Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game

Understanding the mechanisms that can lead to the evolution of cooperation through natural selection is a core problem in biology. Among the various attempts at constructing a theory of cooperation, game theory has played a central role. Here, we review models of cooperation that are based on two simple games: the Prisoner's Dilemma, and the Snowdrift game. Both games are two‐person games with two strategies, to cooperate and to defect, and both games are social dilemmas. In social dilemmas, cooperation is prone to exploitation by defectors, and the average payoff in populations at evolutionary equilibrium is lower than it would be in populations consisting of only cooperators. The difference between the games is that cooperation is not maintained in the Prisoner's Dilemma, but persists in the Snowdrift game at an intermediate frequency. As a consequence, insights gained from studying extensions of the two games differ substantially. We review the most salient results obtained from extensions such as iteration, spatial structure, continuously variable cooperative investments, and multi‐person interactions. Bridging the gap between theoretical and empirical research is one of the main challenges for future studies of cooperation, and we conclude by pointing out a number of promising natural systems in which the theory can be tested experimentally.     

Cognitive cooperation

Cooperation can evolve in the context of cognitive activities such as perception, attention, memory, and decision making, in addition to physical activities such as hunting, gathering, warfare, and childcare. The social insects are well known to cooperate on both physical and cognitive tasks, but the idea of cognitive cooperation in humans has not received widespread attention or systematic study. The traditional psychological literature often gives the impression that groups are dysfunctional cognitive units, while evolutionary psychologists have so far studied cognition primarily at the individual level. We present two experiments that demonstrate the superiority of thinking in groups, but only for tasks that are sufficiently challenging to exceed the capacity of individuals. One of the experiments is in a brain-storming format, where advantages of real groups over nominal groups have been notoriously difficult to demonstrate. Cognitive cooperation might often operate beneath conscious awareness and take place without the need for overt training, as evolutionary psychologists have stressed for individual-level cognitive adaptations. In general, cognitive cooperation should be a central subject in human evolutionary psychology, as it already is in the study of the social insects. David Sloan Wilson is an evolutionary biologist interested in a broad range of issues relevant to human behavior. He has published in psychology, anthropology, and philosophy journals in addition to his mainstream biological research. He is author of Darwin’s Cathedral: Evolution, Religion, and the Nature of Society (University of Chicago Press, 2002) and co-author with philosopher Elliott Sober of Unto Others: The Evolution and Psychology of Unselfish Behavior (Harvard University Press, 1998). John J. Timmel received his Ph.D. from Binghamton University in 2001. Ralph R. Miller is Distinguished Professor of Psychology at Binghamton University. His research interests include information processing in animals, with an emphasis on elementary, evolutionarily derived, fundamentals of learning and memory that might be expected to generalize across species, including humans.     

Evolution of cooperation: cooperation defeats defection in the cornfield model

"Cooperation" defines any behavior that enhances the fitness of a group (e.g. a community or species), but which, by its nature, can be exploited by selfish individuals, meaning, firstly, that selfish individuals derive an advantage from exploitation which is greater than the average advantage that accrues to unselfish individuals. Secondly, exploitation has no intrinsic fitness value except in the presence of the "cooperative behavior". The mathematics is described by the simple Prisoner's Dilemma Game (PDG). It has previously been shown that koinophilia (the avoidance of sexual mates displaying unusual or atypical phenotypic features, such as mutations) stabilizes any inherited strategy in the simple or iterated PDG, meaning that it cannot be displaced by rare forms of alternative behavior which arise through mutation or occasional migration. In the present model equal numbers of cooperators and defectors (in the simple PDG) were randomly spread in a two-dimensional "cornfield" with uniformly distributed resources. Every individual was koinophilic, and interacted (sexually and in the PDG tournaments) only with individuals from within its immediate neighborhood. This model therefore tested whether cooperation can outcompete defection or selfishness in a straight, initially equally matched, evolutionary battle. The results show that in the absence of koinophilia cooperation was rapidly driven to extinction. With koinophilia there was a very rapid loss of cooperators in the first few generations, but thereafter cooperation slowly spread, ultimately eliminating defection completely. This result was critically dependent on sampling effects of neighborhoods. Small samples (resulting from low population densities or small neighborhood sizes) increase the probability that a chance neighborhood comes to consist predominantly of cooperators. A sexual preference for the most common phenotype in the neighborhood then makes that phenotype more common still. Once this occurs cooperation's spread becomes almost inevitable.     

The evolution of cooperation

Darwin recognized that natural selection could not favor a trait in one species solely for the benefit of another species. The modern, selfish-gene view of the world suggests that cooperation between individuals, whether of the same species or different species, should be especially vulnerable to the evolution of noncooperators. Yet, cooperation is prevalent in nature both within and between species. What special circumstances or mechanisms thus favor cooperation? Currently, evolutionary biology offers a set of disparate explanations, and a general framework for this breadth of models has not emerged. Here, we offer a tripartite structure that links previously disconnected views of cooperation. We distinguish three general models by which cooperation can evolve and be maintained: (i) directed reciprocation--cooperation with individuals who give in return; (ii) shared genes--cooperation with relatives (e.g., kin selection); and (iii) byproduct benefits--cooperation as an incidental consequence of selfish action. Each general model is further subdivided. Several renowned examples of cooperation that have lacked explanation until recently--plant-rhizobium symbioses and bacteria-squid light organs--fit squarely within this framework. Natural systems of cooperation often involve more than one model, and a fruitful direction for future research is to understand how these models interact to maintain cooperation in the long term.     

Spatial invasion of cooperation

The evolutionary puzzle of cooperation describes situations where cooperators provide a fitness benefit to other individuals at some cost to themselves. Under Darwinian selection, the evolution of cooperation is a conundrum, whereas non-cooperation (or defection) is not. In the absence of supporting mechanisms, cooperators perform poorly and decrease in abundance. Evolutionary game theory provides a powerful mathematical framework to address the problem of cooperation using the prisoner's dilemma. One well-studied possibility to maintain cooperation is to consider structured populations, where each individual interacts only with a limited subset of the population. This enables cooperators to form clusters such that they are more likely to interact with other cooperators instead of being exploited by defectors. Here we present a detailed analysis of how a few cooperators invade and expand in a world of defectors. If the invasion succeeds, the expansion process takes place in two stages: first, cooperators and defectors quickly establish a local equilibrium and then they uniformly expand in space. The second stage provides good estimates for the global equilibrium frequencies of cooperators and defectors. Under hospitable conditions, cooperators typically form a single, ever growing cluster interspersed with specks of defectors, whereas under more hostile conditions, cooperators form isolated, compact clusters that minimize exploitation by defectors. We provide the first quantitative assessment of the way cooperators arrange in space during invasion and find that the macroscopic properties and the emerging spatial patterns reveal information about the characteristics of the underlying microscopic interactions.     

Signaling without cooperation

Ethological theories usually attribute semantic content to animal signals. To account for this fact, many biologists and philosophers appeal to some version of teleosemantics. However, this picture has recently came under attack: while mainstream teleosemantics assumes that representational systems must cooperate, some biologists and philosophers argue that in certain cases signaling can evolve within systems lacking common interest. In this paper I defend the standard view from this objection.     

When cooperation begets cooperation: the role of key individuals in galvanizing support

Life abounds with examples of conspecifics actively cooperating to a common end, despite conflicts of interest being expected concerning how much each individual should contribute. Mathematical models typically find that such conflict can be resolved by partial-response strategies, leading investors to contribute relatively equitably. Using a case study approach, we show that such model expectations can be contradicted in at least four disparate contexts: (i) bi-parental care; (ii) cooperative breeding; (iii) cooperative hunting; and (iv) human cooperation. We highlight that: (a) marked variation in contributions is commonplace; and (b) individuals can often respond positively rather than negatively to the contributions of others. Existing models have surprisingly limited power in explaining these phenomena. Here, we propose that, although among-individual variation in cooperative contributions will be influenced by differential costs and benefits, there is likely to be a strong genetic or epigenetic component. We then suggest that selection can maintain high investors (key individuals) when their contributions promote support by increasing the benefits and/or reducing the costs for others. Our intentions are to raise awareness in—and provide testable hypotheses of—two of the most poorly understood, yet integral, questions regarding cooperative ventures: why do individuals vary in their contributions and when does cooperation beget cooperation?     

The hard problem of cooperation

Based on individual variation in cooperative inclinations, we define the “hard problem of cooperation” as that of achieving high levels of cooperation in a group of non-cooperative types. Can the hard problem be solved by institutions with monitoring and sanctions? In a laboratory experiment we find that the answer is affirmative if the institution is imposed on the group but negative if development of the institution is left to the group to vote on. In the experiment, participants were divided into groups of either cooperative types or non-cooperative types depending on their behavior in a public goods game. In these homogeneous groups they repeatedly played a public goods game regulated by an institution that incorporated several of the key properties identified by Ostrom: operational rules, monitoring, rewards, punishments, and (in one condition) change of rules. When change of rules was not possible and punishments were set to be high, groups of both types generally abided by operational rules demanding high contributions to the common good, and thereby achieved high levels of payoffs. Under less severe rules, both types of groups did worse but non-cooperative types did worst. Thus, non-cooperative groups profited the most from being governed by an institution demanding high contributions and employing high punishments. Nevertheless, in a condition where change of rules through voting was made possible, development of the institution in this direction was more often voted down in groups of non-cooperative types. We discuss the relevance of the hard problem and fit our results into a bigger picture of institutional and individual determinants of cooperative behavior.     

The origins of human cooperation

Bowles and Gintis argue that recent work in behavioural economics shows that humans have other-regarding preferences, i.e., are not purely self-interested. They seek to explain how these preferences may have evolved using a multi-level version of gene-culture coevolutionary theory. In this review essay I critically examine their main arguments.     

The paradox of cooperation benefits

It seems obvious that as the benefits of cooperation increase, the share of cooperators in the population should also increase. It is well known that positive assortment between cooperative types, for instance in spatially structured populations, provide better conditions for the evolution of cooperation than complete mixing. This study demonstrates that, assuming positive assortment, under most conditions higher cooperation benefits also increase the share of cooperators. On the other hand, under a specified range of payoff values, when at least two payoff parameters are modified, the reverse is true. The conditions for this paradox are determined for two-person social dilemmas: the Prisoner's Dilemma, the Hawks and Doves game, and the Stag Hunt game, assuming global selection and positive assortment.