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.
"Moreover, because the gain sequences of these games have at most two sign changes, our characterization results provide all the information necessary to recover the results on the number and stability of rest points obtained in previous studies. We demonstrate these claims for two classes of public goods games, namely threshold games (e.g., Dugatkin, 1990; Weesie and Franzen, 1998; Zheng et al., 2007; Souza et al., 2009) and constant cost games (e.g., Motro, 1991; Bach et al., 2006; Hauert et al., 2006; Pacheco et al., 2009; Archetti and Scheuring, 2011), and two additional examples taken from Hauert et al. (2006) and van Segbroeck et al. (2012), thus supporting the claim that the approach developed here unifies, simplifies, and extends much of the previous work on multi-player matrix games. "
[Show abstract][Hide abstract] 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.
"In the absence of genetic relatedness between individuals, in which case kin selection provides the traditional framework (Hamilton 1964), several mechanisms promoting the emergence of cooperation have been extensively studied in the last few decades, such as mutualism (Brown 1983; Stevens & Hauser 2004), direct reciprocity through repeated interactions (Trivers 1971; Axelrod & Hamilton 1981; Melis et al. 2008; Van Segbroeck et al. 2012), preplay communication (in the form of costless or costly) signalling (Skyrms 2004, 2010; Santos et al. 2011), indirect reciprocity through reputation (Alexander 1974; Sugden 1986; Alexander 1987), punishment (Boyd & Richerson 1992; Brandt et al. 2003), voluntary participation (Hauert et al. 2002) and network reciprocity (Santos & Pacheco 2005; Ohtsuki et al. 2006; Szabó & Fáth 2007; Addessi & Rossi 2011), among others. None of the previous models focused on or considered cognition explicitly, although they recognized that maintaining tabs on individuals (such as reputation markers) is cognitively challenging (Nowak & Sigmund 2005). "
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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
New Journal of Physics 07/2012; 14(7):073035. DOI:10.1088/1367-2630/14/7/073035 · 3.56 Impact Factor
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