Payoff dominance

Payoff dominance is an equilibrium selection criterion that favors the equilibrium yielding the highest joint payoff for all players — the Pareto-optimal outcome. In a coordination game, when multiple Nash equilibria exist, payoff dominance selects the one that is best for everyone. Unlike risk dominance, which favors the safest equilibrium, payoff dominance favors the most efficient one.

The tension between payoff dominance and risk dominance is the central strategic dilemma of the Assurance Game. In the standard Stag Hunt, the mutual stag equilibrium is both payoff-dominant and risk-dominant — a rare alignment. But in many real-world coordination problems — choosing technical standards, adopting new currencies, or reforming institutions — the efficient equilibrium is not the safe one. Societies often remain trapped in risk-dominant equilibria even when payoff-dominant alternatives are available, because the transition requires coordinated belief revision that no individual can trigger alone.