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In the collective-risk social dilemma, players lose their personal endowments if contributions to the common pool are too small. This fact alone, however, does not always deter selfish individuals from defecting. The temptations to free ride on the prosocial efforts of others are strong because we are hardwired to maximize our own fitness regardless of the consequences which might have for the public good. Here we show that the addition of risky assets to the personal endowments, both of which are lost if the collective target is not reached, can contribute to solving the collective-risk social dilemma. In infinite well-mixed populations, risky assets introduce new stable and unstable mixed steady states, whereby the stable mixed steady state converges to full cooperation as either the risk of collective failure or the amount of risky assets increases. Similarly, in finite well-mixed populations, the introduction of risky assets enforces configurations where cooperative behavior thrives. In structured populations cooperation is promoted as well, but the distribution of assets among the groups is crucial. Surprisingly, we find that the completely rational allocation of assets only to the most successful groups is not optimal, and this regardless of whether the risk of collective failure is high or low. Instead, in low-risk situations bounded rational allocation of assets works best, while in high-risk situations the simplest uniform distribution of assets among all the groups is optimal. These results indicate that prosocial behavior depends sensitively on the potential losses individuals are likely to endure if they fail to cooperate. [ABSTRACT FROM AUTHOR]

A recent experimental study [Traulsen et al., Proc. Natl. Acad. Sci. 107, 2962 (2010)] shows that human strategy updating involves both direct payoff comparison and the cost of switching strategy, which is equivalent to inertia. However, it remains largely unclear how such a predisposed inertia affects 2x2 games in a well-mixed population of finite size. To address this issue, the "inertia bonus" (strategy switching cost) is added to the learner payoff in the Fermi process. We find how inertia quantitatively shapes the stationary distribution and that stochastic stability under inertia exhibits three regimes, with each covering seven regions in the plane spanned by two inertia parameters. We also obtain the extended "1/3" rule with inertia and the speed criterion with inertia; these two findings hold for a population above two. We illustrate the above results in the framework of the Prisoner's Dilemma game. As inertia varies, two intriguing stationary distributions emerge: the probability of coexistence state is maximized, or those of two full states are simultaneously peaked. Our results may provide useful insights into how the inertia of changing status quo acts on the strategy evolution and, in particular, the evolution of cooperation. [ABSTRACT FROM AUTHOR]

"Voting with feet" describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized. [ABSTRACT FROM AUTHOR]