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Equilibria in symmetric games: theory and applications

Author

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  • Hefti, Andreas

    (Department of Economics, University of Zurich and School of Management and Law, Zurich Unisversity of Applied Sciences)

Abstract

This article presents a new approach to analyze the equilibrium set of symmetric, differentiable games by separating between multiple symmetric equilibria and asymmetric equilibria. This separation allows to investigate, for example, how various parameter constellations affect the scope for multiple symmetric or asymmetric equilibria, or how the equilibrium set depends on the nature of the strategies. The approach is particularly helpful in applications because (1) it allows to reduce the complexity of the uniqueness-problem to a two-player game, (2) boundary conditions are less critical compared to standard procedures, and (3) best-replies need not be everywhere differentiable. The usefulness of the separation approach is illustrated with several examples, including an application to asymmetric games and to a two-dimensional price-information game.

Suggested Citation

  • Hefti, Andreas, 2017. "Equilibria in symmetric games: theory and applications," Theoretical Economics, Econometric Society, vol. 12(3), September.
    • Handle: RePEc:the:publsh:2151
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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