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ESSEC Working Papers,
ESSEC Research Center, ESSEC Business School

No WP1606: Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection

Anastasios Dosis
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Anastasios Dosis: Essec Business School, Economics Department

Abstract: I analyse a market with adverse selection in which companies competè a la Bertrand by offering menus of contracts. Contrary to Rothschild and Stiglitz (1976), I allow for any finite number of types and states and more general utility functions. I define the generalised Rothschild-Stiglitz Profile of Actions (RSPA), and I show that, in every possible market, if the RSPA is efficient, it is also a pure strategy Nash equilibrium profile of actions. On the contrary, I show that in markets in which the RSPA is not efficient, preferences admit an expected utility representation with strictly increasing and strictly concave VNM utilities and a weak sorting condition holds, no pure strategy Nash equilibrium exists.

Keywords: Nash Equilibrium; Adverse Selection; Bertrand Competition

JEL-codes: C62; C72; D86; L13

8 pages, February 17, 2016

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