Market Equilibria via Integer Programming

Abstract

We study a model of price competition in a multiproduct oligopoly market. The products are of general nature. Sellers fix prices to maximize their profits and the representative buyer, after observing prices, selects a bundle of products according to his/her reservation value. Consumers are characterized by a set function which determines their willingness to pay for every subset of products. The existence and characterization of Nash equilibria is reached via integer programming. We start with the simplest model where firms produce only one product and extend the equilibrium characterization of Tauman, Urbano and Watanabe (1997) to non-monotonic consumer value functions. Then, we generalize the model to multiproduct firms, and show that Nash equilibria with non-linear prices always exists. We also offer the sufficient conditions which guarantee the existence of linear-price equilibria.