Consequences of fluctuating group size for the evolution of cooperation

TL;DR

This paper investigates how fluctuations in group size influence the evolution of cooperation in continuous games, revealing that the effects depend on the structure of payoff functions and can either promote or hinder cooperative strategies.

Contribution

It provides analytical conditions and a classification scheme for understanding how group size fluctuations affect evolutionary branching in continuous cooperation games.

Findings

Fluctuating group size reduces likelihood of evolutionary branching in additive payoff games.

Large fluctuations can stabilize cooperation by preventing branching.

In multiplicative payoff games, fluctuations can either promote or inhibit cooperation.

Abstract

Studies of cooperation have traditionally focused on discrete games such as the well-known prisoner's dilemma, in which players choose between two pure strategies: cooperation and defection. Increasingly, however, cooperation is being studied in continuous games that feature a continuum of strategies determining the level of cooperative investment. For the continuous snowdrift game, it has been shown that a gradually evolving monomorphic population may undergo evolutionary branching, resulting in the emergence of a defector strategy that coexists with a cooperator strategy. This phenomenon has been dubbed the 'tragedy of the commune'. Here we study the effects of fluctuating group size on the tragedy of the commune and derive analytical conditions for evolutionary branching. Our results show that the effects of fluctuating group size on evolutionary dynamics critically depend on the structure of payoff functions. For games with additively separable benefits and costs, fluctuations in group size make evolutionary branching less likely, and sufficiently large fluctuations in group size can always turn an evolutionary branching point into a locally evolutionarily stable strategy. For games with multiplicatively separable benefits and costs, fluctuations in group size can either prevent or induce the tragedy of the commune. For games with general interactions between benefits and costs, we derive a general classification scheme based on second derivatives of the payoff function, to elucidate when fluctuations in group size help or hinder cooperation.