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Merging and Splitting in Cooperative Games: Some (Im-)Possibility Results

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  • Peter Holch Knudsen

    (Department of Economics, University of Copenhagen)

  • Lars Peter Østerdal

    (Department of Economics, University of Copenhagen)

Abstract

Solutions for cooperative games with side-payments can be manipulated by merging a coalition of players into a single player, or, conversely, splitting a player into a number of smaller players. This paper establishes some (im-)possibility results concerning merging- or splitting-proofness of core solutions of balanced and convex games.

Suggested Citation

  • Peter Holch Knudsen & Lars Peter Østerdal, 2005. "Merging and Splitting in Cooperative Games: Some (Im-)Possibility Results," Discussion Papers 05-19, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0519
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    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. Carreras, Francesc, 1996. "On the Existence and Formation of Partnerships," Games and Economic Behavior, Elsevier, vol. 12(1), pages 54-67, January.
    3. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(2), pages 89-99.
    4. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    6. Biung-Ghi Ju, 2003. "Manipulation via merging and splitting in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 8(2), pages 205-215, October.
    7. Legros, Patrick, 1987. "Disadvantageous syndicates and stable cartels: The case of the nucleolus," Journal of Economic Theory, Elsevier, vol. 42(1), pages 30-49, June.
    8. Jean Derks & Stef Tijs, 2000. "On Merge Properties Of The Shapley Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 249-257.
    9. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    10. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    11. Maschler, Michael, 1976. "An advantage of the bargaining set over the core," Journal of Economic Theory, Elsevier, vol. 13(2), pages 184-192, October.
    12. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    13. Andrew Postlewaite, 1974. "Disadvantageous Syndicates in Exchange Economies," Discussion Papers 105, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Ilya Segal, 2003. "Collusion, Exclusion, and Inclusion in Random-Order Bargaining," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 439-460.
    15. Jens Leth Hougaard & Lars Thorlund-Petersen & Bezalel Peleg, 2001. "On the set of Lorenz-maximal imputations in the core of a balanced game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 147-165.
    16. Hart, Sergiu, 1974. "Formation of cartels in large markets," Journal of Economic Theory, Elsevier, vol. 7(4), pages 453-466, April.
    17. Hougaard, Jens Leth & Østerdal, Lars Peter, 2010. "Monotonicity of social welfare optima," Games and Economic Behavior, Elsevier, vol. 70(2), pages 392-402, November.
    18. Postlewaite, Andrew & Rosenthal, Robert W., 1974. "Disadvantageous syndicates," Journal of Economic Theory, Elsevier, vol. 9(3), pages 324-326, November.
    19. Haviv, Moshe, 1995. "Consecutive amalgamations and an axiomatization of the Shapley value," Economics Letters, Elsevier, vol. 49(1), pages 7-11, July.
    20. 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, December.
    21. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
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    Cited by:

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    3. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "Manipulability in the cost allocation of transport systems," ThE Papers 20/08, Department of Economic Theory and Economic History of the University of Granada..

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    More about this item

    Keywords

    cooperative games; manipulation; Dutta-Ray solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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