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Evolutionary implementation in aggregative games

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  • Lahkar, Ratul
  • Mukherjee, Saptarshi

Abstract

Due to externalities, the equilibrium behavior in aggregative games is not efficient in the sense of maximizing aggregate payoff. We characterize conditions such that efficiency can be globally implemented in such games under evolutionary dynamics. If payoffs satisfy certain important concavity conditions, then the aggregate payoff function of these games has a unique maximizer. Once the planner imposes a transfer equal to the externality generated by agents, we obtain a new externality adjusted game. This is a potential game with the aggregate payoff function of the original game being its potential function. Evolutionary dynamics converge globally to the maximizer of this potential function, thereby implementing efficiency in the original game. Our earlier paper on public goods (Lahkar and Mukherjee, 2019) emerges as an example of the present general analysis. Two new applications are public bads and the tragedy of the commons.

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  • Lahkar, Ratul & Mukherjee, Saptarshi, 2021. "Evolutionary implementation in aggregative games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 137-151.
    • Handle: RePEc:eee:matsoc:v:109:y:2021:i:c:p:137-151
    DOI: 10.1016/j.mathsocsci.2020.11.004
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    Cited by:

    1. Sarvesh Bandhu & Ratul Lahkar, 2022. "A Large Population Approach to Implementing Efficiency with Minimum Inequality," Working Papers 76, Ashoka University, Department of Economics.
    2. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    3. Sarvesh Bandhu & Ratul Lahkar, 2021. "Implementation in Large Population Games with Multiple Equilibria," Working Papers 62, Ashoka University, Department of Economics.
    4. Sarvesh Bandhu & Ratul Lahkar, 2023. "Evolutionary robustness of dominant strategy implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 685-721, August.
    5. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2023. "The logit dynamic in supermodular games with a continuum of strategies: A deterministic approximation approach," Games and Economic Behavior, Elsevier, vol. 139(C), pages 133-160.
    6. Ratul Lahkar & Vinay Ramani, 2022. "An Evolutionary Approach to Pollution Control in Competitive Markets," Dynamic Games and Applications, Springer, vol. 12(3), pages 872-896, September.
    7. Ratul Lahkar & Vinay Ramani, 2021. "An Evolutionary Approach to Pollution Control in Competitive Markets," Working Papers 68, Ashoka University, Department of Economics.
    8. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    9. Bandhu, Sarvesh & Lahkar, Ratul, 2023. "Survival of altruistic preferences in a large population public goods game," Economics Letters, Elsevier, vol. 226(C).
    10. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.
    11. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    12. Ratul Lahkar & Sayan Mukherjee & Souvik Roy, 2022. "A Deterministic Approximation Approach to the Continuum Logit Dynamic with an Application to Supermodular Games," Working Papers 79, Ashoka University, Department of Economics.
    13. RatulLahkar & Sayan Mukherjee & Souvik Roy, 2021. "Generalized Perturbed Best Response Dynamics with a Continuum of Strategies," Working Papers 51, Ashoka University, Department of Economics.

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