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

Jean-Baptiste André

Evolutionary game theory loses much of its predictive power in games with multi- ple equilibria. For such games, this paper introduces a simple and general refinement principle, grounded in evolutionary dynamics, that sharply narrows the set of possi- ble 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 mutations always occur first, ignoring the unlikely possibility that larger- effect mutations appear earlier. This approximation leads to a principle of adaptive parsimony: at each step, evolution always follows the simplest possible path. 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 behavioral patterns predicted by the folk theorem in repeated games.