Technical Note—Existence and Uniqueness of Price Equilibria in Defender
- 1 February 1988
- journal article
- Published by Institute for Operations Research and the Management Sciences (INFORMS) in Marketing Science
- Vol. 7 (1) , 92-93
- https://doi.org/10.1287/mksc.7.1.92
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
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