Game Theoretic Approach to Supply Chain Management

This dissertation studies the competitive behavior of firms in supply chain management and revenue management contexts. A game theoretic approach is employed. We analyze capacity allocation and pricing strategies and derive equilibrium solutions for multiple competing firms. We also study channel coordination mechanisms to bring the competing firms together for chain-wide optimality and conduct sensitivity analysis of equilibrium solutions.First we consider a single-period distribution system with one supplier and two retailers. When a stockout occurs at one retailer the customer may go to the other retailer. The supplier may have infinite or finite capacity. In the latter case, if the total quantity ordered (claimed) by the retailers exceeds the supplier's capacity, an allocation policy is invoked to assign the capacity to the retailers. We show that a unique Nash equilibrium exists when the supplier has infinite capacity. While, when the capacity is finite, a Nash equilibrium exists only under certain conditions. For the finite capacity case, we also use the concept of Stackelberg game to develop optimal strategies for both the leader and the follower. In addition to the decentralized inventory control problem, we study the centralized inventory control problem and obtain the optimal allocation that maximizes the expected profit of the entire supply chain. We also design perfect coordination mechanisms, i.e., a decentralized cost structure resulting in a Nash equilibrium with chain-wide profits equal to those achieved under a fully centralized system.As an extension to the capacity allocation models above, we then consider two firms where each firm has a local store and an online store. Customers may shift among these stores upon encountering a stockout. Each firm makes the capacity allocation decision to maximize its profit. We consider two scenarios of a single-product single-period model and derive corresponding existence and stability conditions of a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. Finally we extend the results to a multi-period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding sequential game.Finally, we consider the pricing strategies of multiple firms providing same service and competing for a common pool of customers in a revenue management context. The demand at each firm depends on the selling prices charged by all firms, each of which satisfies demand up to a given capacity limit. We use game theory to analyze the systems under both deterministic and general stochastic demand. We derive the existence and uniqueness conditions for a Nash equilibrium and calculate the explicit Nash equilibrium point when the demand at each firm is a linear function of price.