Non-Cooperative Joint Replenishment Under Asymmetric Information
Posted: 18 Aug 2012
Date Written: August 17, 2012
We consider jointly replenishing n ex--ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exits and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm's type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs.
Keywords: Joint replenishment, Economic Order Quantity model, Non-cooperative game theory, Information asymmetry
JEL Classification: C72, M11, D82
Suggested Citation: Suggested Citation