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Conditional and Unconditional Multiple Equilibria with Strategic Complementarities

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  • Stefania Borla
  • Peter Simmons

Abstract

We take a general model of externalities matching the Cooper & John framework with identical agents. If each agent's payoff depends on a parameter interpreted as the favourableness of the environment, we explore how the number of Nash equilibria varies with this parameter, especially in the cases in which the reaction curves are either concave or convex. In many examples the environmental conditions are themselves endogenous because either market or regulatory forces interact with agents' Nash equilibrium actions. This gives the idea of a simultaneous equilibrium in the environment and players' symmetric actions. We analyse how this generalised equilibrium behaves as a function of some additional parameters conditioning the environmental response to players actions. We show that generally there is a fold bifurcation in these equilibria. We illustrate the principles with two examples from industrial economics (cost spillovers between firms and demand spillovers under imperfect competition).

Suggested Citation

  • Stefania Borla & Peter Simmons, 2009. "Conditional and Unconditional Multiple Equilibria with Strategic Complementarities," Discussion Papers 09/07, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:09/07
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    References listed on IDEAS

    as
    1. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 441-463.
    2. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February.
    3. Xavier Vives, 2007. "Games of strategic complementarities: an application to Bayesian games," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(4), pages 237-247, December.
    4. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
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    More about this item

    Keywords

    cost spillovers; Nash and Market equilibrium; coordination failure.;
    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
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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