Abstract
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.
Highlights
Cooperation in humans is different from other animals [1]
Repetitive interactions opened new paths for the evolution of cooperation in populations. Individuals can condition their current behavior on previous interactions
In a two-person repeated prisoner’s dilemma game, it was shown that TFT can invade a population of ALLD if a player decision to leave the game depends on whether she cooperated or defected in the previous round [12]
Summary
Cooperation in humans is different from other animals [1]. Humans have developed cooperative strategies that rely on advanced cognitive capacities [2,3,4]. In a two-person repeated prisoner’s dilemma game, it was shown that TFT can invade a population of ALLD if a player decision to leave the game depends on whether she cooperated or defected in the previous round [12]. Another approach to deal with variable group size is to keep the multiplicative factor constant In this case, the marginal return can vary and the game may change from a regime where defection is the best option to a regime where cooperation is best one. Since most players do not participate in the game, the average size of the groups playing the public goods game is small and the social dilemma disappears: the payoff of cooperators are, on average, larger than the payoff of defectors. We show that cooperation is favored by selection if players stay playing the game, but not for too long
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