On the Existence of Equilibrium in a Dynamic Supply Chain Game with Vertical Coordination, Horizontal Competition and Cournot Complementary Goods

Explore a 49-minute seminar on dynamic games and applications that delves into the existence of equilibrium in a dynamic supply chain game with vertical coordination, horizontal competition, and Cournot complementary goods. Presented by Bertrand Crettez from Université Panthéon-Assas, Paris II, France, at the GERAD Research Center on November 24, 2022, this talk examines supply chain competition and vertical coordination in a differential linear-quadratic game setting. Analyze the complex dynamics of supply chains producing complementary goods, where each chain consists of a single supplier/manufacturer and a single seller/retailer coordinating through revenue-sharing contracts. Investigate the Stackelberg game structure within supply chains, Nash competition between retailers in pricing, and manufacturers' competition in production capacity choices. Consider both reversible and irreversible investment scenarios, exploring how manufacturers exploit retailers' equilibrium price decisions. Discover the conditions for equilibrium existence, including the finding that equilibria only exist when manufacturers' production capacities are equal in the irreversible investment case, resulting in time-consistent strategies. Understand the reasons behind the non-existence of equilibrium in certain scenarios, particularly due to discontinuities in manufacturers' instant profit functions relative to their production capacities.