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Evolutionary implementation in a public goods game

Author

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  • Lahkar, Ratul
  • Mukherjee, Saptarshi
Abstract
We consider implementation of the efficient state in a large population public goods game. Due to positive externalities, the efficient state is different from the Nash equilibrium of the game. We apply a transfer scheme equal to the externality in the game. The externality adjusted public goods game is a potential game with a unique Nash equilibrium, which is the efficient state of the original game. It is also a continuous–strategy aggregative game. We introduce the best response dynamic for such aggregative potential games to show evolutionary implementation. Agents converge to the efficient state under this dynamic in the externality adjusted game. We extend this result to other prominent evolutionary dynamics. The pure externality price scheme, however, causes a budget deficit. A modification of this scheme solves this problem while evolutionarily implementing efficiency.

Suggested Citation

  • Lahkar, Ratul & Mukherjee, Saptarshi, 2019. "Evolutionary implementation in a public goods game," Journal of Economic Theory, Elsevier, vol. 181(C), pages 423-460.
    • Handle: RePEc:eee:jetheo:v:181:y:2019:i:c:p:423-460
    DOI: 10.1016/j.jet.2019.03.009
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    Citations

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    Cited by:

    1. Ratul Lahkar & Rezina Sultana, 2020. "Affirmative Action in Large Population Contests," Working Papers 40, Ashoka University, Department of Economics.
    2. Sarvesh Bandhu & Ratul Lahkar, 2022. "A Large Population Approach to Implementing Efficiency with Minimum Inequality," Working Papers 76, Ashoka University, Department of Economics.
    3. 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.
    4. 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.
    5. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    6. Lahkar, Ratul, 2019. "Elimination of non-individualistic preferences in large population aggregative games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 150-165.
    7. Ryoji Jinushi, 2024. "Costly Advertising and Information Congestion: Insights from Pigou's Successors," Working Papers e210, Tokyo Center for Economic Research.
    8. Ratul Lahkar & Vinay Ramani, 2021. "An Evolutionary Approach to Pollution Control in Competitive Markets," Working Papers 68, Ashoka University, Department of Economics.
    9. Shuo Wang & Zhuang Li & Weidong Li & Hua Jiang, 2022. "Continuous Spatial Public Goods Game Based on Particle Swarm Optimization with Memory Stability," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    10. Lahkar, Ratul & Mukherjee, Saptarshi, 2020. "Dominant strategy implementation in a large population public goods game," Economics Letters, Elsevier, vol. 197(C).
    11. Cheng, Yuan & Xue, Yanbo & Chang, Meng, 2020. "Career choice as an extended spatial evolutionary public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    12. Bandhu, Sarvesh & Lahkar, Ratul, 2023. "Survival of altruistic preferences in a large population public goods game," Economics Letters, Elsevier, vol. 226(C).
    13. Ratul Lahkar, 2020. "Convergence to Walrasian equilibrium with minimal information," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 553-578, July.
    14. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.
    15. Sarvesh Bandhu & Ratul Lahkar, 2021. "Implementation in Large Population Games with Multiple Equilibria," Working Papers 62, Ashoka University, Department of Economics.
    16. 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.
    17. 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).
    18. Lahkar, Ratul & Mukherjee, Saptarshi, 2021. "Evolutionary implementation in aggregative games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 137-151.
    19. 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.
    20. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of the Hawk-Dove game with different stochastic noises in infinite populations," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    21. 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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    More about this item

    Keywords

    Public goods; Externalities; Potential games; VCG mechanism; Evolutionary dynamics; Budget balance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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