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Sequential Contracting with Multiple Principals

Author

Listed:
  • Giacomo Calzolari
  • Alessandro Pavan
Abstract
This paper considers dynamic games in which multiple principals contract sequentially and non-cooperatively with the same agent and provides characterization results useful for applications. Our benchmark model is one of private contracting in which downstream principals do not observe upstream mechanisms, nor the decisions taken in these mechanisms. We show that any equilibrium outcome that can be sustained with any arbitrary strategy space for the principals can also be sustained by restricting the principals to offer excended direct mechanisms. In these mechanisms, the agent first reports his extended type (i.e. his exogenous private information along with the endogenous payoff-relevant decisions contracted upstream), the principal then responds by offering the agent a (possibly degenerate) menu of contracts that are payoff-equivalent for that extended type, and finally the agent selects a contract from this menu and the contract is executed. We also show that characterizing equilibria through extended direct mechanisms is facilitated by the fact that (i) each principal can be restricted to offer a single mechanism; (ii) when the agent's strategy is Markov (i.e. it depends only on payoff-relevant information), each mechanism can be restricted to offer a single contract to each extended type; and (iii) restricting the agent's strategy to be Markov is without loss in the case of deterministic decisions, e.g. when the contracts are deterministic and the agent does not mix over effort. We finally show how the aforementioned results must be adjusted to occommodate alternative assumptions on the observability of upstream histories and/or the sequence of contracting examined in the literature.

Suggested Citation

  • Giacomo Calzolari & Alessandro Pavan, 2007. "Sequential Contracting with Multiple Principals," Discussion Papers 1457, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1457
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      • Matteo Escud'e & Ludvig Sinander, 2019. "Slow persuasion," Papers 1903.09055, arXiv.org, revised Apr 2022.
    3. Andrea Attar & Eloisa Campioni & Thomas Mariotti & Alessandro Pavan, 2021. "Keeping the Agents in the Dark: Private Disclosures in Competing Mechanisms," CEIS Research Paper 519, Tor Vergata University, CEIS, revised 21 Oct 2021.
    4. V. Bhaskar & Nikita Roketskiy, 2021. "Consumer privacy and serial monopoly," RAND Journal of Economics, RAND Corporation, vol. 52(4), pages 917-944, December.
    5. Calzolari, Giacomo & Pavan, Alessandro, 2008. "On the use of menus in sequential common agency," Games and Economic Behavior, Elsevier, vol. 64(1), pages 329-334, September.
    6. Alessandro Acquisti & Curtis Taylor & Liad Wagman, 2016. "The Economics of Privacy," Journal of Economic Literature, American Economic Association, vol. 54(2), pages 442-492, June.
    7. Andrea Attar & Catherine Casamatta & Arnold Chassagnon & Jean Paul Décamps, 2019. "Contracting Sequentially with Multiple Lenders: The Role of Menus," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(4), pages 977-990, June.
    8. Andrea Attar & Catherine Casamatta & Arnold Chassagnon & Jean Paul Décamps, 2017. "On the Role of Menus in Sequential Contracting: a Multiple Lending Example," CEIS Research Paper 409, Tor Vergata University, CEIS, revised 13 Jul 2017.
    9. Han, Seungjin, 2014. "Implicit collusion in non-exclusive contracting under adverse selection," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 85-95.
    10. Peters, Michael, 2015. "Reciprocal contracting," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 102-126.
    11. Wu, Wenhao, 2023. "Sequential Bayesian persuasion," Journal of Economic Theory, Elsevier, vol. 214(C).
    12. Piotr Dworczak, 2020. "Mechanism Design With Aftermarkets: Cutoff Mechanisms," Econometrica, Econometric Society, vol. 88(6), pages 2629-2661, November.
    13. Peters, Michael, 2014. "Competing Mechanisms," Microeconomics.ca working papers michael_peters-2014-7, Vancouver School of Economics, revised 19 Feb 2014.
    14. Seungjin Han & Siyang Xiong, 2021. "A Unified Approach to Equilibrium Analysis in Competing Mechanism Games," Department of Economics Working Papers 2021-09, McMaster University.
    15. Graham Mallard, 2014. "Static Common Agency And Political Influence: An Evaluative Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 17-35, February.
    16. Krasteva, Silvana & Yildirim, Huseyin, 2012. "On the role of confidentiality and deadlines in bilateral negotiations," Games and Economic Behavior, Elsevier, vol. 75(2), pages 714-730.
    17. Rivera Mora, Ernesto, 2024. "Mechanism design with belief-dependent preferences," Journal of Economic Theory, Elsevier, vol. 216(C).
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    19. Seungjin Han, 2020. "Quasi Ex-Post Equilibrium in Competing Mechanisms," Department of Economics Working Papers 2020-11, McMaster University.
    20. Michael Peters, 2014. "Competing mechanisms," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(2), pages 373-397, May.
    21. Giacomo Calzolari & Carlo Scarpa, 2016. "Conglomerates And Regulation," Economic Inquiry, Western Economic Association International, vol. 54(3), pages 1648-1669, July.
    22. Susumu Cato & Akifumi Ishihara, 2017. "Transparency and Performance Evaluation in Sequential Agency," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 33(3), pages 475-506.
    23. Ghosh, Sambuddha & Han, Seungjin, 2012. "Repeated Contracting in Decentralised Markets," Microeconomics.ca working papers seungjin_han-2012-12, Vancouver School of Economics, revised 02 May 2013.
    24. Thomas A. Gresik & Kai A. Konrad, 2017. "Tax Havens, Accounting Experts, and Fee-Setting Rules," CESifo Working Paper Series 6774, CESifo.
    25. Peck, James, 2018. "Competing mechanisms with multi-unit consumer demand," Journal of Economic Theory, Elsevier, vol. 177(C), pages 126-161.

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    More about this item

    Keywords

    Sequential common agency; mechanism design; contracts; endogenous types.;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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