On the maximal reduction of games

TL;DR

This paper investigates conditions for order independence in iterated elimination of strategies, identifying classes of discontinuous games where order does not affect outcomes, and extends results to mixed strategy dominance.

Contribution

It answers an open problem on order independence in game reduction and generalizes previous results to include mixed strategy dominance.

Findings

Identifies classes of discontinuous games with order-independent reductions

Provides conditions for existence and uniqueness of maximal game reductions

Extends theory to cases where strategies are dominated by mixed strategies

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.