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Tempered Best Response Dynamics

Author

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  • Dai Zusai

    (Department of Economics, Temple University)

Abstract

We propose a new deterministic evolutionary dynamic—the tempered best response dynamic (tBRD)---to capture two features of economic decision making: optimization and continuous sensitivity to incentives. That is, in the tBRD, an agent is more likely to revise his action when his current payoff is further from the optimal payoff, and he always switches to an optimal action when revising. The tBRD is a payoff monotone selection like the replicator dynamic, which makes medium and long-run outcomes more consistent with predictions from equilibrium refinement than the BRD in some situations. The technical contribution of the tBRD is continuous sensitivity, which allows us to apply results of a system of piecewise differential equations in order to obtain conditions for uniqueness and stability of solutions.

Suggested Citation

  • Dai Zusai, 2013. "Tempered Best Response Dynamics," DETU Working Papers 1301, Department of Economics, Temple University.
    • Handle: RePEc:tem:wpaper:1301
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    File URL: http://www.cla.temple.edu/RePEc/documents/DETU_13_01.pdf
    File Function: First version, 2013
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    Cited by:

    1. Dai Zusai, 2020. "On forward invariance in Lyapunov stability theorem for local stability," Papers 2006.04280, arXiv.org.
    2. Sawa, Ryoji & Zusai, Dai, 2019. "Evolutionary dynamics in multitasking environments," Journal of Economic Behavior & Organization, Elsevier, vol. 166(C), pages 288-308.
    3. Dai Zusai, 2018. "Net gains in evolutionary dynamics: A unifying and intuitive approach to dynamic stability," Papers 1805.04898, arXiv.org, revised Oct 2023.
    4. Paolo Crosetto & Alexia Gaudeul, 2017. "Choosing not to compete: Can firms maintain high prices by confusing consumers?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 26(4), pages 897-922, December.
    5. Sawa, Ryoji & Zusai, Dai, 2014. "Evolutionary imitative dynamics with population-varying aspiration levels," Journal of Economic Theory, Elsevier, vol. 154(C), pages 562-577.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.

    More about this item

    Keywords

    best response dynamic; payoff monotonicity; status-quo bias; switching costs; proper equilibrium; piecewise differential equations;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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