Game theory methodology for optimizing retailers’ pricing and shelf-space allocation decisions on competing substitutable products

Abstract

This paper examines the influence of competition among supply chain partners on product demand. A power law demand function that depends on product pricing and shelf-space allocation (SSA) is used. The exponents in the power law are given by the elasticities of demand. In order to achieve the optimal pricing and SSA strategies in the presence of competition, game-theory-based methodologies—Cournot and Stackelberg games—are employed. For each type of game, a Nash equilibrium is achieved by optimizing the profit as a function of demand and price. A case study is presented to demonstrate the potential of this methodology. The results of this study indicate (1) how to achieve optimal pricing and SSA strategies, (2) how manufacturers can influence demand for a product, (3) that both prices and profits decrease using the Stackelberg game as compared with the Cournot game, and (4) that coordination beyond simple knowledge of price would be beneficial for improving overall profits.