Jean-Baptiste André

Many games, especially repeated games, have multiple Nash equilibria, which limits the predictive power of game theory for understanding animal behavior. In this article, I propose a solution to this problem inspired by the notion of stability by convergence from adaptive dynamics. The multiplicity of equilibria is due to the possibility of strategies that are arbitrary in the sense that they are individually adaptive only because others use them. While arbitrary rules of behavior are a possibility in standard game theory, since it is always possible to design patterns of behavior as complex as one wishes, they cannot be gradually shaped by biological evolution because they are never under directional selection. I propose an equilibrium refinement, the concept of evolutionarily parsimonious equilibrium, that captures this constraint by relying on the premise that a complex strategy cannot evolve as a by-product of selection for a simple strategy. Using examples, I show that this refinement supports the selection of biologically plausible equilibria in several of the most important games in the literature. In particular, in repeated games, it eliminates the vast majority of equilibria and reveals that the conditions necessary for the evolution of reciprocal cooperation are not consistent with the prisoner's dilemma, but rather correspond to a situation in which individuals have some degree of immediate interest in cooperating.