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A correspondence principle for cooperative differential equations

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  • Kwong, Kai-Sun

Abstract

This paper establishes a correspondence principle in a system of cooperative differential equations. Equilibria that are locally asymptotically stable must exhibit monotone comparative statics. In a wider context, all equilibria that exhibit monotone comparative statics are locally asymptotically stable. The orbits of such systems are nondecreasing in the parameter and the adjustment dynamics after a parameter change are monotone and convergent to a unique limit. Our results can be applied to such models as adaptive play in games with strategic complementarities, stochastic fictitious play in supermodular games, and the Matsuyama [6] model of global financial market liberalization with multiple capital goods.

Suggested Citation

  • Kwong, Kai-Sun, 2014. "A correspondence principle for cooperative differential equations," Journal of Economic Theory, Elsevier, vol. 150(C), pages 878-887.
    • Handle: RePEc:eee:jetheo:v:150:y:2014:i:c:p:878-887
    DOI: 10.1016/j.jet.2013.10.004
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    References listed on IDEAS

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    1. Federico Echenique, 2002. "Comparative Statics by Adaptive Dynamics and the Correspondence Principle," Econometrica, Econometric Society, vol. 70(2), pages 833-844, March.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Kiminori Matsuyama, 2004. "Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations," Econometrica, Econometric Society, vol. 72(3), pages 853-884, May.
    4. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
    5. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-459, June.
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    Cited by:

    1. Christensen, Finn & Cornwell, Christopher R., 2018. "A strong correspondence principle for smooth, monotone environments," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 15-24.

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    More about this item

    Keywords

    Correspondence principle; Monotone comparative statics; Asymptotic stability; Differential equations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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