Game theoretic analysis of an inventory problem with substitution, random demand and yield

A game theoretic approach is used to analyze an inventory problem with two products, random demand, and random supply. The supply chain analyzed includes two retailers that sell two substitutable products and two suppliers. Each retailer faces a stochastic demand for the product she sells and replenishes her inventory from her supplier. The supplier provides a random fraction of the quantity requested. A given percentage of customers with unmet demand will substitute the product sold by the other retailer. We assume that the two retailers who make ordering decisions are rational players. Since each retailer's decision affects the single period expected profit of the other retailer, game theory is used to find the order quantities when the retailers use a Nash strategy.