When selection pays: Structured public goods game with a generalized interaction mode

The public goods game is a broadly used paradigm for studying the evolution of cooperation in structured populations. According to the basic assumption, the interaction graph determines the connections of a player where the focal actor forms a common venture with the nearest neighbors. In reality, however, not all of our partners are involved in every game. To elaborate this observation, we propose a model where individuals choose just some selected neighbors from the complete set to form a group for public goods. We explore the potential consequences by using a pair-approximation approach in a weak selection limit. We theoretically analyze how the number of total neighbors and the actual size of the restricted group influence the critical enhancement factor where cooperation becomes dominant over defection. Furthermore, we systematically compare our model with the traditional setup and show that the critical enhancement factor is lower than in the case when all players are present in the social dilemma. Hence, the suggested restricted interaction mode offers a better condition for the evolution of cooperation. Our theoretical findings are supported by numerical calculations.