"Third down and a yard to go": the Dixit-Skeath conundrum on equilibria in competitive games

Abstract

In strictly competitive games, equilibrium mixed strategies are invariant to changes in the ultimate prizes. Dixit & Skeath (1999) argue that this seems counter-intuitive. We show that this invariance is robost to dropping the independence axiom, but it removed if we drop the reduction axiom. The conditions on the resulting recurrsive expected-utility model to get the desired outcome are analogous to conditions used in the standard model of comparative statics under risk. Show more