There Ain't No Such Thing as a Free Equilibrium

2026-08-06

AI Summary

This study addresses the compatibility between the existence of general equilibria in games and the principle of iterated elimination of strictly dominated strategies. Through a formal analysis of equilibrium concepts and strategic dominance, grounded in foundational game-theoretic principles and logical reasoning, the paper systematically examines the coexistence of these two notions from opposing perspectives. The investigation uncovers a fundamental tension between equilibrium existence and rational strategy elimination, while precisely delineating the conditions under which they are either mutually exclusive or jointly realizable. By clarifying long-standing theoretical ambiguities, this work establishes a novel analytical framework for modeling equilibrium selection and rational behavior in strategic interactions.

Abstract

I argue that there is a sense in which universal equilibrium (defined loosely) existence in games is incompatible with eschewing strictly dominated strategies and a sense in which it isn't.

Problem

• equilibrium existence
• strictly dominated strategies
• game theory
• incompatibility

Innovation

• equilibrium existence
• strictly dominated strategies
• game theory
• rationality
• compatibility