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A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games

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  • C. Ling

    (Southwestern University of Finance and Economics)

  • M. R. Caputo

    (University of Central Florida)

Abstract

The local stability, steady state comparative statics, and local comparative dynamics of symmetric open-loop Nash equilibria for the ubiquitous class of discounted infinite horizon differential games are investigated. It is shown that the functional forms and values of the parameters specified in a differential game are crucial in determining the local stability of a steady state and, in turn, the steady state comparative statics and local comparative dynamics. A simple sufficient condition for a steady state to be a local saddle point is provided. The power and reach of the results are demonstrated by applying them to two well-known differential games.

Suggested Citation

  • C. Ling & M. R. Caputo, 2011. "A Qualitative Characterization of Symmetric Open-Loop Nash Equilibria in Discounted Infinite Horizon Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 151-174, April.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:1:d:10.1007_s10957-010-9779-x
    DOI: 10.1007/s10957-010-9779-x
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    1. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    2. L. Lambertini, 2010. "Oligopoly with Hyperbolic Demand: A Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 108-119, April.
    3. Ragnar Arnason, 1990. "Minimum Information Management in Fisheries," Canadian Journal of Economics, Canadian Economics Association, vol. 23(3), pages 630-653, August.
    4. Cellini, Roberto & Lambertini, Luca, 2007. "A differential oligopoly game with differentiated goods and sticky prices," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1131-1144, January.
    5. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    6. Fershtman, Chaim & Muller, Eitan, 1984. "Capital accumulation games of infinite duration," Journal of Economic Theory, Elsevier, vol. 33(2), pages 322-339, August.
    7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    8. Reynolds, Stanley S, 1987. "Capacity Investment, Preemption and Commitment in an Infinite Horizon Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 69-88, February.
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    Cited by:

    1. Chen Ling & Shravan Luckraz & Bruno Antonio Pansera, 2023. "Comparative Dynamics in Differential Games: A Note on the Differentiability of Solutions," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1093-1105, March.
    2. Simon Hoof, 2021. "Dynamic Monopolistic Competition," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 560-577, May.

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