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Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection

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  • Anastasios Dosis

    (ESSEC Business School and THEMA (UMR 8184) - ESSEC Business School - THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université)

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.

Suggested Citation

  • Anastasios Dosis, 2016. "Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection," Working Papers hal-01285185, HAL.
    • Handle: RePEc:hal:wpaper:hal-01285185
    Note: View the original document on HAL open archive server: https://essec.hal.science/hal-01285185
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    References listed on IDEAS

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    1. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    2. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    3. Wilson, Charles, 1977. "A model of insurance markets with incomplete information," Journal of Economic Theory, Elsevier, vol. 16(2), pages 167-207, December.
    4. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
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    Cited by:

    1. Anastasios Dosis, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," Working Papers hal-01285188, HAL.
    2. Dosis, Anastasios, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," ESSEC Working Papers WP1607, ESSEC Research Center, ESSEC Business School.

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    Keywords

    Adverse Selection; Bertrand Competition; Nash Equilibrium;
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