A newsvendor pricing game

This paper considers a horizontal market of multiple firms that face stochastic price-dependent demand. The firms make joint pricing/inventory decisions and use price to compete for market demand. With fairly general demand models that are price-dependent, stochastic, and substitutable among firms, we prove the existence and uniqueness of the pure-strategy Nash equilibrium. The market at the equilibrium exhibits a bias toward under-pricing caused by competition; specifically, raising prices at any equilibrium of the game increases the total system profit, and at any joint-optimal set of pricing levels each self-interested firm has an incentive to lower its price. This result closely parallels that obtained in the inventory competition games in which prices are fixed and the bias is toward overstocking.