An oligopolistic market model is considered where n firms supply a single homogeneous commodity to m different markets. In contrast to perfect competition, the model is oligopolistic in the sense that each firm decides not only the total production quantity of the commodity and its allocation to different markets, but also offering prices for individual markets. Consumers in one market would buy the commodity with the least price in that market. Furthermore, consumers may move from one market to another when the price discrepancy between the two markets is sufficiently large. The demand of one market is given by a linear combination of the least prices of m markets plus a potential demand in that market. Assuming that cost functions of all firms are strictly convex, it is shown that there exists a unique set of prices over m different markets, which achieves the optimal pricing strategy for all firms and balances the demand and supply in all individual markets.