A Review of Stackelberg Differential Game Models in Supply Chain Management

Abstract

Over the last two decades, differential game (DG) models have been used extensively to study such issues in dynamic environments as competitive advertising and pricing for new products in the marketing literature, capacity investments in the energy industry, government's subsidy policy in new technology, and monetary and fiscal policies in economics. Recently, a number of papers have applied DGs to treat dynamic interactions between the channel members in decentralized supply chains. This review focuses on these applications. Specifically, we review papers that analyze dynamic retail-wholesale pricing strategies, joint slotting and pricing decisions to launch an innovative durable product, and investment in supply chain infrastructure. We consider Stackelberg equilibria as the solution concept for the games under consideration. We shall begin our review with an introduction to the basics of the Stackelberg DGs. We then summarize the important managerial insights obtained in each of the studies being reviewed. Finally, we point out future research avenues for applications of DGs in supply chain management.

Keywords: differential games, Stackelberg equilibrium, supply chain management, coordination, pricing

JEL Classification: C61, M31, M37, M31, M00, C71, C73