Cooperation in public goods games: stay, but not for too long

Cooperation in repeated public goods game is hardly achieved, unless contingent behavior is present. Surely, if mechanisms promoting positive assortment between cooperators are present, then cooperators may beat defectors, because cooperators would collect greater payoffs. In the context of evolutionary game theory, individuals that always cooperate cannot win the competition against defectors in well-mixed populations. Here, we study the evolution of a population where fitness is obtained in repeated public goods games and players have a fixed probability of playing the next round. As a result, the group size decreases during the game. The population is well-mixed and there are only two available strategies: always cooperate (ALLC) or always defect (ALLD). Through numerical calculation and analytical approximations we show that cooperation can emerge if the players stay playing the game, but not for too long. The essential mechanism is the interaction between the transition from strong to weak altruism, as the group size decreases, and the existence of an upper limit to the number of rounds representing limited time availability

Adoption of simultaneous different strategies against different opponents enhances cooperation

The emergence of cooperation has been widely studied in the context of game theory on structured populations. Usually the individuals adopt one strategy against all their neighbors. The structure can provide reproductive success for the cooperative strategy, at least for low values of defection tendency. Other mechanisms, such punishment, can also be responsible for cooperation emergence. But what happens if the players adopt simultaneously different strategies against each one of their opponents, not just a single one? Here we study this question in the prisoner dilemma scenario structured on a square lattice and on a ring. We show that if an update rule is defined in which the players replace the strategy that furnishes the smallest payoff, a punishment response mechanism against defectors without imputing cost to the punishers appears, cooperation dominates and, even if the tendency of defection is huge, cooperation still remains alive

On the synchronization of coupled random walks and applications to social systems

Some political strategies to win elections over the last years were based heavily on fomenting general distrust in information institutions and favoring distrustful sources. The misinformation pandemic has the straightforward consequence that people do not believe any information unless it is compatible with their own beliefs. We present a simple model to study the emergence of consensus in opinion pools of uncertain agents that trust (couple to) their neighbors (information sources) with strength K. We focus the studies on regular lattices and linear coupling. Depending on the coupling constant, K, and the propensity to choose an opinion (the probability to manifest a given opinion in solitude), p_0, we get regions where consensus is surely reached even in infinity systems (K greater than or equal to K_c), regions where not-consensus is the only steady state (K lesser than K_c), and a region where consensus on any opinion is transitory with each agent presenting periods of strong oscillation of opinions before changing polarization (p_0 equal to p_c and K greater than or equal K_c. The first model in this last region presents transition probabilities identical to the voter model (p_0 equal to p_c and K equal to K_c). Different upbringings, exposition to education biased to a single political view, and previous coexistence with opinion polarized people can change the opinion of agents in isolation. We model such characteristics with heterogeneous populations (p^i_0 not equal to p^j_0 for some pairs of nodes i,j). Such systems present regions where the coexistence of local consensus (bulk-stable clusters of like-minded opinions), weak consensus (bulk-unstable temporary clusters where contrary opinions emerge inside the cluster), and distrust (random orientations that do not form clusters) are possible.Comment: 14 pages, 7 figures, 4 section appendi

Distinguishing the opponents in the prisoner dilemma in well-mixed populations

Here we study the effects of adopting different strategies against different opponent instead of adopting the same strategy against all of them in the prisoner dilemma structured in well-mixed populations. We consider an evolutionary process in which strategies that provide reproductive success are imitated and players replace one of their worst interactions by the new one. We set individuals in a well-mixed population so that network reciprocity effect is excluded and we analyze both synchronous and asynchronous updates. As a consequence of the replacement rule, we show that mutual cooperation is never destroyed and the initial fraction of mutual cooperation is a lower bound for the level of cooperation. We show by simulation and mean-field analysis that for synchronous update cooperation dominates while for asynchronous update only cooperations associated to the initial mutual cooperations are maintained. As a side effect of the replacement rule, an "implicit punishment" mechanism comes up in a way that exploitations are always neutralized providing evolutionary stability for cooperation

Role-separating ordering in social dilemmas controlled by topological frustration

"Three is a crowd" is an old proverb that applies as much to social interactions, as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anti-coordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.Comment: 9 two-column pages, 9 figures; accepted for publication in Physical Review