Evolutionary parsimony: an equilibrium refinement that sharply constrains the space of outcomes in games with multiple equilibria.

Evolutionary game theory loses much of its predictive power in games with multiple equilibria. For such games, this article introduces a simple and general refinement principle, grounded in evolutionary dynamics, that sharply narrows the set of possible outcomes. Rather than designing strategies from scratch, evolution shapes them gradually through the accumulation of adaptive mutations, the vast majority of which have small effects. This process can be approximated heuristically by assuming that smaller-effect (and therefore more probable) mutations always occur first, while ignoring the unlikely possibility that larger-effect mutations arise earlier. This approximation gives rise to a principle of adaptive parsimony: at each step, evolution proceeds through the simplest beneficial change available. As a result, most theoretically possible equilibria are actually unreachable, as they would require a transition where a large-effect mutation fixes despite a simpler alternative being available. What remains is a small subset of equilibria that seem intuitively reasonable from a biological perspective: those that (i) preserve ecological symmetry, (ii) do not rely on non-credible threats and (iii) avoid the bizarre behavioural patterns predicted by the folk theorem in repeated games.