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Home , Coevolution, Reciprocal altruism, Robert Axelrod

The of Cooperation

Robert Axelrod; William D. Hamilton

Science, New Series, Vol. 211, No. 4489. (Mar. 27, 1981), pp. 1390-1396.

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http://www.jstor.org Fri Jan 4 15:02:00 2008 The latest data for 1978 suggests that the situa- ary 1975) the Committee on Science and Tech- budget appropriations." In other words, it tion may, in fact, be deteriorating. . . . we may nology received jurisdiction over envlron- seems that work on highly relevant matters be losing the war on air pollution." mental research" as a result of several changes might be funded even if of poor quality. [See 3. For examples see House Subcommittee on the in the rules of the House of Representatives. EPA and the Academic Community (EPA-60018- Environment and the Atmosphere, The Erzviron- The Subcommittee on the Environment and the 80-010, Environmental Protection Agency, Cin- mentcrl Protection Agerzcy's Resecrrch Progrcrm Atmosphere was formed to handle this juris- cinnati, Ohio, 19801, p. 2.1 with Prirnury F,'rnphusis on the Community diction and for 4 years (two Congresses), with 19. National Academy of Sciences, Materials Advi- lfecrlth und Environmenrul Surveillance Syatem Congressman Brown as chairman, had respon- sory Board, Repor1 of the Ad Hoc Committ~eon (CHESS):An lnveatigative Report (Government sibility for ORD. In January 1979, as a re- Principles i?fReseurch-Engineerinx Interuc'tion Printing Office, Washington, D.C., 1976). espe- sult of reorganization within the Committee on (National Academy of Sciences, Washington, cially chapters 4 to 6. Science and Technology, Congressman Brown D.C., 1966), p. 16. 4. Without trying to be entirely rigorous, we will moved to the chair of the Subcommittee on 20. W. 0. Baker, in House Committee on Science use an NSF definition: "Basic research is that Science, Research, and Technology. The Sub- and Technology, Serninur on Reaeurch, Produc- type of research which is directed toward in- committee on the Environment and Atmosphere tivity, und the Natiorzul Economy, 18Jrrne I980 crease of knowledge in science. It is research was renamed Subcommittee on Natural Re- (Government Printing Office, Washington, where the primary aim of the investigator is a sources and Environment and given some addi- D.C., 1980). fuller knowledge or understanding of the subject tional jurisdiction. 21. Testimony of J. N. Pitts, in 1980 Aulhorizcltion under study, rather than a practical application 13. Eni~ironmrnterlProtection Agency Reseurch und ,for the Office of Resecrrch und Developnzenl, thereof." This was given by A. T. Waterman, Development laarres: 1978, hearings before the Eni~ironmrntulProtection Ayency, hearings be- then director of NSF, in Symposium on Ruaic House Subcommittee on the Environment and fore the House Subcommittee on Science and Reaeurch, D. Wolfle, Ed. (American Associ- the Atmosphere, 19 July and 13 and 14 Septem- Technology, 13 and 15 February 1979 (Govern- ation for the Advancement of Science, Washing- ber 1978 (Government Printing Office, Washing- ment Printing Office, Washington, D.C., 1979). ton, D.C., 1959). p. 20. ton, D.C., 1979). 22. H. W. Bode, in nusic Resecrrch und Nrrtioncrl 5. For example, the EPA administrator, D. Costle, 14. In making funding decisions, the agency uses a Gorrls, a report to the House Committee on in a letter dated 12 June 1978 to Senator William zero-base budgeting (ZBB) process in which Science and Astronautics (National Academy of Proxmire, chairman of the HUD-lndependent programs are approved by a~consensusof the Sciences, Washington, D.C., 1965), p. 74. Agencies Subcommittee of the Senate Appropri- administrator and the six assistant administra- 23. At present the program offices guide EPA's atrons Committee, said concerning enviionmen- tors. In the ZBB process, the ORD has only research not only through the ZBB process but tal research, "I've had to make too many billion about one of six votes, and thus research pro- also through the mechanism of 13 research com- dollar decisions over the last year without the grams are vulnerable to a great deal of influence mittees. These committees translate program critical information this sort of investment, from the program offices. Because they play ofice needs into "research docu- made five years ago, would have provided." such a substantial role in defining the program of ments" which guide all EPA research (10). 6. U.S. Congress, Office of Technology Assess- research ultimately conducted by ORD, the 24. This provision is contained in section 6 of Public ment, A Review if the U.S. F,'nvironmrntul administrator and all assistant administrators Law 95-155, the FY 1978 authorization act for Protection Agency Environmentcrl Resecrrch were asked to testify on what they expect from ORD. For explanation of congressional intent Outlook FY I976 through 1980 (Government that office. see Conference Report to Accompcrny H.R. Printing Office, Washington, D.C., 1976). 15. Speciul Urban Air Pollution Problema: Denver 5101, 95th Congress, Report No. 95-722 (Gov- 7. National Academy of Sciences, Commission on und Houaton, hearings before the House Sub- ernment Printing Office, Washington, D.C., Natural Resources, Ar~ul),ticcrlStudies for the committee on the Environment and the Atmo- 1977).. ,. U.S. Environmentul Protection Agency, vol. 3, sphere, 19 and 21 November 1977 (Government 25. This provision is contained in section 11 of Research and Development in the Environmen- Printing Office, Washington, D.C., 1978). Public Law 95-155. For explanation see the tul Protection Agency (National Academy of 16. Long-Term Environmental Research in the En- report cited in (10), and also Report lo Acc'om- Sciences, Washington, D.C., 1977). i~ironmenterlProtection Agency, hearings before puny H.R. 5101, 95th Congress, Report No. 95- 8. National Advisory Committee on Oceans and the House Subcommittee on the Environment 157 (Government Printing Office, Washington, Atmosphere, A Report lo the President crnd the and the Atmosphere, 30 June 1977 (Government D.C.. 1977). Congress, fifth annual report (Government Printing Office, Washington, D.C., 1978). See 26. This was cbntained in section 4(a) of H.R. 7099, Printing Ofice, Washington, D.C., 1976). the testimony of R. L. Sansom, especially his the House version of the FY 1981 authorization 9. ORD Progrcrm Guide (EPA-60019-79-038, Envi- supplemental statement, 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). 10.- ~ agency strenuously (if informally) opposed it 10. Kesecrrch ~rrtlook,1980 (EPA-60019-80-006, En- 18. For example, the agency has instituted a new and succeeded in having it removed from the vironmental Protection Agency, Washington, system of research grants putatively aimed at Senate-passed version of the bill. For cxplana- D.C., 1980). This presents the agency's 5-year bringing new work of high quality into its pro- tion of intent, see Report to Accompan)~H.K. environmental research plan in response to stat- gram. Despite this aim the published solicitation 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 report issued annually. unambiguously state that funding decisions will 1980). 11. Many examples of the environmental problems be based on scientific quality. Instead the fol- 27. J. Bronowski, The Common Senae of Science EPA faces are reported in Environmentcrl Oul- lowing appears: "Scientific merit and relevance (Harvard Univ. Press, Cambridge, Mass., 19781, look 1980 (EPA 60018-80-003, Environmental of proposals will be significant and balanced p. 143. Protection Agency, Washington, D.C., 1980). factors in the evaluation procedures since all 28. We thank A. V. Applegate for substantial assist- 12. At the beginning of the 94th Congress (Janu- projects must be in concert with the Agency's ance in the preparation of this paper.

To account for the manifest existence of cooperation and related group behav- ior, such as and restraint in competition, evolutionary theory has re- cently acquired two kinds of extension. The Evolution of Cooperation These extensions are, broadly, genetical kinship theory (3) and reciprocation the- ory (4, 5). Most of the recent activity, Robert Axelrod and William D. Hamilton both in field work and in further develop- ments of theory, has been on the side of kinship. Formal approaches have varied, but kinship theory has increasingly taken The theory of evolution is based on the the level of populations or whole spe- a gene's-eye view of struggle for 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 members of the same and adaptive. Recent reviews of the evolu- tially immortal set of its replicas existing even between members of different spe- 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 sufficiently closely related, al- evolutionary process largely dismissed benefit view of selection; at the level of a cooperative phenomena as not requiring species or a population, the processes of Dr. Axelrod is a professor of and research scientist at the Institute ol' Public Policy special attention. This position followed selection are weak. The original individ- Studies, , Ann Arbor 48109. Dr. Hamilton is a professor of from a misreading of theory that as- ualistic emphasis of Darwin's theory is in the Museum of Zoology and the Division of signed most to selection at more valid (1, 2). Biological Sciences, University of Michigan. 1390 0036-807518110327-1390$01 .SO10 Copyright O 1981 AAAS SCIENCE, VOL. 21 1, 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 individual altru- 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 stringency of its conditions (15). elegant embodiment of the problem of most observed cooperation, occur in Our contribution in this area is new in achieving mutual cooperation (16), and contexts of high relatedness, usually be- three ways. therefore provides 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 probabilistic treatment 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 paradigm for this line of theory (7). teract again. This allows us to shed new involve interactions between pairs of Conspicuous examples of cooperation (although almost never of ultimate self- sacrifice) also occur where relatedness is Summary. Cooperation in organisms, whether bacteria or primates, has been a low or absent. Mutualistic symbioses difficulty for evolutionary theory since Darwin. On the assumption that interactions offer striking examples such as these: the between pairs of individuals occur on a probabilistic basis, a model is developed fungus and alga that compose a lichen; based on the concept of an evolutionarily stable strategy in the context of the the and -acacias, where the trees Prisoner's Dilemma game. Deductions from the model, and the results of a computer house and feed the ants which, in turn, tournament show how cooperation based on reciprocity can get started in an asocial protect the trees (8); and the fig world, can thrive while interacting with 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 obligate parasites of fig , serve as territoriality, mating, and disease. the tree's sole means of and seed set (9).Usually the course of coop- eration in 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 spontaneous or 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 stability of a given strategy, but also the (survival and 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 higher payoff evolutionary theory, the theory of recip- individuals, as well as the robustness of a than cooperation. But if both defect, rocation. strategy in a variegated environment both do worse than if both had cooperat- Cooperation per se has received com- composed of other individuals using a ed. paratively little 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. reward for mutual cooperation) or defec- tion, a new concept, that of an evolution- 3) Our applications include behavioral tion which yields T (the temptation to arily stable strategy, has been formally interaction at the microbial level. This aefect). By assumption, T > K,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 remained cloud- 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- cooperation which yields S (the sucker's ation from a previously asocial state (12) tain class of chromosomal nondisjunc- payof) or defection which yields P (the and its stable maintenance once estab- tion, exemplified by Down's syndrome. for mutual defection). By lished. A formal theory of cooperation is assumption P > S, so it pays to defect if increasingly needed. The renewed em- the other player defects. Thus, no matter phasis on individualism has 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 rather than the larger value of R that they stability of even mutualistic symbioses things are disproportionally available to both could have gotten had both cooper- appear more questionable than under the cooperating groups. While there are con- ated. Hence the dilemma (17). old view of adaptation for species bene- siderable differences in what is meant by With two individuals destined never to fit. At the same time other cases that the terms "benefits" and "sought," this meet again, the only strategy that 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 kinship theory now begin to reveal rela- a fundamental basis for all social life. always despite the seemingly paradox- tednesses of interactants that are too low The problem is that while an individual ical 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 breeding in (13) and to cooperative exploiting the 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 appearances of co- individuals may interact again, allowing come of inevitable evolutionary trends operation are deceptive-they are cases for complex patterns of strategic interac- through and natural selection: of part-kin altruism and part cheat- tions. in general, and the if the payofs are in terms of fitness, and 27 MARCH 1981 Player B tive to others. A bacterium might easily C D have production of its own bacteriocin Cooperation Defection dependent on the perceived presence of 7 like hostile products in its environment, play"* I R=3 I Fig. 1. The Prisoner's Dilem- C Reward for 1 I ma game. The payoff to player but it could not aim the toxin produced Cooperation mutual cooperation Sucker's payoff A is with toward an offending initiator. From ex- 1 1 numerical values. The game is C------i------+ ' defined by T > R > P > S isting evidence, so far from an individual level, discrimination seems to be by spe- ! T=5 I P=l 1 and R > (S + T)/2. cies rather even than variety. For exam- D ' Temptation to / Punishment for 1 Defection i defect 1 mutual defection I ple, a Rhizobium strain may occur in nodules which it causes on the roots of many species of leguminous , but it may fix nitrogen for the benefit of the in only a few of these species (20). the interactions between pairs of individ- individuals will meet again. Factors that Thus, in many legumes the Khizohium uals are random and not repeated, then affect the magnitude of this probability of seems to be a pure parasite. In the light any population with a mixture of herita- meeting again include the average life- of theory to follow, it would be interest- ble strategies evolves to a state where all span, relative mobility, and health of the ing to know whether these parasitized individuals are 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 Khizohirnm in the surrounding better than others when the population is (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 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 stability is essential to other strategies may be evolutionarily crimination by a Rhizobium seems 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 evolutionarily stable if a population strategy regardless of the behavior of the As one moves up the evolutionary of individuals using 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 behavior becomes 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 stability of 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 strategy can do better with the defecting Before turning to the development of determine the next action as a function individuals than the P achieved by the the theory, let us consider the range of of the interaction so far, a better estimate defecting players who interact with each biological reality that is encompassed by 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 organism does not need a brain ability to distinguish between different tionarily stable strategy. to employ a strategy. Bacteria, for exam- individuals. The discrimination of 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, interactions with many individuals with- previous interactant and remember some 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 cooperation from one individual and the Prisoner's Dilemma with a much richer around them are doing; (iii) these condi- punishing of defection from another. set of possibilities. A strategy would 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 behavior of a Dilemma is much less restricted than it mined the probability of cooperation or bacterium can affect the fitness of other may at first appear. Not only can it apply defection as a function of the history of organisms around it, just as the behavior to interactions between two bacteria or the interaction so far. But if there is a of other organisms can affect the fitness interactions between two primates, but it known number of interactions between a of a bacterium. can also apply to the interactions be- pair of individuals, to defect always is While the strategies can easily include tween a colony of bacteria and, say, a still evolutionarily stable and is still the differential responsiveness to recent primate serving as a . There is no only strategy which is. The reason is that changes in the environment or to cumu- assumption of commensurability of defection on the last interaction would lative averages over time, in other ways payoffs between 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. l), the results of the anal- first interaction. changes, and they probably cannot dis- ysis will be applicable. Our model is based on the more realis- tinguish alternative origins of adverse or The model does assume that the tic assumption that the number of 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- analytic purposes, this is equivalent to a the current interaction the same two teria of the producing strain, but destruc- continuous interactiun over time, with SCIENCE, VOL. 21 1 the time period of the model correspond- winner of the first round, Professor Ana- begins with C, the second round has the ing to the minimum time between a to1 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 . model treats the choices as simulta- were made in the second round identified But such a rule will not do better than neous, it would make little difference if the impressive robustness of TIT FOR TIT FOK 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 cooperation can provocable into retaliation by a defection D, then this first D induces a switch in be conceptualized in 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 I) 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 manifest in 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 maximal to 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 initial D, the game is then reset as for the lished, resist invasion by mutant strate- interacting with each other. This analysis first move; so it must be maximal to gies'? was based on what would happen if each repeat the sequence of DC indefinitely. 3) Initial viability. Even if a strategy is 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 environment which is pre- round in proportion to its success in the rules of behavior for one potentially dominantly noncooperative? previous round. The process was then capable of invading TIT FOR TAT is repeated to generate the time path of the really easier than it seemed: if neither distribution of strategies. The results ALL D nor alternation of 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 strategy can thrive ued to do well with the rules which To see when these strategies can in- in a variegated environment 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 nlh interaction actually occurs is (R.A.) conducted a computer tourna- other rules and went to fixation (24). wn- l . Therefore, the expression for the ment for the Prisoner's Dilemma. The This provides further evidence that TIT total payoff is easily found by applying strategies were submitted by game theo- FOR TAT'S cooperation based on reci- the weights 1, w, w2 . . . to the payoff rists in economics, , political procity is a robust strategy that can sequence and summing the resultant se- science, and mathematics (22). The rules thrive in a variegated environment. ries. When TIT FOR TAT plays another implied the payoff matrix shown in Fig. I 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 + W*R 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 Ton the first robin tournament. 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 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 long run. However, the possible mutant strategy provided that result of the tournament was that the the individuals who interact have a suffi- 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 cooperating on the first move and As a first step in the proof we note that then doing whatever the 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 sufficient to reset of w, we find that neither of these two on reciprocity. the situation as it was at the beginning of strategies (and hence no strategy at all) The results of the first round were then the game. Likewise, one D sets the situa- can invade TIT FOR TAT if and only if circulated and 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 2 (T - R)I(T - P) and entries from six countries (23). Most of there is a fixed chance, w, of the interac- w 2 (T - R)I(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 demonstrates that TIT FOR TAT is evolutionary biology, 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 thing both at the first occurrence of interactions between the individuals plines represented in the first round. TIT a given state and at each resetting to 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 Initial Viability cooperation based on reciprocity can strategy like 'SIT 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 population with no relatedness at all. teresting asymmetry here. Let us define that can be evolutionarily stable. In fact, A case of cooperation that fits this a nice strategy as one, such as TIT FOR ALL D is evolutionarily stable no matter scenario, at least on first evidence, has TAS, 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 roughly may be said to take turns at an individual can get when interacting the first place. being the high investment partner (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 plausible escape from the equilibrium of viding sperm to fertilize eggs). Up to ten and is evolutionarily stable, it cannot be ALL D. Close relatedness of interac- spawnings occur 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 individual for 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 appears to allow the average of how it does with others of its when the conditions of cost, benefit, and evolution of 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-causing genes that are resident in the that the testis condition may have equal to the score achieved by the pre- related individuals (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- truism of a kind (the individual is forego- ing would imply relatedness in the pairs riving in a cluster cannot intrude on the ing proceeds that might have 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 cooperation un- to make TIT FOR TAT an evolutionarily recalculation of the payoff matrix in such needful of relatedness. stable strategy it can resist intrusion by a way that an individual has a part inter- Another mechanism that can get coop- any cluster of any other strategy. The est in the partner's gain (that is, reckon- eration started when virtually everyone gear wheels of social evolution have a ing payoffs in terms of ) is using ALL D is clustering. Suppose ratchet. can often eliminate the inequalities that a small group of individuals is using The chronological story that emerges 7' > 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 certain proportion, 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 members of the cluster. Then the invasion of any strategy that has oner's Dilemma-like situations 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 gards pairs, a parent and its off'spring or a mechanisms. First, there can be kinship plR!(l - w)l pair of siblings would be especially + between mutant strategies, giving the (I - p)[S wP!(l - w)] promising, and in fact many examples of + genes of the mutants some stake in each cooperation or restraint of 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 cooperative behavior on cues in the (1 - w). When p and MJ are large mechanism to overcome total defection environment (4). Such factors as promis- enough, a cluster of TI'S 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 uncertain relatedness among potential whelmingly of ALL D (19). even if they are so few as to provide a interactants. The recognition of 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 SCIENCI- VOL ?I I started in a predominantly noncoopera- All progeny of the then perish. show much more aggressive reactions tive world, can thrive in a variegated Another mechanism to 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 pairing of 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 individuals if dis- Applications isms in which a small fish or a crustacean crimination can cover a wide variety of removes and eats ectoparasites from 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 approach follows from two mouth) of a larger fish which is its poten- this ability is well developed, and is of the requirements for the evolution of tial predator. These aquatic cleaner mu- largely based on the recognition of Faces. cooperation. The basic idea is that an tualisms occur in coastal and reef situa- The extent to which this function has individual must 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- ranges or territories (4, 5). They seem to brain disorder called prosopagnosia. A uals being able to retaliate effectively be unknown in the free-mixing circum- normal person can name someone from (29). The response requires that the de- stances of the open sea. facial features alone, even if the features fecting individual not be lost in an anony- Other mutualisms are also characteris- have changed substantially over the mous sea of others. Higher organisms tic of situations where continued associ- years. People with prosopagnosia are not avoid this problem by their well-devel- ation is likely, and normally they involve able to make this association, but have oped ability to recognize many different quasi-permanent pairing of individuals or 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 organisms must rely on mechanisms that individuals with such stocks (7,31). Con- field. The lesions responsible for proso- drastically limit the number of different versely, conditions of free-mixing and pagnosia occur in an identifiable part of individuals or colonies with which they transitory pairing conditions where rec- the brain: the underside of both occipital can interact effectively. 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- surface of the temporal lobes. This local- effective is that the probability, w, of the ism, disease, and the like. Thus, whereas i~ationof cause, and specificity of effect, same two individuals' meeting again ant colonies participate in many sym- indicates that the recognition of individ- must be sufficiently high. bioses and are sometimes largely depen- ual faces has been an important enough When an organism is 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's resources to be devoted to it (35). prior interaction, a substitute mechanism 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 interactant is invaluable in extend- tions are with the same interactant. This water animal Chlorohydru viridissima ing the range of stable cooperation, the can be done by maintaining continuous has a permanent stable association with ability to monitor cues for the likelihood contact with the other. This method is green algae that are always naturally of continued interaction is helpful as an applied in most interspecies , found in its tissues and are very difficult indication of when reciprocal cooper- whether a hermit crab 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 transmitted to new generations by way when the value of w falls below the microorganismic colonies housed in its of the egg. Hydru vulguris and H. atten- threshold for stability given in condition body, or a tree and its mycorrhizal fungi. uutu also associate with algae but do not (I), it will no longer pay to reciprocate The ability of such partners to respond have egg transmission. In these species it the other's cooperation. Illness in one specifically to defection is not known but is said that " is preceded by partner leading to reduced viability seems posible. A host that carries enfeeblement of the animals and is ac- would be one detectable sign of declining symbionts often carries several kinds companied by pathological symptoms in- w. Both animals in a partnership would (for example, yeasts and bacteria). Dif- dicating a definite 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 partner would 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 probability of future retaliation against a particular exploita- discriminate between other members of interaction becomes small enough. tive colony. Where host and colony are the same species, reciprocal cooperation These mechanisms could operate even not permanently paired, a method for can be stable with the aid of a mecha- at the microbial level. Any symbiont that immediate drastic retaliation is some- nism that reduces the amount of dis- still has a transmission "horizontally" times apparent instead. This is so with crimination necessary. Philopatry in gen- (that is, infective) as well as vertically fig wasps. By nature of their remarkable eral and territoriality in 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 territories means that there are two quite pected to shift from mutualism to para- gamete. Through the extreme protogyny dilferent kinds of interaction: those in sitism when the probability of continued and simultaneity in flowering, fig wasps neighboring territories where the prob- interaction with the host lessened. In the cannot remain with a single tree. It turns ability of interaction is high, and strang- more parasitic phase it could exploit the out in many cases that if a ers whose probability of 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 parasitic infection that threatened death, 27 MARCH 1981 or when it manifested signs of age. In ally stand to gain by steadily cooperating rionary Approach, J. Krebs and N. Davies, E~S. fact, bacteria that are normal and seem- in a diploid organism, the situation in ~",~~;.,"w~~';~)~~$bf~~8Q:!&::;$$., B. ingly harmless or even beneficial in the oogenesis is a Prisoner's Dilemma: a 14. A. H. Harcourt, Z.fierpsychol. 48, 401 (1978); C. Packer, Anim. Rehov. 27, 1 (1979); K. W. gut can be found contributing to sepsis in chromosome which can be "first to de- Wrangham, SOc, Sci, Infb. 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, Nrtrure (London) 276, 496 (1978). (implying a severe wound) (36). And rather than the polar body. We may 16. A. kapoport and A. M. Chammah, Prisonerrs normal inhabitants of the body surface hypothesize that such an action triggers ~)ilemhu(Univ. of Michigan Press, Ann Arbor, 1965). There are many other patterns of interac- (like Candida alhicans) can become in- similar attempts by the homolog in sub- tion which allow gains for cooperation. See for example the model of intraspecific combat in J. vasive and dangerous in either sick or sequent meioses, and when both mem- Maynard Smith and G. K. Price, in (11). elderly persons. bers of a homologous pair try it at once, 17. The condition that R > (S t n12 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 Mun and Bertst: ('ornpclru- cancer, insofar as it turns out to be due ness of the bearers of extra chromo- rive Sociul Behuvior (Smithsonian Press, Wash- to viruses potentially latent in the somes is generally extremely low, but a ington, 1971), p. 57. K.M. Fagen [in (31 shows some conditions for single encounters where genome (37). Cancers do tend to have chromosome which lets itself be sent to defection is not the solution. 19. For a formal proof, see K. Axelrod, Am. Politi- their onset at ages when the chances of the polar body makes a fitness contribu- cal Sci. Rcv., in press. For related results on the vertical transmission are rapidly declin- tion of zero. Thus P > S holds. For the potential stability of cooperative behavior see K. D. Luce and H. KaiEa, Gumes und Decisions ing (38). One oncogenic virus, that of model to work, an incident of "defec- (Wiley, New York, 1957). p. 102; M. Taylor, Burkitt's lymphoma, does not have ver- tion" in one developing egg would have Anarchy und C:ooperrction (Wiley, New York, 1976); M. Kurz, in Econornic Progress. Privutc tical transmission but may have alterna- to be perceptible by others still waiting. Vrtlues clnci Public Policy, B. Balassa and K. tives of slow or fast production of infec- That this would occur is pure specula- Nelson, Eds. (North-Holland, Amsterdam, 1977). D. 177. tious propagules. The slow form appears tion, as is the feasibility of self-promot- 20. M. ~lexander,Microhicll (Wiley, New York, 1971). as a chronic mononucleosis, the fast as ing behavior by chromosomes during a 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 sufl- ciently high. In the case of sequential moves, phoma (39). The point of interest is that, not seem inconceivable: a bacterium, suppose there is a fixed chance, p, that a given as some evidence suggests, lymphoma after all, with its single chromosome, can interactant of the pair will he the next one to need help. The critical value of w can be shown can be triggered by the host's contract- do complex conditional things. Given to be the minimum of the two side's value of A/ ing malaria. The lymphoma grows ex- such effects, our model would explain p(A + H) where A is the cost of giving assist- ance, and H is the benefit of assistance when tremely fast and so can probably com- the much greater incidence of abnormal received. See also P. K. Thompson, Soc. SC;. Injo. 19, 341 (1980). pete with malaria for transmission (pos- chromosome increase in eggs (and not 22. K. Axelrod, J. ('onjlict Resolution 24, 3 (1980). sibly by mosquitoes) before death re- sperm) with parental age. 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- simultaneous infection 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 strains of Conclusion matched in five games (24). the same one, our theory may have rel- 24. K. Axelrod, J. Conflict Resollition 24, 379 (1980). evance more generally to whether a dis- Darwin's emphasis on individual ad- 25. K. A. Fisher, The Gmericrtl Theory ofNrtturrt1 Selection (Oxford Univ. Press, Oxford, 1930); J. ease will follow a slow, joint-optimal vantage has been formalized in terms of B. S. Haldane, Nrtrure (Loncion) New Hiol. 18, exploitation course ("chronic" for the game theory. This establishes conditions 34 (1955); W. D. Hamilton, Am. Nut. 97, 354 (1963). host) or a rapid severe exploitation under which cooperation based on reci- 26. M. J. Wade and F. Breden, Behuv. Ecol. Socio- ("acute" for the host). With single infec- procity can evolve. biol, in press. 27. K. D. Alexander, Annu. Rev. Ecol. Syst. 5, 325 tion the slow course would be expected. \.,'11474) .,. With double infection, crash exploitation References and Notes 28. E. Fischer, Anim. Hehuv. 28, 620 (1980); E. G. Lei~h.Jr.. Proc. Nutl. Accld. Sci. U.S.A. 74. might, as dictated by implied payoff 1. G. C. Williams, Adupturions and Nuturul Selec- 4542 (1977). tion (Princeton Univ. Press, Princeton, 1966); 29. For economic theory on this point see G. Aker- functions, begin immediately, or have W. D. Hamilton, in Hisociul Anthropology, K. lof, Q. J. Econ. 84,488 (1970); M. K.Darby and onset later at an appropriate stage of Fox, Ed. (Malaby, London, 1975), p. 133. E. Karni, J. I.rtw Econ. 16, 67 (1973); 0. E. 2. For the best recent case for effective selection at Williamson. Mrtrkers and Hierrtrchies (Free senescence (40). group levels and for altruism based on genetic Press, ~ewYork, 1975). Our model (with symmetry of the two correction of non-kin interactants see D. S. 30. P. Buchner, Endosyrnbiosis oj Animals with Wilson, Nuturrtl Selection of Populutions and Plunt Microor~unisrns (Interscience. New parties) could also be tentatively applied ('ornmuniries (BenjaminICummings, Menlo York, 1965). to the increase with maternal age of Park, Calif., 1979). 31. W. D. Hamilton, in Diversity oflnsect Fuunus, 3. W. D. Hamilton, J. Theoret. Hiol. 7, 1 (1964). L. A. Mound and N. Waloff. Eds. (Blackwell. chromosomal nondisjunction during 4. K. Trivers, Q. Rev. Hiol. 46, 35 (1971). Oxford, 1978). 5. For additions to the theory of biological cooper- 32. E. 0. Wilson, The Insect Societies (Bellknap, ovum formation (oogenesis) (41). This ation see I. D. Chase [Am. Nrtt. 115, 827 (1980)j. Cambridge, Mass., 1971); M. Treisman, Anim. effect leads to various conditions of se- R. M. Fagen [ibid., p. 858 (1980)], and S. A. Hehav. 28, 31 1 (1980). Boorman and P. R. Levitt [The Genetics of 33. C. M. Yonge [Nature (I.ondon) 134, 12 (197911 verely handicapped ofspring, Down's Altruisrn (Academic Press, New York, 1980)J. gives other examples of invertebrates with unl- syndrome (caused by an extra copy of 6. K. Dawkins, The SeEsh Gene (Oxford Univ. cellular algae. Press, Oxford, 1976). 34. E. 0. Wilson, (Harvard Univ. chromosome 21) being the most familiar 7. W. D. Hamilton, Annu. Rev. Ecol. Syst. 3, 193 Press, Cambridge, Mass., 1975), p. 273. example. It depends almost entirely on (1972). 35. N. Geschwind, Sci. Am. 241, (No. 3), 180 8. D. H. Janzen, Evolution 20, 249 (1966). /\""I.1470~ failure of the normal separation of the 9. J. T. Wiebes, Grtrd. Bull. (Singrtpore) 29, 207 36. D. C. Savage, In Microbial Ecology ofthe Gut, (1976); D. H. Janzen, Annu. Rev. Ecol. Syst. 10, K. T. J. Clarke and T. Baucho~.Eds. (Academic paired chromosomes in the mother, and 31 (1979). Press, New York, 1977). p. 3b0. this suggests the possible connection 10. M. Caullery, Purrtsitism clnci 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 svmhioses. For the examole of waso-ant 39. W. Henle. G. Henle. E. T. Lenette. Sci. Am. symbiosk, see (7). 241 (No. I), 48 (1979). are characteristically unsymmetrical, ll. J. Maynard Smith and G. K. Price, Nuturv 40. See also 1. Eshel, Theoret. Pop. Hiol. 11, 410 with rejection (as a so-called polar body) (Londqn)246, 15 (1973); J. Maynard Smith and (1977) for a related possible implication of multi- G. A. Parker, Anim. Hehav. 24, 159 (1976); G. clonal infection. of chromosomes that go to the unlucky A. Parker, Nuturv (I.ondon) 274, 849 (1978). 41. C. Stern, Principles oj H~imclnGenetics (12ree- 12. J. Elster, U1ysse.s unci the Sirens (Cambridge man, San Francisco, 1973). pole of the cell. It seems possible that, Univ. Press, London, 1979). 42. For helpful suggestions we thank Robert Boyd, while homologous chromosomes gener- 13. S. T. Emlen, in Behuvic)rul Ecology: An Evolu- Michael Cohen, and . 1396 SCIENCE. VOI.. ?I I http://www.jstor.org

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You have printed the following article: The Evolution of Cooperation Robert Axelrod; William D. Hamilton Science, New Series, Vol. 211, No. 4489. (Mar. 27, 1981), pp. 1390-1396. Stable URL: http://links.jstor.org/sici?sici=0036-8075%2819810327%293%3A211%3A4489%3C1390%3ATEOC%3E2.0.CO%3B2-6

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4 The Evolution of Robert L. Trivers The Quarterly Review of Biology, Vol. 46, No. 1. (Mar., 1971), pp. 35-57. Stable URL: http://links.jstor.org/sici?sici=0033-5770%28197103%2946%3A1%3C35%3ATEORA%3E2.0.CO%3B2-S

5 Cooperative and Noncooperative Behavior in Animals Ivan D. Chase The American Naturalist, Vol. 115, No. 6. (Jun., 1980), pp. 827-857. Stable URL: http://links.jstor.org/sici?sici=0003-0147%28198006%29115%3A6%3C827%3ACANBIA%3E2.0.CO%3B2-Z

7 Altruism and Related Phenomena, Mainly in Social W. D. Hamilton Annual Review of Ecology and , Vol. 3. (1972), pp. 193-232. Stable URL: http://links.jstor.org/sici?sici=0066-4162%281972%293%3C193%3AAARPMI%3E2.0.CO%3B2-V

8 of Mutualism Between Ants and Acacias in Central America Daniel H. Janzen Evolution, Vol. 20, No. 3. (Sep., 1966), pp. 249-275. Stable URL: http://links.jstor.org/sici?sici=0014-3820%28196609%2920%3A3%3C249%3ACOMBAA%3E2.0.CO%3B2-%23

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9 How to be a Fig Daniel H. Janzen Annual Review of Ecology and Systematics, Vol. 10. (1979), pp. 13-51. Stable URL: http://links.jstor.org/sici?sici=0066-4162%281979%2910%3C13%3AHTBAF%3E2.0.CO%3B2-K

10 Altruism and Related Phenomena, Mainly in Social Insects W. D. Hamilton Annual Review of Ecology and Systematics, Vol. 3. (1972), pp. 193-232. Stable URL: http://links.jstor.org/sici?sici=0066-4162%281972%293%3C193%3AAARPMI%3E2.0.CO%3B2-V

18 Cooperative and Noncooperative Behavior in Animals Ivan D. Chase The American Naturalist, Vol. 115, No. 6. (Jun., 1980), pp. 827-857. Stable URL: http://links.jstor.org/sici?sici=0003-0147%28198006%29115%3A6%3C827%3ACANBIA%3E2.0.CO%3B2-Z

25 The Evolution of Altruistic Behavior W. D. Hamilton The American Naturalist, Vol. 97, No. 896. (Sep. - Oct., 1963), pp. 354-356. Stable URL: http://links.jstor.org/sici?sici=0003-0147%28196309%2F10%2997%3A896%3C354%3ATEOAB%3E2.0.CO%3B2-8

27 The Evolution of Social Behavior Richard D. Alexander Annual Review of Ecology and Systematics, Vol. 5. (1974), pp. 325-383. Stable URL: http://links.jstor.org/sici?sici=0066-4162%281974%295%3C325%3ATEOSB%3E2.0.CO%3B2-D

28 How Does Selection Reconcile Individual Advantage with the Good of the Group? Egbert G. Leigh Proceedings of the National Academy of Sciences of the United States of America, Vol. 74, No. 10. (Oct., 1977), pp. 4542-4546. Stable URL: http://links.jstor.org/sici?sici=0027-8424%28197710%2974%3A10%3C4542%3AHDSRIA%3E2.0.CO%3B2-9

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29 The Market for "Lemons": Quality Uncertainty and the Market Mechanism George A. Akerlof The Quarterly Journal of Economics, Vol. 84, No. 3. (Aug., 1970), pp. 488-500. Stable URL: http://links.jstor.org/sici?sici=0033-5533%28197008%2984%3A3%3C488%3ATMF%22QU%3E2.0.CO%3B2-6

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