Strategy additions and equilibrium selection

Abstract

In games with multiple equilibria, if one of the players is given the option of burning an appropriately chosen sum of money before the game and the iterated elimination of dominated strategies is used to select strategies for play, then a unique equilibrium can often be made to appear. The usefulness of an equilibrium selection device depends upon the limits on its ability to select equilibria. This paper shows that given any pure strategy Nash equilibrium in a normal form game, then by adding at most one strategy to each player's strategy set and appropriately defining payoffs, one can make that equilibrium the unique outcome surviving the iterated elimination of dominated strategies.