Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. A Nash equilibrium is considered payoff dominant if it is Pareto superior to all other Nash equilibria in the game.1 When faced with a choice among equilibria, all players would agree on the payoff dominant equilibrium since it offers to each player at least as much payoff as the other Nash equilibria. Conversely, a Nash equilibrium is considered risk dominant if it has the largest basin of attraction (i.e. is less risky). This implies that the more uncertainty players have about the actions of the other player(s), the more likely they will choose the strategy corresponding to it.
The payoff matrix in Figure 1 provides a simple two-player, two-strategy example of a game with two pure Nash equilibria. The strategy pair (Hunt, Hunt) is payoff dominant since payoffs are higher for both players compared to the other pure NE, (Gather, Gather). On the other hand, (Gather, Gather) risk dominates (Hunt, Hunt) since if uncertainty exists about the other player's action, gathering will provide a higher expected payoff. The game in Figure 1 is a well-known game-theoretic dilemma called stag hunt. The rationale behind it is that communal action (hunting) yields a higher return if all players combine their skills, but if it is unknown whether the other player helps in hunting, gathering might turn out to be the better individual strategy for food provision, since it does not depend on coordinating with the other player. In addition, gathering alone is preferred to gathering in competition with others. Like the Prisoner's dilemma, it provides a reason why collective action might fail in the absence of credible commitments.
Famous quotes containing the words risk and/or dominance:
“I saw the man my friend ... wants pardoned, Thomas Flinton. He is a bright, good-looking fellow.... Of his innocence all are confident. The governor strikes me as a man seeking popularity, who lacks the independence and manhood to do right at the risk of losing popularity. Afraid of what will be said. He is prejudiced against the Irish and Democrats.”
—Rutherford Birchard Hayes (18221893)
“It is better for a woman to compete impersonally in society, as men do, than to compete for dominance in her own home with her husband, compete with her neighbors for empty status, and so smother her son that he cannot compete at all.”
—Betty Friedan (b. 1921)