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Since M. A. Nowak & R. May's (1992) influential paper, limiting each agent's interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments-reciprocal cooperation and unconditional defection-in a networked prisoner's dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.

We show that when selection is extreme-the fittest strategy always reproduces or is imitated-the unequivalence between the possible evolutionary game scenarios in finite and infinite populations resolves, in the sense that the three generic outcomes-dominance, coexistence, and mutual exclusion-emerge in well-mixed populations of any size. We consider the simplest setting of a 2-player-2-strategy symmetric game and the two most common microscopic definitions of strategy spreading-the frequency-dependent Moran process and the imitation process by pairwise comparison-both in the case allowing any intensity of selection. We show that of the seven different invasion and fixation scenarios that are generically possible in finite populations-fixation being more or less likely to occur and rapid compared to the neutral game-the three that are possible in large populations are the same three that occur for sufficiently strong selection: (1) invasion and fast fixation of one strategy; (2) mutual invasion and slow fixation of one strategy; (3) no invasion and no fixation. Moreover (and interestingly), in the limit of extreme selection 2 becomes mutual invasion and no fixation, a case not possible for finite intensity of selection that better corresponds to the deterministic case of coexistence. In the extreme selection limit, we also derive the large population deterministic limit of the two considered stochastic processes.

The fixation of cooperation among unrelated individuals is one of the fundamental problems in biology and social sciences. It is investigated by means of public goods games, the generalization of the prisoner's dilemma to more than two players. In compulsory public goods games, defect is the dominant strategy, while voluntary participation overcomes the social dilemma by allowing a cyclic coexistence of cooperators, defectors, and non-participants. Experimental and theoretical research has shown how the combination of voluntary participation and altruistic punishment-punishing antisocial behaviors at a personal cost-provides a solution to the problem, as long as antisocial punishment-the punishing of cooperators-is not allowed. Altruistic punishment can invade at low participation and pave the way to the fixation of cooperation. Specifically, defectors are overpunished, in the sense that their payoff is reduced by a sanction proportional to the number of punishers in the game. Here we show that qualitatively equivalent results can be achieved with a milder punishing mechanism, where defectors only risk a fixed penalty per round-as in many real situations-and the cost of punishment is shared among the punishers. The payoffs for the four strategies-cooperate, defect, abstain, and cooperate-&-punish-are derived and the corresponding replicator dynamics analyzed in full detail., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

We propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success, and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of adaptive dynamics. Our results link the so-called horizontal dynamics-- the primary driver of fashion evolution, compared with the vertical dynamics accounting for interclass and economic drivers--to style variety. [ABSTRACT FROM AUTHOR]

Network reciprocity has been successfully put forward (since M. A. Nowak and R. May's, 1992, influential paper) as the simplest mechanism—requiring no strategical complexity—supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents' interactions localized, while network reciprocity is the property of the underlying evolutionary process to favor cooperation in sparse rather than dense networks. In theoretical models, the property holds under imitative evolutionary processes, whereas cooperation disappears in any network if imitation is replaced by the more rational best-response rule of strategy update. In social experiments, network reciprocity has been observed, although the imitative behavior did not emerge. What did emerge is a form of conditional cooperation based on direct reciprocity—the propensity to cooperate with neighbors who previously cooperated. To resolve this inconsistency, network reciprocity has been recently shown in a model that rationally confronts the two main behaviors emerging in experiments—reciprocal cooperation and unconditional defection—with rationality introduced by extending the best-response rule to a multi-step predictive horizon. However, direct reciprocity was implemented in a non-standard way, by allowing cooperative agents to temporarily cut the interaction with defecting neighbors. Here, we make this result robust to the way cooperators reciprocate, by implementing direct reciprocity with the standard tit-for-tat strategy and deriving similar results. [ABSTRACT FROM AUTHOR]