Complexity of Behavioural Strategies and Cooperation in the Optional Public Goods Game

The problem of collective action where—beside the standard options of cooperating and defecting—there is also the possibility of opting out has been extensively studied through the optional public good game (OPGG). Within this and other social dilemma games, reputation systems, composed of a social norm—assigning reputations to agents—and a set of behavioural strategies using this information to condition their behaviour, are able to sustain cooperation. However, while the relationship between the complexity of social norms and cooperation has been extensively studied, the same cannot be said with respect to behavioural strategies, due to high dimensionality of the strategy spaces involved. We deal with this problem by building an agent-based model where agents adopt simple social norms, play the OPGG and learn behavioural strategies through a genetic algorithm. We show that while social norms which assign different reputations to defectors and to agents opting out achieve the highest levels of cooperation, the social norms that do not distinguish between these actions do improve cooperation levels with respect to the baseline when behavioural strategies are sufficiently complex. Furthermore, we find that cooperation increases when the interaction groups are small enough for agents to accurately distinguish between different behaviours.