Equilibrium Play in Voluntary Ultimatum Games: Beneficence Cannot Be Extorted

Abstract

One robust result in experimental economics is the failure to observe equilibrium play in the ultimatum game. A heretofore unnoticed feature of the game is that neither player voluntarily chooses to play the game. Motivated by Adam Smith’s proposition that beneficence — like that of nonequilibrium play in the ultimatum game — cannot be extorted by force, we offer the responder the opportunity to opt out of the game for a mere $1 payoff for both players. We observe high rates of equilibrium play with highly unequal splits when responders choose to play such ultimatum games with both fixed and variable sums.