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Equilibrium in secure strategies

Author

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  • iskakov, Mikhail

    (Institute of Control Sciences RAS, Moscow)

  • ISKAKOV, Alexey

    (Institute of Control Sciences RAS, Moscow)

Abstract

A new concept of equilibrium in secure strategies (EinSS) in non-cooperative games is presented. The EinSS coincides with the Nash-Cournot Equilibrium when Nash-Cournot Equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against actions of other players. The new concept is illustrated by a number of matrix game examples and compared with other closely related theoretical models. We prove the existence of equilibrium in secure strategies in four classic games that fail to have Nash-Cournot equilibria. On an infinite line we obtain the solution in secure strategies of the classic Hotelling’s price game (1929) with a restricted reservation price and linear transportation costs. New type of monopolistic solution in secure strategies is discovered in the Tullock Contest (1967, 1980) of two players. For the model of insurance market we prove that the contract pair found by Rothschild, Stiglitz and Wilson (1976) is always an equilibrium in secure strategies. We characterize all equilibria in secure prices in the Bertrand-Edgeworth duopoly model with capacity constraints.

Suggested Citation

  • iskakov, Mikhail & ISKAKOV, Alexey, 2012. "Equilibrium in secure strategies," CORE Discussion Papers 2012061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2012061
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    File URL: http://uclouvain.be/cps/ucl/doc/core/documents/coredp2012_61web.pdf
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    References listed on IDEAS

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    1. Shy, Oz, 2002. "A quick-and-easy method for estimating switching costs," International Journal of Industrial Organization, Elsevier, vol. 20(1), pages 71-87, January.
    2. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," Review of Economic Studies, Oxford University Press, vol. 53(2), pages 175-204.
    3. Baye, M.R. & Kovenock, D., 1993. "The Solution to the Tullock Rent-Seeking Game When R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 9368, Tilburg - Center for Economic Research.
    4. Iskakov, Mikhail & Iskakov, Alexey, 2012. "Solution of the Hotelling’s game in secure strategies," Economics Letters, Elsevier, vol. 117(1), pages 115-118.
    5. Baye, M.R. & Kovenock, D., 1993. "The Solution to the Tullock Rent-Seeking Game When R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 9368, Tilburg - Center for Economic Research.
    6. Dixon, Huw, 1984. "The existence of mixed-strategy equilibria in a price-setting oligopoly with convex costs," Economics Letters, Elsevier, vol. 16(3-4), pages 205-212.
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    Citations

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    Cited by:

    1. ISKAKOV, Mikhail & ISKAKOV, Alexey & ZAKHAROV, Alexey, 2014. "Equilibria in secure strategies in the Tullock contest," CORE Discussion Papers 2014010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    equilibrium in secure strategies; Hotelling model; Tullock contest; insurance market; Bertrand-Edgeworth duopoly;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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