A game theoretic mixed integer program model is introduced to determine optimal store closing decisions in a competitive market. The model considers the case of two rival firms seeking to downsize operations in a region. Both firms are looking to reduce operating costs by closing a number of stores while minimizing demand lost to its rival. We assume a competitive game and apply the model is to find the equilibrium store closing decisions. The model is first applied to a competitive environment for a single period and then incorporated into a solution procedure for a multi-period game. The model facilitates the analysis of different strategies that can be used by a retail chain to maximize revenue in depressed market conditions. We find that the profitability is not always the most important factor to consider when determining the number and locations of stores to be closed and that an increase in demand variance will increase the likelihood that an unprofitable store will be kept open for an extended period of time. Our results further indicate that, depending on individual store characteristics it may be optimal to close a profitable store. Our results provide guidelines for developing effective strategies to systematically reduce the number of stores so that net revenue is maximized while competitive pressure is exerted on rival stores.