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Existence of Equilibrium Mechanisms in Generalized Principal-Agent Problems with Interacting Teams

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  • Brian Roberson

Abstract

We study incentive design when multiple principals simultaneously design mechanisms for their respective teams in environments with strategic spillovers. In this environment, each principal’s set of incentive-compatible mechanisms—those that satisfy their own agents’ incentive compatibility constraints—depends on the mechanisms offered by the other teams. Following a classic example by Myerson (1982), such games may lack equilibrium due to discontinuities in the correspondence of incentive-compatible mechanisms. We establish general conditions for equilibrium existence by introducing a novel approach that involves tracking both the outcome distributions along the truthful-obedient path and the sets of outcome distributions achievable through unilateral deviations, thereby providing a foundation for analyzing a wide range of multi-principal mechanism design with team production and agency problems.

Suggested Citation

  • Brian Roberson, 2026. "Existence of Equilibrium Mechanisms in Generalized Principal-Agent Problems with Interacting Teams," Purdue University Economics Working Papers 1356, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1356
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    1. d'Aspremont, Claude & Jacquemin, Alexis, 1990. "Cooperative and Noncooperative R&D in Duopoly with Spillovers: Erratum," American Economic Review, American Economic Association, vol. 80(3), pages 641-642, June.
    2. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01396183, HAL.
    3. Joan Esteban & Debraj Ray, 2008. "Collective Action and the Group Size Paradox," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 379-388, Springer.
    4. Rongzhu Ke & Xinyi Xu, 2023. "The existence of an optimal deterministic contract in moral hazard problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 375-416, August.
    5. Bastani, Spencer & Giebe, Thomas & Gürtler, Oliver, 2022. "Simple equilibria in general contests," Games and Economic Behavior, Elsevier, vol. 134(C), pages 264-280.
    6. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    7. Francesco Trevisan, 2020. "Optimal prize allocations in group contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 431-451, October.
    8. Shmuel Nitzan & Kaoru Ueda, 2018. "Selective incentives and intragroup heterogeneity in collective contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(4), pages 477-498, August.
    9. Barbieri, Stefano & Malueg, David A., 2016. "Private-information group contests: Best-shot competition," Games and Economic Behavior, Elsevier, vol. 98(C), pages 219-234.
    10. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    11. Moscarini, Giuseppe & Squintani, Francesco, 2010. "Competitive experimentation with private information: The survivor's curse," Journal of Economic Theory, Elsevier, vol. 145(2), pages 639-660, March.
    12. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," Post-Print hal-01396183, HAL.
    13. Ryvkin, Dmitry & Drugov, Mikhail, 2020. "The shape of luck and competition in winner-take-all tournaments," Theoretical Economics, Econometric Society, vol. 15(4), November.
    14. Eliaz, Kfir & Wu, Qinggong, 2018. "A simple model of competition between teams," Journal of Economic Theory, Elsevier, vol. 176(C), pages 372-392.
    15. René Kirkegaard, 2023. "Contest Design with Stochastic Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 15(1), pages 201-238, February.
    16. Itoh, Hideshi, 1991. "Incentives to Help in Multi-agent Situations," Econometrica, Econometric Society, vol. 59(3), pages 611-636, May.
    17. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    18. Henrique Castro-Pires & Hector Chade & Jeroen Swinkels, 2024. "Disentangling Moral Hazard and Adverse Selection," American Economic Review, American Economic Association, vol. 114(1), pages 1-37, January.
    19. Ozerturk, Saltuk & Yildirim, Huseyin, 2021. "Credit attribution and collaborative work," Journal of Economic Theory, Elsevier, vol. 195(C).
    20. Nitzan, Shmuel & Ueda, Kaoru, 2011. "Prize sharing in collective contests," European Economic Review, Elsevier, vol. 55(5), pages 678-687, June.
    21. Shmuel Nitzan & Kaoru Ueda, 2014. "Intra-group heterogeneity in collective contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 219-238, June.
    22. Huseyin Yildirim, 2023. "Who fares better in teamwork?," RAND Journal of Economics, RAND Corporation, vol. 54(2), pages 299-324, June.
    23. Pau Balart & Sabine Flamand & Orestis Troumpounis, 2016. "Strategic choice of sharing rules in collective contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(2), pages 239-262, February.
    24. Philip Brookins & Dmitry Ryvkin, 2016. "Equilibrium existence in group contests," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 265-276, October.
    25. Bich, Philippe & Laraki, Rida, 2017. "On the existence of approximate equilibria and sharing rule solutions in discontinuous games," Theoretical Economics, Econometric Society, vol. 12(1), January.
    26. Prokopovych, Pavlo & Yannelis, Nicholas C., 2023. "On monotone pure-strategy Bayesian-Nash equilibria of a generalized contest," Games and Economic Behavior, Elsevier, vol. 140(C), pages 348-362.
    27. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    28. Anat R. Admati & Motty Perry, 1991. "Joint Projects without Commitment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 259-276.
    29. Oriol Carbonell-Nicolau & Richard P. McLean, 2018. "On the Existence of Nash Equilibrium in Bayesian Games," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 100-129, February.
    30. 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.
    31. Katsuya Kobayashi & Hideo Konishi & Kaoru Ueda, 2025. "Prize-allocation rules in generalized team contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(1), pages 151-179, February.
    32. Gottlieb, Daniel & Moreira, Humberto, 2022. "Simple contracts with adverse selection and moral hazard," Theoretical Economics, Econometric Society, vol. 17(3), July.
    33. Huseyin Yildirim, 2006. "Getting the Ball Rolling: Voluntary Contributions to a Large‐Scale Public Project," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(4), pages 503-528, October.
    34. Katsuya Kobayashi & Hideo Konishi, 2021. "Effort complementarity and sharing rules in group contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(2), pages 205-221, February.
    35. Kamien, Morton I & Muller, Eitan & Zang, Israel, 1992. "Research Joint Ventures and R&D Cartels," American Economic Review, American Economic Association, vol. 82(5), pages 1293-1306, December.
    36. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    37. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    38. Gottlieb, Daniel & Moreira, Humberto, 2022. "Simple contracts with adverse selection and moral hazard," Theoretical Economics, Econometric Society, vol. 17(3), July.
    39. Philippe Bich & Rida Laraki, 2017. "On the Existence of approximative Equilibria and Sharing Rule Solutions in Discontinuous Games," PSE-Ecole d'économie de Paris (Postprint) hal-01396183, HAL.
    40. Erik J. Balder, 1988. "Generalized Equilibrium Results for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 265-276, May.
    41. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    42. Cetemen, Doruk & Hwang, Ilwoo & Kaya, Ayça, 2020. "Uncertainty-driven cooperation," Theoretical Economics, Econometric Society, vol. 15(3), July.
    43. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
    44. T. Renee Bowen & George Georgiadis & Nicolas S. Lambert, 2019. "Collective Choice in Dynamic Public Good Provision," American Economic Journal: Microeconomics, American Economic Association, vol. 11(1), pages 243-298, February.
    45. Shmuel Nitzan, 2008. "Collective Rent Dissipation," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 309-321, Springer.
    46. Paulo Barelli & Idione Meneghel, 2013. "A Note on the Equilibrium Existence Problem in Discontinuous Games," Econometrica, Econometric Society, vol. 81(2), pages 813-824, March.
    47. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
    48. Bo Chen & Yu Chen & David Rietzke, 2020. "Simple contracts under observable and hidden actions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1023-1047, June.
    49. Marina Halac & Elliot Lipnowski & Daniel Rappoport, 2021. "Rank Uncertainty in Organizations," American Economic Review, American Economic Association, vol. 111(3), pages 757-786, March.
    50. Andrew McLennan & Paulo K. Monteiro & Rabee Tourky, 2011. "Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem," Econometrica, Econometric Society, vol. 79(5), pages 1643-1664, September.
    51. Taylor, Curtis R, 1995. "Digging for Golden Carrots: An Analysis of Research Tournaments," American Economic Review, American Economic Association, vol. 85(4), pages 872-890, September.
    52. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    53. Crutzen, Benoît S Y & Flamand, Sabine & Sahuguet, Nicolas, 2020. "A model of a team contest, with an application to incentives under list proportional representation," Journal of Public Economics, Elsevier, vol. 182(C).
    54. 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.
    55. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    56. Carmona, Guilherme, 2009. "An existence result for discontinuous games," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1333-1340, May.
    57. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    58. Olszewski, Wojciech & Siegel, Ron, 2023. "Equilibrium existence in games with ties," Theoretical Economics, Econometric Society, vol. 18(2), May.
    59. Hideo Konishi & Nicolas Sahuguet & Benoît S. Y. Crutzen, 2024. "Allocation rules of indivisible prizes in team contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 69-100, August.
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