A decentralized multi-level leader-follower game for network design of a competitive supply chain

This paper develops a decentralized leader-follower game for network design of a competitive supply chain problem in which a new chain as the leader enters a market with one existing supply chain as a follower. Both chains produce an identical product, customer demand is inelastic and customer utility function is based on Huff gravity-based model. The leader wants to shape his network and set assignments where the follower will show reactions by changing her networks in a sequential manner. Multi-level mixed integer nonlinear programming model is used to model the problem. Each chain can enter the market in centralized, decentralized or cooperative modes. Enumeration method is applied to solve the problem by the help of Stackelberg equilibrium concept. Finally, some numerical examples are used to explore the algorithm and different mode structures affect the equilibrium solution.