and with the predominant strategy. relatedness yield net gains for the altru- testes, but Fischer (28) has suggested Each of these components is less than or ism-causinggenes that are residentin the that the testis condition may have equal to the score achieved by the pre- relatedindividuals (25). Not defecting in evolved when the species was more dominant, nice, evolutionarily stable a single-move Prisoner's Dilemma is al- sparse and inclined to inbreed. Inbreed- strategy, and therefore the strategy ar- truismof a kind (the individualis forego- ing would imply relatedness in the pairs riving in a cluster cannot intrude on the ing proceeds that mighthave been taken) and this initially may have transferred nice, evolutionarily stable strategy (19). and so can evolve if the two interactants the system to attractance of tit-for-tat This means that when w is large enough are sufficiently related (18). In effect, cooperation-that is, to cooperationun- to make TIT FOR TAT an evolutionarily recalculationof the payoffmatrix in such needful of relatedness. stable strategy it can resist intrusion by a way that an individualhas a part inter- Anothermechanism that can get coop- any cluster of any other strategy. The est in the partner'sgain (that is, reckon- eration started when virtually everyone gear wheels of social evolution have a ing payoffs in terms of inclusive fitness) is using ALL D is clustering. Suppose ratchet. can often eliminate the inequalities that a small group of individualsis using The chronological story that emerges T > R and P > S, in which case cooper- a strategy such as TIT FOR TAT and from this analysis is the following. ALL ation becomes unconditionally favored that a certainproportion, p, of the inter- D is the primeval state and is evolution- (18, 26). Thus it is possible to imagine actions of members of this cluster are arily stable. This means that it can resist that the benefits of cooperation in Pris- with other membersof the cluster. Then the invasion of any strategy that has oner's Dilemma-likesituations can begin the average score attained by the mem- virtually all of its interactions with ALL to be harvested by groups of closely bers of the cluster in playing the TIT D. But cooperation based on reciprocity related individuals. Obviously, as re- FOR TAT strategy is can gain a foothold through two different gardspairs, a parentand its offspringor a mechanisms. First, there can be kinship p[RI(1 - w)] + pair of siblings would be especially between mutant strategies, giving the (1 -p)[S + wP/(1 - w)] promising,and in fact many examples of genes of the mutants some stake in each cooperationor restraintof selfishness in If the members of the cluster provide a other's success, thereby altering the such pairs are known. negligible proportion of the interactions effective payoff matrix of the interaction Once the genes for cooperation exist, for the other individuals, then the score when viewed from the perspective of the selection will promote strategies that attained by those using ALL D is still PI gene rather than the individual. A second base cooperativebehavior on cues in the (1 - w). When p and w are large mechanism to overcome total defection environment(4). Such factors as promis- enough, a cluster of TIT FOR TAT indi- is for the mutant strategies to arrive in a cuous fatherhood (27) and events at ill- viduals can then become initially viable cluster so that they provide a nontrivial defined group margins will always lead in an environment composed over- proportion of the interactions each has, to uncertainrelatedness among potential whelmingly of ALL D (19). even if they are so few as to provide a interactants.The recognitionof any im- Clustering is often associated with kin- negligible proportion of the interactions proved correlates of relatedness and use ship, and the two mechanisms can rein- which the ALL D individuals have. Then of these cues to determine cooperative force each other in promoting the initial the tournament approach demonstrates behavior will always permit advance in viability of reciprocal cooperation. How- that once a variety of strategies is pres- inclusive fitness (4). When a cooperative ever, it is possible for clustering to be ent, TIT FOR TAT is an extremely ro- choice has been made, one cue to relat- effective without kinship (3). bust one. It does well in a wide range of edness is simply the fact of reciprocation We have seen that TIT FOR TAT can circumstances and gradually displaces of the cooperation. Thus modifiers for intrude in a cluster on a population of all other strategies in a simulation of a more selfish behavior after a negative ALL D, even though ALL D is evolu- great variety of more or less sophisticat- response from the other are advanta- tionarily stable. This is possible because ed decision rules. And if the probability geous whenever the degree of related- a cluster of TIT FOR TAT's gives each that interaction between two individuals ness is low or in doubt. As such, condi- member a nontrivial probability of meet- will continue is great enough, then TIT tionality is acquired, and cooperation ing another individual who will recipro- FOR TAT is itself evolutionarily stable. can spread into circumstances of less cate the cooperation. While this suggests Moreover, its stability is especially se- and less relatedness. Finally, when the a mechanism for the initiation of cooper- cure because it can resist the intrusion of probability of two individuals meeting ation, it also raises the question about whole clusters of mutant strategies. Thus each other again is sufficiently high, whether the reverse could happen once a cooperation based on reciprocity can get 1394 SCIENCE, VOL. 211 started in a predominantlynoncoopera- All progeny of the wasp then perish. show much more aggressive reactions tive world, can thrive in a variegated Another mechanismto avoid the need when the song of an unfamiliar male environment,and can defend itself once for recognition is to guarantee the rather than a neighbor is reproduced fully established. uniqueness of the pairingof interactants nearby (34). by employing a fixed place of meeting. Reciprocal cooperation can be stable Consider, for example, cleaner mutual- with a larger range of individualsif dis- Applications isms in which a smallfish or a crustacean criminationcan cover a wide variety of removes and eats ectoparasitesfrom the others with less reliance on supplemen- A variety of specific biological appli- body (or even from the inside of the tary cues such as location. In humans cations of our approachfollows from two mouth)of a largerfish which is its poten- this ability is well developed, and is of the requirementsfor the evolution of tial predator.These aquatic cleaner mu- largelybased on the recognitionof faces. cooperation. The basic idea is that an tualisms occur in coastal and reef situa- The extent to which this function has individualmust not be able to get away tions where animals live in fixed home become specialized is revealed by a with defecting without the other individ- rangesor territories(4, 5). They seem to brain disorder called prosopagnosia. A uals being able to retaliate effectively be unknown in the free-mixing circum- normalperson can name someone from (29). The response requires that the de- stances of the open sea. facial features alone, even if the features fectingindividual not be lost in an anony- Othermutualisms are also characteris- have changed substantially over the mous sea of others. Higher organisms tic of situationswhere continued associ- years. People with prosopagnosiaare not avoid this problem by their well-devel- ation is likely, and normallythey involve able to make this association, but have oped ability to recognize many different quasi-permanentpairing of individualsor few other neurological symptoms other individuals of their species, but lower of endogamous or asexual stocks, or of than a loss of some part of the visual organismsmust rely on mechanismsthat individualswith such stocks (7, 31). Con- field. The lesions responsible for proso- drasticallylimit the number of different versely, conditions of free-mixing and pagnosia occur in an identifiablepart of individualsor colonies with which they transitorypairing conditions where rec- the brain:the undersideof both occipital can interacteffectively. The other impor- ognition is impossible are much more lobes, extending forward to the inner tant requirement to make retaliation likely to result in exploitation-parasit- surfaceof the temporallobes. This local- effective is that the probability,w, of the ism, disease, and the like. Thus, whereas ization of cause, and specificity of effect, same two individuals' meeting again ant colonies participate in many sym- indicates that the recognition of individ- must be sufficientlyhigh. bioses and are sometimes largely depen- ual faces has been an importantenough Whenan organismis not able to recog- dent on them, honeybee colonies, which task for a significant portion of the nize the individual with which it had a are much less permanent in place of brain'sresources to be devoted to it (35). priorinteraction, a substitutemechanism abode, have no known symbionts but Just as the ability to recognize the is to make sure that all of one's interac- many parasites (32). The small fresh- other interactantis invaluablein extend- tions are with the same interactant.This water animal Chlorohydra viridissima ing the range of stable cooperation, the can be done by maintainingcontinuous has a permanentstable association with ability to monitorcues for the likelihood contact with the other. This method is green algae that are always naturally of continued interactionis helpful as an applied in most interspecies mutualism, found in its tissues and are very difficult indication of when reciprocal cooper- whethera hermitcrab and his sea-anem- to remove. In this species the alga is ation is or is not stable. In particular, one partner, a cicada and the varied transmittedto new generations by way when the value of w falls below the microorganismiccolonies housed in its of the egg. Hydra vulgaris and H. atten- thresholdfor stability given in condition body, or a tree and its mycorrhizalfungi. uata also associate with algae but do not (1), it will no longer pay to reciprocate The abilityof such partnersto respond have egg transmission.In these species it the other's cooperation. Illness in one specificallyto defection is not known but is said that "infection is preceded by partner leading to reduced viability seems posible. A host insect that carries enfeeblement of the animals and is ac- would be one detectable sign of declining symbionts often carries several kinds companiedby pathologicalsymptoms in- w. Both animals in a partnershipwould (for example, yeasts and bacteria). Dif- dicating a definite parasitism by the then be expected to become less cooper- ferences in the roles of these are almost plant" (33). Again, it is seen that imper- ative. Aging of a partnerwould be very wholly obscure (30). Perhaps roles are manence of association tends to destabi- like disease in this respect, resulting in actually the same, and being host to lize symbiosis. an incentive to defect so as to take a one- more than one increases the security of In species with a limited ability to time gain when the probabilityof future retaliationagainst a particularexploita- discriminatebetween other members of interactionbecomes small enough. tive colony. Where host and colony are the same species, reciprocalcooperation These mechanismscould operate even not permanently paired, a method for can be stable with the aid of a mecha- at the microbiallevel. Any symbiontthat immediate drastic retaliation is some- nism that reduces the amount of dis- still has a transmission "horizontally" times apparentinstead. This is so with criminationnecessary. Philopatryin gen- (that is, infective) as well as vertically fig wasps. By natureof their remarkable eral and territorialityin particular can (that is, transovarial, or more rarely role in pollination, female fig wasps serve this purpose. The phrase stable through sperm, or both) would be ex- serve the fig tree as a motile aerial male territoriesmeans that there are two quite pected to shift from mutualismto para- gamete. Throughthe extreme protogyny different kinds of interaction: those in sitism when the probabilityof continued and simultaneityin flowering, fig wasps neighboringterritories where the prob- interactionwith the host lessened. In the cannot remainwith a single tree. It turns ability of interactionis high, and strang- more parasiticphase it could exploit the out in many cases that if a fig wasp ers whose probabilityof future interac- host more severely by producing more entering a young fig does not pollinate tion is low. In the case of male territorial infective propagules. This phase would enough flowers for seeds and instead birds, songs are used to allow neighbors be expected when the host is severely lays eggs in almost all, the tree cuts to recognize each other. Consistent with injured, contracted some other wholly off the developing fig at an early stage. our theory, such male territorial birds parasiticinfection that threateneddeath, 27 MARCH 1981 1395 or when it manifested signs of age. In ally standto gain by steadily cooperating tionary Approach, J. Krebs and N. Davies, Eds. and seem- in a (Blackwell, Oxford, 1978), p. 245; P. B. Stacey, fact, bacteriathat are normal diploid organism, the situation in Behav. Ecol. Sociobiol. 6, 53 (1979). ingly harmless or even beneficial in the oogenesis is a Prisoner's Dilemma: a 14. A. H. Harcourt, Z. Tierpsychol. 48, 401 (1978); C. Packer, Anim. Behav. 27, 1 (1979); R. W. gut can be found contributingto sepsis in chromosome which can be "first to de- Wrangham, Soc. Sci. Info. 18, 335 (1979). the body when the gut is perforated fect" can get itself into the egg nucleus 15. J. D. Ligon and S. H. Ligon, Nature (London) 276, 496 (1978). (implying a severe wound) (36). And rather than the polar body. We may 16. A. Rapoport and A. M. Chammah, Prisoner's normal inhabitantsof the body surface hypothesize that such an action Dilemma (Univ. of Michigan Press, Ann Arbor, triggers 1965). There are many other patterns of interac- (like Candida albicans) can become in- similarattempts by the homolog in sub- tion which allow gains for cooperation. See for vasive and in either sick or and when both mem- example the model of intraspecific combat in J. dangerous sequent meioses, Maynard Smith and G. R. Price, in (11). elderly persons. bers of a homologous pair try it at once, 17. The condition that R > (S + T)/2 is also part of the definition to rule out the possibility that It is possible also that this argument an extra chromosome in the offspring alternating exploitation could be better for both has some bearing on the etiology of could be the occasional result. The fit- than mutual cooperation. 18. W. D. Hamilton, in Man and Beast: Compara- cancer, insofar as it turns out to be due ness of the bearers of extra chromo- tive Social Behavior (Smithsonian Press, Wash- to viruses potentially latent in the somes is generally extremely low, but a ington, 1971), p. 57. R. M. Fagen [in (5)] shows some conditions for single encounters where genome (37). Cancers do tend to have chromosomewhich lets itself be sent to defection is not the solution. their onset at when the chances of the makes a fitness contribu- 19. For a formal proof, see R. Axelrod, Am. Politi- ages polar body cal Sci. Rev., in press. For related results on the vertical transmissionare rapidly declin- tion of zero. Thus P > S holds. For the potential stability of cooperative behavior see R. D. Luce and H. Raiffa, Games and Decisions ing (38). One oncogenic virus, that of model to work, an incident of "defec- (Wiley, New York, 1957), p. 102; M. Taylor, Burkitt'slymphoma, does not have ver- tion" in one developing egg would have Anarchy and Cooperation(Wiley, New York, 1976); M. Kurz, in Economic Progress, Private tical transmissionbut may have alterna- to be perceptibleby others still waiting. Values and Public Policy, B. Balassa and R. tives of slow or fast of infec- That this would occur is Nelson, Eds. (North-Holland, Amsterdam, production pure specula- 1977), p. 177. tious propagules.The slow form appears tion, as is the feasibility of self-promot- 20. M. Alexander, Microbial Ecology (Wiley, New as a chronic the fast as behavior chromosomes a York, 1971). mononucleosis, ing by during 21. In either case, cooperation on a tit-for-tat basis an acute mononucleosis or as a lym- gametic cell division. But the effects do is evolutionarily stable if and only if w is suffi- is not seem ciently high. In the case of sequential moves, phoma(39). The point of interest that, inconceivable: a bacterium, suppose there is a fixed chance, p, that a given as some evidence suggests, lymphoma afterall, with its single chromosome,can interactant of the pair will be the next one to need help. The critical value of w can be shown can be triggeredby the host's contract- do complex conditional things. Given to be the minimum of the two side's value of A/ malaria. The ex- such our model would p(A + B) where A is the cost of giving assist- ing lymphoma grows effects, explain ance, and B is the benefit of assistance when tremely fast and so can probably com- the much greater incidence of abnormal received. See also P. R. Thompson, Soc. SciL with malariafor transmission chromosome increase in not Info. 19, 341 (1980). pete (pos- eggs (and 22. R. Axelrod, J. Conflict Resolution 24, 3 (1980). sibly by mosquitoes) before death re- sperm)with parentalage. 23. In the second round, the length of the games was uncertain, with an expected probability of 200 sults. Considering other cases of moves. This was achieved by setting the prob- simultaneousinfection by two or more ability that a given move would not be the last at w = .99654. As in the first round, each pair was species of pathogen, or by two strainsof Conclusion matched in five games (24). the same our have rel- 24. R. Axelrod, J. Conflict Resolution 24, 379 one, theory may (1980). evance more generally to whether a dis- Darwin's emphasis on individual ad- 25. R. A. Fisher, The Genetical Theoryof Natural ease will follow a has been formalizedin terms of Selection (Oxford Univ. Press, Oxford, 1930); J. slow, joint-optimal vantage B. S. Haldane,Nature (London)New Biol. 18, exploitation course ("chronic" for the game theory. This establishes conditions 34 (1955); W. D. Hamilton, Am. Nat. 97, 354 (1963). host) or a rapid severe exploitation under which cooperation based on reci- 26. M. J. Wade and F. Breden, Behav. Ecol. Socio- ("acute" for the host). With single infec- procity can evolve. biol, in press. 27. R. D. Alexander, Annu. Rev. Ecol. Syst. 5, 325 tion the slow course would be expected. (1974). Withdouble infection, crash exploitation Referencesand Notes 28. E. Fischer, Anim. Behav. 28, 620 (1980); E. G. Leigh, Jr., Proc. Natl. Acad. Sci. U.S.A. 74, might, as dictated by implied payoff 1. G. C. Williams,Adaptations and NaturalSelec- 4542 (1977). functions, or have tion (Princeton Univ. Press, Princeton, 1966); 29. For economic theory on this point see G. Aker- begin immediately, W. D. Hamilton, in Bisocial Anthropology, R. lof, Q. J. Econ. 84, 488 (1970); M. R. Darby and onset later at an appropriate stage of Fox, Ed. (Malaby, London, 1975), p. 133. E. Karni, J. Law Econ. 16, 67 (1973); 0. E. 2. For the best recent case for effective selection at Williamson, Markets and Hierarchies (Free senescence (40). group levels and for altruism based on genetic Press, New York, 1975). Our model (with symmetryof the two correction of non-kin interactants see D. S. 30. P. Buchner, Endosymbiosisof Animals with Wilson, Natural Selection of Populations and Plant Microorganisms (Interscience, New parties)could also be tentatively applied Communities (Benjamin/Cummings, Menlo York, 1965). to the increase with maternal age of Park, Calif., 1979). 31. W. D. Hamilton, in Diversity of Insect Faunas, 3. W. D. Hamilton, J. Theoret. Biol. 7, 1 (1964). L. A. Mound and N. Waloff, Eds. (Blackwell, chromosomal nondisjunction during 4. R. Trivers, Q. Rev. Biol. 46, 35 (1971). Oxford, 1978). ovum formation This 5. For additions to the theory of biological cooper- 32. E. O. Wilson, The Insect Societies (Bellknap, (oogenesis) (41). ation see I. D. Chase [Am. Nat. 115, 827 (1980)], Cambridge, Mass., 1971); M. Treisman, Anim. effect leads to various conditions of se- R. M. Fagen [ibid., p. 858 (1980)], and S. A. Behav. 28, 311 (1980). Boorman and P. R. Levitt [The Genetics of 33. C. M. Yonge [Nature (London) 134, 12 (1979)] verely handicapped offspring, Down's Altruism (Academic Press, New York, 1980)]. gives other examples of invertebrates with uni- syndrome (caused by an extra copy of 6. R. Dawkins, The Selfish Gene (Oxford Univ. cellular algae. Press, Oxford, 1976). 34. E. O. Wilson, Sociobiology (Harvard Univ. chromosome21) being the most familiar 7. W. D. Hamilton,Annu. Rev. Ecol. Syst. 3, 193 Press, Cambridge, Mass., 1975), p. 273. It almost entirely on (1972). 35. N. Geschwind, Sci. Am. 241, (No. 3), 180 example. depends 8. D. H. Janzen, Evolution 20, 249 (1966). (1979). failure of the normal separation of the 9. J. T. Wiebes, Gard. Bull. (Singapore) 29, 207 36. D. C. Savage, in Microbial Ecology of the Gut, chromosomes in the and (1976); D. H. Janzen, Annu. Rev. Ecol. Syst. 10, R. T. J. Clarke and T. Bauchop, Eds. (Academic paired mother, 31 (1979). Press, New York, 1977), p. 300. this suggests the possible connection 10. M. Caullery, Parasitism and Symbiosis (Sidg- 37. J. T. Manning, J. Theoret. Biol. 55, 397 (1975); wick and Jackson, London, 1952). This gives M. J. Orlove, ibid. 65, 605 (1977). with our story. Cell divisions of oogene- examples of antagonism in orchid-fungus and 38. W. D. Hamilton, ibid. 12, 12 (1966). sis, but not usually of spermatogenesis, lichen symbioses. For the example of wasp-ant 39. W. Henle, G. Henle, E. T. Lenette, Sci. Am. symbiosis, see (7). 241 (No. 1), 48 (1979). are characteristically unsymmetrical, 11. J. Maynard Smith and G. R. Price, Nature 40. See also I. Eshel, Theoret. Pop. Biol. 11, 410 with (as a so-called (London) 246, 15 (1973); J. Maynard Smith and (1977) for a related possible implication of multi- rejection polar body) G. A. Parker,Anim. Behav. 24, 159 (1976);G. clonal infection. of chromosomes that go to the unlucky A. Parker, Nature (London) 274, 849 (1978). 41. C. Stern, Principles of Human Genetics (Free- of the cell. It seems 12. J. Elster, Ulysses and the Sirens (Cambridge man, San Francisco, 1973). pole possible that, Univ. Press, London, 1979). 42. For helpful suggestions we thank Robert Boyd, while homologous chromosomes gener- 13. S. T. Emlen, in Behavioral Ecology: An Evolu- Michael Cohen, and David Sloan Wilson. 1396 SCIENCE, VOL. 211