Learning in inventory competition games

Abstract

In a noncooperative game with rational players, Nash strategies are one of the strategies that players can agree on, because none of the players are willing to impose damage to the competitor by lowering their own expected profit. In this dissertation, we incorporate fixed-ordering costs in an inventory competition game; we study the existence of pure Nash equilibrium and behavior of players at Nash equilibrium in a one-period game. We establish the non-existence of pure Nash equilibrium for a large class of multi-period competition games. In real life, decision-makers are limited in their observations or information about their competitors. In this dissertation, we focus on an imperfect-information competition game in which players do not have any information about their competitors, other than the implicit information encoded in their own observations affected by their competitors' past inventory decisions. We introduce simple learning algorithms which allow players to make their decisions in a repeated inventory competition. We prove that the inventory decisions generated by the learning algorithms converge, with probability one, to certain threshold values that constitute an equilibrium in pure Markov strategies for the inventory competition game.