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Cores of Combined Games

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Abstract

This paper studies the core of combined games, obtained by summing two coalitional games. It is shown that the set of balanced transferable utility games can be partitioned into equivalence classes of component games to determine whether the core of the combined game coincides with the sum of the cores of its components. On the other hand, for non-balanced games, the binary relation associating two component games whose combination has an empty core is not transitive. However, we identify a class of non-balanced games which, combined with any other non-balanced game, has an empty core.

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  • Francis Bloch & Geoffroy de Clippel, 2009. "Cores of Combined Games," Working Papers 2009-1, Brown University, Department of Economics.
    • Handle: RePEc:bro:econwp:2009-1
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    2. Currarini, S. & Marchiori, C., 2022. "Issue linkage," Games and Economic Behavior, Elsevier, vol. 135(C), pages 16-40.
    3. Christian Trudeau, 2023. "Minimum cost spanning tree problems as value sharing problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 253-272, March.
    4. Effrosyni Diamantoudi & Inés Macho-Stadler & David Pérez-Castrillo & Licun Xue, 2015. "Sharing the surplus in games with externalities within and across issues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 315-343, October.
    5. Dénes Pálvölgyi & Hans Peters & Dries Vermeulen, 2018. "Linearity of the core correspondence," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1159-1167, November.
    6. Hirbod Assa & Sheridon Elliston & Ehud Lehrer, 2016. "Joint games and compatibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 91-113, January.
    7. Sylvain Béal & Stéphane Gonzalez & Philippe Solal & Peter Sudhölter, 2023. "Axiomatic characterizations of the core without consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 687-701, September.
    8. Larry G Epstein & Kaushil Patel, 2024. "Identifying Heterogeneous Decision Rules From Choices When Menus Are Unobserved," Papers 2405.09500, arXiv.org.
    9. Lehrer, Ehud & Teper, Roee, 2020. "Allocation in multi-agenda disputes: A set-valued games approach," Games and Economic Behavior, Elsevier, vol. 122(C), pages 440-452.
    10. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.

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