Intransitivity and coexistence in four species cyclic games

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We show that, contrary to the mean field prediction, on a square lattice the model presents a transition, as the parameter setting the rate at which one species invades another changes, from a coexistence to a state in which one species gets extinct. Such a dependence on the invasion rates shows that the interaction graph structure alone is not enough to predict the outcome of such models. In addition, different invasion rates permit to tune the level of transitiveness, indicating that for the coexistence of all species to persist, there must be a minimum amount of intransitivity.Comment: Final, published versio

Acculturation and the evolution of cooperation in spatial public goods games

Cooperation is one of the foundations of human society. Many solutions to cooperation problems have been developed and culturally transmitted across generations. Since immigration can play a role in nourishing or disrupting cooperation in societies, we must understand how the newcomers’ culture interacts with the hosting culture. Here, we investigate the effect of different acculturation settings on the evolution of cooperation in spatial public goods games with the immigration of defectors and efficient cooperators. Here, immigrants may be socially influenced, or not, by the native culture according to four acculturation settings: integration, where immigrants imitate both immigrants and natives; marginalization, where immigrants do not imitate either natives nor other immigrants; assimilation, where immigrants only imitate natives; and separation, where immigrants only imitate other immigrants. We found that cooperation is greatly facilitated and reaches a peak for moderate values of the migration rate under any acculturation setting. Most interestingly, we found that the main acculturation factor driving the highest levels of cooperation is that immigrants do not avoid social influence from their fellow immigrants. We also show that integration may not promote the highest level of native cooperation if the benefit of cooperation is low

Cyclic Competition and Percolation in Grouping Predator-Prey Populations

We study, within the framework of game theory, the properties of a spatially distributed population of both predators and preys that may hunt or defend themselves either isolatedly or in group. Specifically, we show that the properties of the spatial Lett-Auger-Gaillard model, when different strategies coexist, can be understood through the geometric behavior of clusters involving four effective strategies competing cyclically,without neutral states. Moreover, the existence of strong finite-size effects, a form of the survival of the weakest effect, is related to a percolation crossover. These results may be generic and of relevance to other bimatrix games

Invasion of Optimal Social Contracts

The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods