Aggregate Nash Attainability and Boundary Equilibria under Behavioral Heterogeneity
Philipp Külpmann; Wieland Müller; Alexander K. Wagner
Working paper (2026). Version: 15 July 2026.
Abstract
We study which Nash equilibria of a finite normal-form game can still arise as aggregate play when each player role is represented by a population containing both behavioral and optimizing agents. In each role, a fixed fraction of agents follows an exogenous action distribution, while the remaining agents best respond to aggregate play. A Nash equilibrium survives if and only if, for every role and every action, the behavioral mass assigned to that action does not exceed its Nash equilibrium probability. When this condition holds, optimizing agents choose the residual distribution and aggregate play reproduces the original Nash equilibrium. When it fails, behavioral types assign too much probability mass to some action, and exact aggregate recovery is impossible. We further show that any additional aggregate equilibria generated by behavioral heterogeneity must lie on the boundary of the aggregate-feasible set and are sustained by behavioral types playing non-optimal actions. Behavioral heterogeneity may thus prune some Nash equilibria and create genuinely new ones, and we characterize both.Links and resources
Keywords: Nash Equilibrium; Behavioral Heterogeneity; Mixed Strategies; Population Games; Bounded Rationality; Experimental Game Theory