COMPETITIVE STORE CLOSING DURING AN ECONOMIC DOWNTURN: A MATHEMATICAL PROGRAMMING APPROACH

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

Min-Max Payoffs in a Two-Player Location Game

We consider a two-player, sequential location game with arbitrarily distributed consumer demand. Players alternately select locations from a feasible set so as to maximize the consumer mass in their vicinity. Our main result is a complete characterization of feasible market shares, when locations form a finite set in Rd

Min-Max Payoffs in a Two-Player Location Game

We consider a two-player, sequential location game in d-dimensional Euclidean space with arbitrarily distributed consumer demand. The objective for each player is to select locations so as to maximize their market share—the mass of consumers in the vicinity of their chosen locations. At each stage, the two players (Leader and Follower) choose one location each from a feasible set in sequence. We first show that (i) if the feasible locations form a finite set in R d, Leader (the first mover) must obtain at least a 1 d+1 fraction of the market share in equilibrium in the single-stage game, and there exist games in which Leader obtains no more than 1 d+1; (ii) in the original Hotelling game (uniformly distributed consumers on the unit interval), Leader obtains 1 2 even in the multiple stage game, using a strategy which is oblivious of Follower’s locations. Furthermore, we exhibit a strategy for Leader, such that even if she has no information about the number of moves, her payoff must equal at least half the payoff of the single-stage game