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Stochastic stability in best shot network games

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  • Boncinelli, Leonardo
  • Pin, Paolo

Abstract

The best shot game applied to networks is a discrete model of many processes of contribution to local public goods. It generally has a wide multiplicity of equilibria that we refine through stochastic stability. We show that, depending on how we define perturbations – i.e., possible mistakes that agents make – we can obtain very different sets of stochastically stable states. In particular and non-trivially, if we assume that the only possible source of error is that of a contributing agent that stops doing so, then the only stochastically stable states are Nash equilibria with the largest contribution.

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  • Boncinelli, Leonardo & Pin, Paolo, 2012. "Stochastic stability in best shot network games," Games and Economic Behavior, Elsevier, vol. 75(2), pages 538-554.
    • Handle: RePEc:eee:gamebe:v:75:y:2012:i:2:p:538-554
    DOI: 10.1016/j.geb.2012.03.001
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    Cited by:

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    3. Boris van Leeuwen & Theo Offerman & Arthur Schram, 2020. "Competition for Status Creates Superstars: an Experiment on Public Good Provision and Network Formation," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 666-707.
    4. Charness, Gary & Feri, Francesco & Meléndez-Jiménez, Miguel A. & Sutter, Matthias, 2012. "Equilibrium Selection in Experimental Games on Networks," University of California at Santa Barbara, Economics Working Paper Series qt51v6w9hd, Department of Economics, UC Santa Barbara.
    5. Gary Charness & Francesco Feri & Miguel A. Meléndez‐Jiménez & Matthias Sutter, 2014. "Experimental Games on Networks: Underpinnings of Behavior and Equilibrium Selection," Econometrica, Econometric Society, vol. 82(5), pages 1615-1670, September.
    6. Leonardo Boncinelli & Alessio Muscillo & Paolo Pin, 2022. "Efficiency and Stability in a Process of Teams Formation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1101-1129, December.
    7. Liu, Jia & Sonntag, Axel & Zizzo, Daniel John, 2022. "Information defaults in repeated public good provision," Journal of Economic Behavior & Organization, Elsevier, vol. 197(C), pages 356-369.
    8. Yann Bramoullé & Rachel Kranton, 2015. "Games Played on Networks," Working Papers halshs-01180657, HAL.
    9. Ziyi Chen & Kaiyan Dai & Xing Jin & Liqin Hu & Yongheng Wang, 2023. "Aspiration-Based Learning in k -Hop Best-Shot Binary Networked Public Goods Games," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    10. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    11. Ying Chen & Tom Lane & Stuart McDonald, 2023. "Endogenous Network Formation in Local Public Goods: An Experimental Analysis," Discussion Papers 2023-02, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    12. Dunia Lopez-Pintado, 2016. "Influence networks and public goods," UMASS Amherst Economics Working Papers 2016-12, University of Massachusetts Amherst, Department of Economics.
    13. Francesco Feri & Paolo Pin, 2020. "Externalities Aggregation In Network Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1635-1658, November.
    14. Dunia López-Pintado, 2015. "Influence Networks and Public Goods," Working Papers 15.04, Universidad Pablo de Olavide, Department of Economics.
    15. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
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    20. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    21. Cui, Zhiwei & Wang, Shouyang & Zhang, Jin & Zu, Lei, 2013. "Stochastic stability in one-way flow networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 410-421.
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    23. Ghosh, Papiya & Kundu, Rajendra P., 2019. "Best-shot network games with continuous action space," Research in Economics, Elsevier, vol. 73(3), pages 225-234.

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    More about this item

    Keywords

    Networks; Best shot game; Stochastic stability;
    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
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

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