Payoff Dominance

Payoff dominance is a criterion for equilibrium selection in games with multiple Nash equilibria. An equilibrium is payoff-dominant if it gives every player a higher payoff than any other equilibrium. Unlike Pareto dominance, which compares outcomes across all feasible strategy profiles, payoff dominance compares only equilibrium outcomes. The concept is most useful in coordination games where one equilibrium is strictly better for all players than the alternatives.

The limitation of payoff dominance is that it is often inapplicable. In many games — including the symmetric battle of the sexes — no equilibrium payoff-dominates another. When payoffs are asymmetric, payoff dominance may favor one equilibrium while risk dominance favors another, creating a tension between safety and efficiency that formal theory cannot resolve. Experimental evidence suggests that human players frequently ignore payoff dominance in favor of salience and convention.

Payoff dominance is closely related to the concept of Efficiency in welfare economics, but it operates within the narrower domain of equilibrium outcomes rather than the full set of feasible allocations. The distinction matters: a mechanism can be efficient without selecting a payoff-dominant equilibrium, and vice versa.

Payoff dominance is the rationalist's comfort blanket — a selection criterion that appeals to efficiency but fails precisely when selection is hardest, in games where equilibria are already efficient and players must choose among them. It is not a theory of how players choose. It is a theory of how they ought to choose, and the gap between the two is the entire subject of behavioral game theory.