Existence and Optimality of Nash Equilibria in Inventory Games

Abstract

This paper studies the stability and optimality of a distributed consensus protocol for n-player repeated non cooperative games under incomplete information. At each stage, the players choose binary strategies and incur in a payo® monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in whether reordering or not from a common warehouse. The authors focus on Pareto optimality as a measure of coordination of reordering strategies, proving that there exists a unique Pareto optimal Nash equilibrium that verifies certain stability conditions.