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The Set of Equilibria in Max-Min Two Groups Contests with Binary Actions and a Private Good Prize

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  • Gilli, Mario
  • Sorrentino, Andrea

Abstract

In this paper we consider a deterministic complete information two groups contest where the effort choices made by the teammates are aggregated into group performance by the weakest-link technology (perfect complementarity), that is a “max-min group contest”, as defined by Chowdhury et al. (2016). However, instead of a continuum effort set, we employ a binary action set. Further, we consider private good prizes, so that there is a sharing issue within the winning group. Therefore, we include two stages: the first one about the setting of a sharing rule parameter and the second one about simultaneous and independent actions’ choices. The binary action set allow us to innovate on the existing literature by (i) characterizing the full set of the second stage equilibrium actions; (ii) computationally characterizing in MATLAB the set of within-group symmetric subgame perfect Nash equilibria in pure strategies in the entire game. We find conditions such that the set of within-group symmetric subgame perfect Nash equilibria in pure strategies have the cardinality of the continuum. We also check whether this paper’s results are due to discreteness or to binary choice, proving that in this case there are no subgame perfect Nash equilibria in pure strategies, as proved in the continuum case in Gilli and Sorrentino (2024).

Suggested Citation

  • Gilli, Mario & Sorrentino, Andrea, 2024. "The Set of Equilibria in Max-Min Two Groups Contests with Binary Actions and a Private Good Prize," FEEM Working Papers 343494, Fondazione Eni Enrico Mattei (FEEM).
    • Handle: RePEc:ags:feemwp:343494
    DOI: 10.22004/ag.econ.343494
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    References listed on IDEAS

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    1. repec:wly:soecon:v:83:1:y:2016:p:105-125 is not listed on IDEAS
    2. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    3. Chowdhury, Subhasish M. & Lee, Dongryul & Sheremeta, Roman M., 2013. "Top guns may not fire: Best-shot group contests with group-specific public good prizes," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 94-103.
    4. Mario Gilli & Andrea Sorrentino, 2024. "Characterization of the Set of Equilibria in Max-Min Group Contests with Continuous Efforts and a Private Good Prize," Working Papers 541, University of Milano-Bicocca, Department of Economics.
    5. Barbieri, Stefano & Malueg, David A., 2016. "Private-information group contests: Best-shot competition," Games and Economic Behavior, Elsevier, vol. 98(C), pages 219-234.
    6. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    7. Baik, Kyung Hwan & Lee, Sanghack, 2001. "Strategic Groups and Rent Dissipation," Economic Inquiry, Western Economic Association International, vol. 39(4), pages 672-684, October.
    8. Stefano Barbieri & David Malueg & Iryna Topolyan, 2014. "The best-shot all-pay (group) auction with complete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 603-640, November.
    9. Baik, Kyung Hwan & Kim, In-Gyu & Na, Sunghyun, 2001. "Bidding for a group-specific public-good prize," Journal of Public Economics, Elsevier, vol. 82(3), pages 415-429, December.
    10. Barbieri, Stefano & Kovenock, Dan & Malueg, David A. & Topolyan, Iryna, 2019. "Group contests with private information and the “Weakest Link”," Games and Economic Behavior, Elsevier, vol. 118(C), pages 382-411.
    11. Kolmar, Martin & Rommeswinkel, Hendrik, 2013. "Contests with group-specific public goods and complementarities in efforts," Journal of Economic Behavior & Organization, Elsevier, vol. 89(C), pages 9-22.
    12. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    13. Nitzan, Shmuel, 1991. "Collective Rent Dissipation," Economic Journal, Royal Economic Society, vol. 101(409), pages 1522-1534, November.
    14. Jack Hirshleifer, 1983. "From weakest-link to best-shot: The voluntary provision of public goods," Public Choice, Springer, vol. 41(3), pages 371-386, January.
    15. Lee, Dongryul, 2012. "Weakest-link contests with group-specific public good prizes," European Journal of Political Economy, Elsevier, vol. 28(2), pages 238-248.
    16. Stefano Barbieri & Iryna Topolyan, 2021. "Private‐information group contests with complementarities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(5), pages 772-800, October.
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