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Cores of Combined Games

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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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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
    3. Laussel, Didier & Le Breton, Michel, 2001. "Conflict and Cooperation: The Structure of Equilibrium Payoffs in Common Agency," Journal of Economic Theory, Elsevier, vol. 100(1), pages 93-128, September.
    4. 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.
    5. Driessen, T. & Tijs, S.H., 1983. "The t-value, the nucleolus and the core for a subclass of games," Other publications TiSEM 73fdfe73-c88c-4a9f-8ee7-c, Tilburg University, School of Economics and Management.
    6. Fershtman, Chaim, 1990. "The importance of the agenda in bargaining," Games and Economic Behavior, Elsevier, vol. 2(3), pages 224-238, September.
    7. Busch, Lutz-Alexander & Horstmann, Ignatius J, 1997. "Bargaining Frictions, Bargaining Procedures and Implied Costs in Multiple-Issue Bargaining," Economica, London School of Economics and Political Science, vol. 64(256), pages 669-680, November.
    8. Peters, Hans, 1985. "A note on additive utility and bargaining," Economics Letters, Elsevier, vol. 17(3), pages 219-222.
    9. Conconi, Paola & Perroni, Carlo, 2002. "Issue linkage and issue tie-in in multilateral negotiations," Journal of International Economics, Elsevier, vol. 57(2), pages 423-447, August.
    10. Inderst, Roman, 2000. "Multi-issue Bargaining with Endogenous Agenda," Games and Economic Behavior, Elsevier, vol. 30(1), pages 64-82, January.
    11. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    12. Younghwan In & Roberto Serrano, 2000. "Agenda Restrictions in Multi-Issue Bargaining," Working Papers 2000-08, Brown University, Department of Economics.
    13. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
    14. Peters, Hans J M, 1986. "Simultaneity of Issues and Additivity in Bargaining," Econometrica, Econometric Society, vol. 54(1), pages 153-169, January.
    15. Bac, Mehmet & Raff, Horst, 1996. "Issue-by-Issue Negotiations: The Role of Information and Time Preference," Games and Economic Behavior, Elsevier, vol. 13(1), pages 125-134, March.
    16. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    17. Perry, Martin K & Porter, Robert H, 1985. "Oligopoly and the Incentive for Horizontal Merger," American Economic Review, American Economic Association, vol. 75(1), pages 219-227, March.
    18. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, March.
    19. In, Younghwan & Serrano, Roberto, 2004. "Agenda restrictions in multi-issue bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 53(3), pages 385-399, March.
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    Cited by:

    1. Currarini, S. & Marchiori, C., 2022. "Issue linkage," Games and Economic Behavior, Elsevier, vol. 135(C), pages 16-40.
    2. 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.
    3. 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.
    4. Messan Agbaglah, 2017. "Overlapping coalitions, bargaining and networks," Theory and Decision, Springer, vol. 82(3), pages 435-459, March.
    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. 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.

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    Keywords

    Cooperative Game; Core; Additivity; Issue Linkage; Multi Issue Bargaining;
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