Game Theory in Supply Chain Analysis

Abstract

Game theory has become an essential tool in the analysis of supply chains with multiple agents, often with conflicting objectives. This chapter surveys the applications of game theory to supply chain analysis and outlines game-theoretic concepts that have potential for future application. We discuss both non-cooperative and cooperative game theory in static and dynamic settings. Careful attention is given to techniques for demonstrating the existence and uniqueness of equilibrium in non-cooperative games. A newsvendor game is employed throughout to demonstrate the application of various tools. 1

Network capacity management under competition

“…The following results are well known in the literature by noting that concavity is preserved under the min-operator, limits, addition and hence under expectation and integration signs; see for example [5], and that the integral is continuously differentiable if the integrand is globally Lipschiz continuous and continuously differentiable almost everywhere; see for example [24,27]. 1) and (2).…”

“…So far, we have proved the uniqueness of a Nash equilibrium for the game defined by (5), in which we impose the condition that x i 1 + x i 2 = C i , i.e., the capacity constraint is binding. We now prove that the Nash equilibrium for the PNLP game is unique.…”

“…If there is a unique equilibrium, firms can choose their strategies without vagueness. The importance of a unique equilibrium is highlighted in a statement of [5]: "The obvious problem with multiple equilibria is that the firms may not know which equilibrium will prevail. Hence, it is entirely possible that a non-equilibrium outcome results because one firm plays one equilibrium strategy while a second firm chooses a strategy associated with another equilibrium.…”

“…Cachon and Netessine [5] present an excellent review on game theory in the area of supply chain management. In particular, they review techniques for proving the existence and uniqueness of a Nash equilibrium for static, dynamic and cooperative games.…”

“…Each airline sells multiple products as in traditional network revenue management problems, see [51]. Demand overflow is taken into account in a deterministic way as in [5,39], i.e., a proportion of the passengers, who do not get the tickets they want from their preferred airline, approach other airlines for similar products. We develop one Nash and one generalized Nash game model to represent capacity management games.…”