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Setting Cournot Versus Lyapunov Games Stability Conditions and Equilibrium Point Properties

Author

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  • Julio B. Clempner

    (Center for Economics, Management and Social Research, National Polytechnic Institute, Lauro Aguirre 120, Col. Agricultura, Del. Miguel Hidalgo, Mexico City, 11360, Mexico)

Abstract

In potential games, the best-reply dynamics results in the existence of a cost function such that each player's best-reply set equals the set of minimizers of the potential given by the opponents' strategies. The study of sequential best-reply dynamics dates back to Cournot and, an equilibrium point which is stable under the game's best-reply dynamics is commonly said to be Cournot stable. However, it is exactly the best-reply behavior that we obtain using the Lyapunov notion of stability in game theory. In addition, Lyapunov theory presents several advantages. In this paper, we show that the stability conditions and the equilibrium point properties of Cournot and Lyapunov meet in potential games.

Suggested Citation

  • Julio B. Clempner, 2015. "Setting Cournot Versus Lyapunov Games Stability Conditions and Equilibrium Point Properties," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-10.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:04:n:s0219198915500115
    DOI: 10.1142/S0219198915500115
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    Citations

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    Cited by:

    1. Julio B. CLEMPNER & Alexander S. POZNYAK, 2016. "Analyzing An Optimistic Attitude For The Leader Firm In Duopoly Models: A Strong Stackelberg Equilibrium Based On A Lyapunov Game Theory Approach," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 41-60.
    2. Julio B. Clempner, 2021. "A Proximal/Gradient Approach for Computing the Nash Equilibrium in Controllable Markov Games," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 847-862, March.

    More about this item

    Keywords

    Cournot; Lyapunov; potential games; dominance-solvable games; routing games; shortest-path; best-reply; 22E46; 53C35; 57S20;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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