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

Author

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  • Dosis, Anastasios

    (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.

Suggested Citation

  • Dosis, Anastasios, 2016. "Bertand Competition and the Existence of Pure Strategy Nash Equilibrium in Markets with Adverse Selection," ESSEC Working Papers WP1606, ESSEC Research Center, ESSEC Business School.
    • Handle: RePEc:ebg:essewp:dr-16006
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    File URL: https://hal-essec.archives-ouvertes.fr/hal-01285185/document
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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. Dosis, Anastasios, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," ESSEC Working Papers WP1607, ESSEC Research Center, ESSEC Business School.
    2. Anastasios Dosis, 2016. "A More General Definition of Equilibrium in Markets with Adverse Selection," Working Papers hal-01285188, HAL.

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    More about this item

    Keywords

    Nash Equilibrium; Adverse Selection; Bertrand Competition;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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