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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).

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Bibliographic Info

Paper provided by Department of Economics, University of York in its series Discussion Papers with number 09/07.

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Date of creation: Mar 2009
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Handle: RePEc:yor:yorken:09/07

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Keywords: cost spillovers; Nash and Market equilibrium; coordination failure.;

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  1. Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February.
  2. Vives, Xavier, 2007. "Games of strategic complementarities: An application to bayesian games," IESE Research Papers D/698, IESE Business School.
  3. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
  4. Cooper, Russell & John, Andrew, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, MIT Press, vol. 103(3), pages 441-63, August.
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