REVIEWS ANDSYNTHESESModels of cooperation based on the Prisoner’sDilemma and the Snowdrift gameMichael Doebeli1* andChristoph Hauert21Department of Zoology andDepartment of Mathematics,University of British Columbia,6270 University Boulevard,Vancouver, BC, Canada2Program for EvolutionaryDynamics, Harvard University,One Brattle Square, Cambridge,MA 02138, USA*Correspondence: E-mail:[email protected] the mechanisms that can lead to the evolution of cooperation throughnatural selection is a core problem in biology. Among the various attempts atconstructing a theory of cooperation, game theory has played a central role. Here, wereview models of cooperation that are based on two simple games: the Prisoner’sDilemma, and the Snowdrift game. Both games are two-person games with twostrategies, to cooperate and to defect, and both games are social dilemmas. In socialdilemmas, cooperation is prone to exploitation by defectors, and the average payoff inpopulations at evolutionary equilibrium is lower than it would be in populationsconsisting of only cooperators. The difference between the games is that cooperation isnot maintained in the Prisoner’s Dilemma, but persists in the Snowdrift game at anintermediate frequency. As a consequence, insights gained from studying extensions ofthe two games differ substantially. We review the most salient results obtained fromextensions such as iteration, spatial structure, continuously variable cooperativeinvestments, and multi-person interactions. Bridging the gap between theoretical andempirical research is one of the main challenges for future studies of cooperation, and weconclude by pointing out a number of promising natural systems in which the theory canbe tested experimentally.KeywordsContinuous games, evolution of cooperation, game theory, iterated games, spatiallystructured, populations, Tragedy of the Commune.Ecology Letters (2005) 8: 748–766INTRODUCTIONCooperation is ubiquitous in biological systems, and so is itsexploitation. Cooperation is a conundrum, whereas itsexploitation is not, at least not at first sight. Cooperativeentities make a sacrifice: they help others at a cost tothemselves. Exploiters, or cheaters, reap the benefits andforego costs. Based on utilitarian principles – be it in theform of evolution by natural selection of the ÔfittestÕ type, orin the form of ÔrationalÕ behaviour generating the highestpayoff – exploitation should prevail, and cooperation shouldbe rare.Yet the history of life on Earth could not have unfoldedwithout the repeated cooperative integration of lower levelentities into higher level units. Thus, major evolutionarytransitions (Maynard Smith & Szathma´ry 1995), such as theevolution of chromosomes out of replicating DNAmolecules, the transition from uni-cellular to multi-cellularorganisms, or the origin of complex ecosystems, could nothave occurred in the absence of cooperative interactions.Similarly, the emergence of complex animal and humansocieties requires cooperation (Maynard Smith & Szathma´ry1995; Crespi & Choe 1997; Dugatkin 1997).Since its invention by von Neumann & Morgenstern(1944), the mathematical framework of game theory hasbeen a central tool for understanding how cooperativeentities can overcome the obvious fitness and payoffdisadvantages and persist in the face of cheating andexploitation. Game theory embodies the concept offrequency dependent selection, which is at the heart of theproblem of cooperation, because the actual costs ofcooperation ultimately depend on the type of individuals acooperator interacts with. Maynard Smith & Price (1973)ingeniously related the economic concept of payofffunctions with evolutionary fitness, thus marking the adventof an entirely new approach to behavioural ecology thatinspired numerous theoretical and empirical investigations.In particular, evolutionary game theory has been usedEcology Letters, (2005) 8: 748–766 doi: 10.1111/j.1461-0248.2005.00773.x2005 Blackwell Publishing Ltd/CNRSextensively to study the problem of cooperation (Nowak &Sigmund 2004).These attempts go back to a seminal paper by Trivers(1971), in which he introduced the notion of reciprocalaltruism. This notion embodies the idea that cooperationmay evolve in a context in which future behaviour may bedetermined by current payoffs. Reciprocal altruism wasfamously embedded into evolutionary game theory byAxelrod & Hamilton (1981). Their models are based onthe Prisoner’s Dilemma game (PD), perhaps the single mostfamous metaphor for the problem of cooperation (Box 1).In this game, natural selection favours defection and therebycreates a social dilemma (Dawes 1980), because wheneverybody defects, the mean population payoff is lower thanif everybody had cooperated. In the past two decades, it hasbeen a major goal of theoretical biology to elucidate themechanisms by which this dilemma can be resolved.The social dilemma of the PD can be relaxed by assumingthat cooperation yields a benefit that is accessible to bothinteracting players, and that costs are shared betweencooperators. This results in the so-called Snowdrift game(SD), which is also known as the Hawk-Dove game, or theChicken game (Maynard Smith 1982; Sugden 1986, Box 1). Itsessential ingredient is that in contrast to the PD, cooperationhas an advantage when rare, which implies that the replicatordynamics (Taylor & Jonker 1978; Hofbauer & Sigmund 1998)of the SD converges to a mixed stable equilibrium at whichboth C and D strategies are present. Starting with MaynardSmith & Price (1973), the SD (or Hawk-Dove game) has beenwell studied in the context of competition and escalation inanimal conflicts, but its role as a simple metaphor in thebroader context of the evolution of cooperation has beenmuch less emphasized. In spite of this, we think that the SDmay actually be widely applicable in natural systems.Here we review models of cooperation that are based onthe PD and SD games. Since the dynamics of these models iseasily understood (Box 1), studying suitable extensions canreveal mechanisms by which cooperation can either beenhanced or reduced as compared with the baseline models.In particular, since the PD does not allow for cooperation, anyextensions that do can be viewed as representing mechanismsthat promote cooperation. The essential feature of anymechanism to promote cooperation is that cooperative actsmust occur more often between cooperators than expectedbased on population