Assortment and the evolution of cooperation in a Moran process with exponential fitness

TL;DR

This paper investigates how assortment influences the evolution of cooperation in finite populations using a Moran process with exponential fitness transformation, revealing conditions under which assortment promotes cooperation.

Contribution

It introduces a model with exponential fitness transformation to analyze assortment effects on cooperation, providing new insights into when assortment favors cooperation.

Findings

Greater assortment increases the probability of cooperative fixation in some dilemmas.

The stronger definition shows assortment favors cooperation in certain games.

Results hold for any strength of selection.

Abstract

We study the evolution of cooperation in a finite population interacting according to a simple model of like-with-like assortment. Evolution proceeds as a Moran process, and payoffs from the underlying cooperator-defector game are translated to positive fitnesses by an exponential transformation. These evolutionary dynamics can arise, for example, in a nest-structured population with rare migration. The use of the exponential transformation, rather than the usual linear one, is appropriate when interactions have multiplicative fitness effects, and allows for a tractable characterization of the effect of assortment on the evolution of cooperation. We define two senses in which a greater degree of assortment can favour the evolution of cooperation, the first stronger than the second: (i) greater assortment increases, at all population states, the probability that the number of cooperators increases, relative to the probability that the number of defectors increases; and (ii) greater assortment increases the fixation probability of cooperation, relative to that of defection. We show that, by the stronger definition, greater assortment favours the evolution of cooperation for a subset of cooperative dilemmas: prisoners' dilemmas, snowdrift games, stag-hunt games, and some prisoners' delight games. For other cooperative dilemmas, greater assortment favours cooperation by the weak definition, but not by the strong definition. Our results hold for any strength of selection.