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For a homogeneous product oligopoly market, possibilities for pure strategy Nash equilibria in prices are studied. Consumers, who each nonstrategically purchase one unit up to a common reservation price, are hypothesized to be more concerned with large price differences (and therefore buy from the cheapest firm) than slightly different prices. For the duopoly case, existence, uniqueness, and characterization results are provided. Linear examples are given with 2 and n firms.