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The equal split-off set for NTU-games

Author

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  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Yanovskaya, Elena

Abstract

This paper introduces and studies the equal split-off set for cooperative games with nontransferable utility. We illustrate the new solution for the famous Roth-Shafer examples and present two axiomatic characterizations based on different consistency properties on the class of exact partition games, i.e. the class of games where it intersects the core. Moreover, we provide explicit expressions for the class of bargaining problems and the class of bankruptcy problems.

Suggested Citation

  • Dietzenbacher, Bas & Yanovskaya, Elena, 2022. "The equal split-off set for NTU-games," Research Memorandum 002, Maastricht University, Graduate School of Business and Economics (GSBE).
  • Handle: RePEc:unm:umagsb:2022002
    DOI: 10.26481/umagsb.2022002
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    1. Lejano, Raul P., 2011. "A note on solution concepts for nontransferable utility games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 777-780.
    2. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.
    3. Bas Dietzenbacher & Elena Yanovskaya, 2021. "Consistency of the equal split-off set," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 1-22, March.
    4. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    5. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    6. Llerena, Francesc & Mauri, Llúcia, 2017. "On the existence of the Dutta–Ray’s egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 92-99.
    7. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    8. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    9. Joseph Greenberg, 1985. "Cores of Convex Games Without Side Payments," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 523-525, August.
    10. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    11. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    12. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    13. Samet, Dov, 1985. "An axiomatization of the egalitarian solutions," Mathematical Social Sciences, Elsevier, vol. 9(2), pages 173-181, April.
    14. Harsanyi, John C, 1980. "Comments on Roth's Paper, "Values for Games without Side Payments"," Econometrica, Econometric Society, vol. 48(2), pages 477-477, March.
    15. Nechemia Asscher, 1976. "An Ordinal Bargaining Set for Games Without Side Payments," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 381-389, November.
    16. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    17. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    18. Tadenuma, K, 1992. "Reduced Games, Consistency, and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 325-334.
    19. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November.
    20. Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
    21. Hart, Sergiu, 1985. "Nontransferable Utility Games and Markets: Some Examples and the Harsanyi Solution," Econometrica, Econometric Society, vol. 53(6), pages 1445-1450, November.
    22. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    23. Roth, Alvin E, 1980. "Values for Games without Sidepayments: Some Difficulties with Current Concepts," Econometrica, Econometric Society, vol. 48(2), pages 457-465, March.
    24. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    25. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    26. Shafer, Wayne J, 1980. "On the Existence and Interpretation of Value Allocation," Econometrica, Econometric Society, vol. 48(2), pages 466-476, March.
    27. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    28. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2021. "Axiomatizations of Dutta-Ray’s egalitarian solution on the domain of convex games," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    29. Bezalel Peleg & Stef Tijs & Peter Borm & Gert-Jan Otten, 1998. "The MC-value for monotonic NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 37-47.
    30. Elena Yanovskaya, 2010. "The Extension Of Dutta–Ray'S Solution To Convex Ntu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 339-361.
    31. Kalai, Ehud & Samet, Dov, 1985. "Monotonic Solutions to General Cooperative Games," Econometrica, Econometric Society, vol. 53(2), pages 307-327, March.
    32. Geoffroy de Clippel & Hans Peters & Horst Zank, 2004. "Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 145-158, January.
    33. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
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    1. Dietzenbacher, Bas & Dogan, Emre, 2024. "Population monotonicity and egalitarianism," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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