Equilibrium Play Without Mutual Knowledge of Rationality

2026-07-20

AI Summary

This work proposes a novel approach to characterizing equilibrium behavior in two-player zero-sum games that dispenses with the strong common knowledge assumptions—such as mutual rationality and shared beliefs—typically required for Nash equilibrium. By recursively defining each player’s “reasonable action set” within subgames, the method derives equilibrium strategies solely from individual rationality and the inheritance of rationality after iteratively eliminating unreasonable actions. Integrating dominance reasoning, best-response analysis, and subgame structure, this framework consistently identifies the support of Nash equilibria in zero-sum settings. Moreover, the payoff structure itself guarantees equilibrium uniqueness, thereby achieving both refinement and unique determination of equilibrium under significantly weaker epistemic conditions.

Abstract

Equilibrium play in two-player zero-sum games is usually justified via epistemic assumptions, such as mutual knowledge of rationality and beliefs, that go far beyond the rationality of the players. We propose a justification that dispenses with these assumptions. To this end, we consider solution concepts that assign to every subgame of a given game a set of plausible actions for each player, and we impose two conditions. Rationality requires that the plausible sets are supports of undominated strategies or, equivalently, that all plausible actions are best responses to a common belief about the opponent. Inheritance requires that plausible actions remain plausible when implausible actions are discarded. In two-player games, the two conditions characterize the solution concepts that consistently select supports of Nash equilibria. Zero-sum payoffs ensure that Nash equilibria -- and hence the selection -- are generically unique. Equilibrium play thus emerges from individual rationality and the mutual understanding that plausibility judgments persist when implausible actions are discarded.

Problem

• equilibrium play
• zero-sum games
• rationality
• epistemic assumptions
• Nash equilibrium

Innovation

• epistemic foundations
• solution concepts
• rationality
• inheritance
• zero-sum games