An impure public good model with lotteries in large groups

We analyze the effect of a large group on an impure public goods model with lotteries. We show that as populations get large, and with selfish preferences, the level of contributions converges to the one given by voluntary contributions. With altruistic preferences (of the warm glow type), the contributions converge to a level strictly higher than those given by voluntary contributions, even though in general they do not yield first-best levels.Lotteries, Public good, Warm glow, Efficiency

Resistance to learning and the evolution of cooperation

In many evolutionary algorithms, crossover is the main operator used in generating new individuals from old ones. However, the usual mechanism for generating offsprings in spatially structured evolutionary games has to date been clonation. Here we study the effect of incorporating crossover on these models. Our framework is the spatial Continuous Prisoner's Dilemma. For this evolutionary game, it has been reported that occasional errors (mutations) in the clonal process can explain the emergence of cooperation from a non-cooperative initial state. First, we show that this only occurs for particular regimes of low costs of cooperation. Then, we display how crossover gets greater the range of scenarios where cooperative mutants can invade selfish populations. In a social context, where crossover involves a general rule of gradual learning, our results show that the less that is learnt in a single step, the larger the degree of global cooperation finally attained. In general, the effect of step-by-step learning can be more efficient for the evolution of cooperation than a full blast one

Rewarding cooperation in social dilemmas

One of the most direct human mechanisms of promoting cooperation is rewarding it. We study the effect of sharing a reward among cooperators in the most stringent form of social dilemma. Thus, individuals confront a new dilemma: on the one hand, they may be inclined to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will obtain a poor reward and defectors will outperform them. By appropriately tuning the amount to be shared we can cast a vast variety of scenarios, including traditional ones in the study of cooperation as well as more complex situations where unexpected behavior can occur. We provide a complete classification of the equilibria of the nplayer game as well as of the evolutionary dynamics. Beyond, we extend our analysis to a general class of public good games where competition among individuals with the same strategy exists