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Stability and equilibrium in decision rules: an application to duopoly

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  • John Bone
  • Huw Dixon

Abstract

This paper analyses an indefinitely-repeated Cournot duopoly. Firms select simple dynamic decision rules which, taken together, comprise a first-order linear difference equation system. A boundedly-rational objective function is assumed, by which the firm’s payoff is its profit at the point of convergence, if any. Stable Nash equilibria are characterised and located in output space, stability in this context being equivalent to subgame-perfection. Comparable results are derived for a conventional discounted-profit objective function, where this equivalence does not hold, but where stability may nevertheless be of intrinsic interest. In either context, stability is incompatible with joint profit maximisation.

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  • John Bone & Huw Dixon, "undated". "Stability and equilibrium in decision rules: an application to duopoly," Discussion Papers 99/33, Department of Economics, University of York.
  • Handle: RePEc:yor:yorken:99/33
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    File URL: https://www.york.ac.uk/media/economics/documents/discussionpapers/1999/9933.pdf
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    1. Doriana Delfino & Peter J. Simmons, "undated". "Infectious disease and economic growth: the case of tuberculosis," Discussion Papers 99/23, Department of Economics, University of York.
    2. Geoffard, Pierre-Yves & Philipson, Tomas, 1996. "Rational Epidemics and Their Public Control," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 603-624, August.
    3. Geoffard, Pierre-Yves & Philipson, Tomas, 1997. "Disease Eradication: Private versus Public Vaccination," American Economic Review, American Economic Association, vol. 87(1), pages 222-230, March.
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