Effects of adaptive dynamical linking in networked games

Role of generosity and forgiveness: Return to a cooperative society

One's reputation in human society depends on what and how one did in the past. If the reputation of a counterpart is too bad, we often avoid interacting with the individual. We introduce a selective cooperator called the goodie, who participates in the prisoner's dilemma game dependent on the opponent's reputation, and study its role in forming a cooperative society. We observe enhanced cooperation when goodies have a small but nonzero probability of playing the game with an individual who defected in previous rounds. Our finding implies that even this small generosity of goodies can provide defectors chances of encountering the better world of cooperation, encouraging them to escape from their isolated world of selfishness.

Evolution of cooperative imitators in social networks

Many evolutionary game models for network reciprocity are based on an imitation dynamics, yet how semirational imitators prevail has seldom been explained. Here we use a model to investigate the coevolutionary dynamics of cooperation and partnership adjustment in a polygenic population of semirational imitators and rational payoff maximizers. A rational individual chooses a strategy best responding to its neighbors when updating strategy and switches to a new partner who can bring it the maximal payoff from all candidates when adjusting the partnership. In contrast, a semirational individual imitates its neighbor's strategy directly and adjusts its partnership based upon a simple reputation rule. Individual-based simulations show that cooperation cannot evolve in a population of all best responders even if they can switch their partners to somebody who can reward them best in game playing. However, when imitators exist, a stable community that consists of cooperative imitators emerges. Further, we show that a birth-death selection mechanism can eliminate all best responders, cultivating a social regime of all cooperative imitators. Compared with parallel simulations that assume fixed networks, cooperative imitators are evolutionarily favored, provided they are able to adjust their partners.

Evolutionary dynamics of synergistic and discounted group interactions in structured populations

The emergence of cooperation between unrelated individuals enables researchers to study how the collective cooperative behavior survives in a world where egoists could get more short-term benefits. The spatial multi-player games, which invoke interactions between individuals who are not directly linked by the interactive networks, are drawing more and more attention in exploring the evolution of cooperation. Here we address the evolutionary dynamics in infinite structured populations with discounted, linear, and synergistic group interactions. The five classical scenarios are recovered from the dynamics: (i) dominating defection, (ii) dominating cooperation, (iii) co-existence, (iv) bi-stability, and (v) neutral variants. For linear interactions, the evolutionary dynamics is equivalent to that in finite as well as the well-mixed counterparts, which can be achieved by a payoff matrix transformation, and it illustrates that the more neighbors there are, the harder the cooperators survive. Yet both cooperation and defection emerge easier in finite populations than in infinite for discounted and synergistic interactions. Counterintuitively, we find that the synergistic group interactions always raise cooperators׳ barriers to occupy the population with the increase of the number of neighbors in infinite structured populations. Our results go against the common belief that synergistic interactions are necessarily beneficial for the cooperative behavior.

Aspiration-based partner switching boosts cooperation in social dilemmas

Most previous studies concerning linking dynamics often assumed that links pairing individuals should be identified and treated differently during topology adjusting procedure, in order to promote cooperation. A common assumption was that cooperators were expected to avoid being exploited by quickly breaking up relationships with defectors. Then the so-called prosocial links linking two cooperators (abbreviated as CC links hereafter) would be much favored by evolution, whereby cooperation was promoted. However, we suggest that this is not always necessary. Here, we developed a minimal model in which an aspiration-based partner switching mechanism was embedded to regulate the evolution of cooperation in social dilemmas. Individuals adjusted social ties in a self-questioning manner in line with the learning theory. Less game information was involved during dynamic linking and all links were tackled anonymously irrespective of their types (i.e., CD links, DD links, or CC links). The main results indicate that cooperation flourishes for a broad range of parameters. The denser the underlying network, the more difficult the evolution of cooperation. More importantly, moderate aspirations do much better in promoting the evolution of altruistic behavior and for most cases there exists the optimal aspiration level that most benefits cooperation. Too strong or too weak selection intensity turns out to be pretty conducive to the evolution of cooperation in such a dynamical system.