Equilibrium Play Without Mutual Knowledge of Rationality

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.