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On the Values of Bayesian Cooperative Games with Sidepayments

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In this paper we explore the relationship between several value-like solution concepts for cooperative games with incomplete information and utility transfers in the form of sidepayments. In our model, state-contingent contracts are required to be incentive compatible, and thus utility might not be not fully transferable (as it would be in the complete information case). When we restrict our attention to games with orthogonal coalitions (i.e., which do not involve strategic externalities), our first main result states that Myerson’s [Cooperative games with incomplete information. Int. J. Game Theory. (1984), 13, 69-96] generalization of the Shapley NTU value and Salamanca’s [A generalization of the Harsanyi NTU value to games with incomplete information. (2016), HAL 01579898] extension of the Harsanyi NTU value are interim utility equivalent. If we allow for arbitrary informational and strategic externalities, our second main result establishes that the ex-ante evaluation of Myerson’s solution equals Kalai and Kalai’s [Cooperation in strategic games revisited. Q. J. Econ. (2013) 128, 917-966] cooperative-competitive value in two-player games with verifiable types.

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  • Salamanca, Andrés, 2018. "On the Values of Bayesian Cooperative Games with Sidepayments," Discussion Papers on Economics 6/2018, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2018_006
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    1. de Clippel, Geoffroy, 2005. "Values for cooperative games with incomplete information: An eloquent example," Games and Economic Behavior, Elsevier, vol. 53(1), pages 73-82, October.
    2. Myerson, Roger B, 1983. "Mechanism Design by an Informed Principal," Econometrica, Econometric Society, vol. 51(6), pages 1767-1797, November.
    3. de Clippel, Geoffroy & Minelli, Enrico, 2004. "Two-person bargaining with verifiable information," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 799-813, November.
    4. Myerson, Roger B., 2007. "Virtual utility and the core for games with incomplete information," Journal of Economic Theory, Elsevier, vol. 136(1), pages 260-285, September.
    5. Françoise Forges & Roberto Serrano, 2013. "Cooperative Games With Incomplete Information: Some Open Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-17.
    6. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
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    8. Myerson, Roger B, 1984. "Two-Person Bargaining Problems with Incomplete Information," Econometrica, Econometric Society, vol. 52(2), pages 461-487, March.
    9. Forges, Francoise & Minelli, Enrico & Vohra, Rajiv, 2002. "Incentives and the core of an exchange economy: a survey," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 1-41, September.
    10. Robert J. Aumann, 1960. "Linearity of unrestrictedly transferable utilities," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 7(3), pages 281-284, September.
    11. Andrés Salamanca, 2020. "A generalization of the Harsanyi NTU value to games with incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 195-225, March.
    12. Francoise Forges & Jean-Francois Mertens & Rajiv Vohra, 2002. "The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects," Econometrica, Econometric Society, vol. 70(5), pages 1865-1892, September.
    13. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November.
    14. Hart, Sergiu, 1985. "Nontransferable Utility Games and Markets: Some Examples and the Harsanyi Solution," Econometrica, Econometric Society, vol. 53(6), pages 1445-1450, November.
    15. Adam Kalai & Ehud Kalai, 2013. "Cooperation in Strategic Games Revisited," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 917-966.
    16. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    17. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
    18. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
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    More about this item

    Keywords

    Cooperative games; incomplete information; sidepayments;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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