Evolution of All-or-None Strategies in Repeated Public Goods Dilemmas

Abstract

Many problems of cooperation involve repeated interactions among the same groups of individuals. When collective action is at stake, groups often engage in Public Goods Games ( PGG), where individuals contribute (or not) to a common pool, subsequently sharing the resources. Such scenarios of repeated group interactions materialize situations in which direct reciprocation to groups may be at work. Here we study direct group reciprocity considering the complete set of reactive strategies, where individuals behave conditionally on what they observed in the previous round. We study both analytically and by computer simulations the evolutionary dynamics encompassing this extensive strategy space, witnessing the emergence of a surprisingly simple strategy that we call All-Or-None ( AoN). AoN consists in cooperating only after a round of unanimous group behavior (cooperation or defection), and proves robust in the presence of errors, thus fostering cooperation in a wide range of group sizes. The principles encapsulated in this strategy share a level of complexity reminiscent of that found already in 2-person games under direct and indirect reciprocity, reducing, in fact, to the well-known Win-Stay-Lose-Shift strategy in the limit of the repeated 2-person Prisoner's Dilemma.

Author Summary

The problem of cooperation has been a target of many studies, and some of the most complex dilemmas arise when we deal with groups repeatedly interacting by means of a Public Goods Game ( PGG), where individuals may contribute to a common pool, subsequently sharing the resources. Here we study generalized direct group reciprocity by incorporating the complete set of reactive strategies, where action is dictated by what happened in the previous round. We compute the pervasiveness in time of each possible reactive strategy, and find a ubiquitous strategy profile that prevails throughout evolution, independently of group size and specific PGG parameters, proving also robust in the presence of errors. This strategy, that we call All-Or-None ( AoN), consists in cooperating only after a round of unanimous group behavior (cooperation or defection); not only is it conceptually very simple, it also ensures that cooperation can self-sustain in a population. AoN contains core principles found, e.g., in the repeated 2-person Prisoner's Dilemma, in which case it reduces to the famous Win-Stay-Lose-Shift strategy.