Emergence of Fairness in Repeated Group Interactions
ABSTRACT Often groups need to meet repeatedly before a decision is reached. Hence, most individual decisions will be contingent on decisions taken previously by others. In particular, the decision to cooperate or not will depend on one's own assessment of what constitutes a fair group outcome. Making use of a repeated N-person prisoner's dilemma, we show that reciprocation towards groups opens a window of opportunity for cooperation to thrive, leading populations to engage in dynamics involving both coordination and coexistence, and characterized by cycles of cooperation and defection. Furthermore, we show that this process leads to the emergence of fairness, whose level will depend on the dilemma at stake.
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ABSTRACT: In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.Journal of Theoretical Biology 12/2013; 346. DOI:10.1016/j.jtbi.2013.12.016 · 2.30 Impact Factor
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ABSTRACT: The social brain hypothesis states that selection pressures associated with complex social relationships have driven the evolution of sophisticated cognitive processes in primates. We investigated how the size of cooperative primate communities depends on the memory of each of its members and on the pressure exerted by natural selection. To this end we devised an evolutionary game theoretical model in which social interactions are modelled in terms of a repeated Prisoner's Dilemma played by individuals who may exhibit a different memory capacity. Here, memory is greatly simplified and mapped onto a single parameter m describing the number of conspecifics whose previous action each individual can remember. We show that increasing m enables cooperation to emerge and be maintained in groups of increasing sizes. Furthermore, harsher social dilemmas lead to the need for a higher m in order to ensure high levels of cooperation. Finally, we show how the interplay between the dilemma individuals face and their memory capacity m allows us to define a critical group size below which cooperation may thrive, and how this value depends sensitively on the strength of natural selection.Animal Behaviour 01/2013; 85(1):233–239. DOI:10.1016/j.anbehav.2012.10.030 · 3.07 Impact Factor
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ABSTRACT: When members of a population engage in dyadic interactions reﬂecting a prisoner’s dilemma game, the evolutionary dynamics depends crucially on the population structure, described by means of graphs and networks. Here, we investigate how selection pressure contributes to change the fate of the population. We ﬁnd that homogeneous networks, in which individuals share a similar number of neighbors, are very sensitive to selection pressure, whereas strongly heterogeneous networks are more resilient to natural selection, dictating an overall robust evolutionary dynamics of coordination. Between these extremes, a whole plethora of behaviors is predicted, showing how selection pressure can change the nature of dilemmas populations effectively face. We further show how the present results for homogeneous networks bridge the existing gap between analytic predictions obtained in the framework of the pairapproximation from very weak selection and simulation results obtained from strong selection.New Journal of Physics 07/2012; 14(7):073035. DOI:10.1088/1367-2630/14/7/073035 · 3.67 Impact Factor