On the maximal reduction of games

Abstract: We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem raised by M. Dufwenberg and M. Stegeman (2002) and generalize their main results. We also establish new theorems concerning the existence and uniqueness of the maximal game reduction when the pure strategies are dominated by mixed strategies.