Evolution of all-or-none strategies in repeated public goods dilemmas

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.This research was supported by FEDER through POFC - COMPETE and by FCT-Portugal through fellowships SFRH/BD/77389/2011 and SFRH/BD/86465/2012, by grants PTDC/MAT/122897/2010 and EXPL/EEI-SII/2556/2013, by multi-annual funding of CMAF-UL, CBMA-UM and INESC-ID (under the projects PEst-OE/MAT/UI0209/2013, PEst-OE/BIA/UI4050/2014 and PEst-OE/EEI/LA0021/2013) provided by FCT-Portugal, and by Fundacao Calouste Gulbenkian through the "Stimulus to Research" program for young researchers. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript