Technical Note—Existence and Uniqueness of Price Equilibria in Defender
John R. Hauser, Birger Wernerfelt
Marketing Science · 1988 · Volume 7 · Issue 1
Abstract
This note provides a formal proof that for the Defender model, with uniformly distributed tastes, the Nash price equilibria exist and, for a given set of positions, that they are unique. We also show that the profit function is well-behaved—continuous and quasi-concave—and that the maximum occurs on the concave portion of the curve.
Keywords
pricing, positioning
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