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Representation of TU games by coalition production economies

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  • Tomoki Inoue

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    (Institute of Mathematical Economics, Bielefeld University)

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    Abstract

    We prove that every transferable utility (TU) game can be generated by a coalition production economy. Given a TU game, the set of Walrasian payoff vectors of the induced coalition production economy coincides with the core of the balanced cover of the given game. Therefore, a Walrasian equilibrium for the induced coalition production economy always exists. The induced coalition production economy has one output and the same number of inputs as agents. Every input is personalized and it can be interpreted as agent's labor. In a Walrasian equilibrium, every agent is permitted to work at several firms. In a Walrasian equilibrium without double-jobbing, in contrast, every agent has to work at exactly one firm. This restricted concept of a Walrasian equilibrium enables us to discuss which coalitions are formed in an equilibrium. If the cohesive cover or the completion of a given TU game is balanced, then the no-double-jobbing restriction does not matter, i.e., there exists no difference between Walrasian payoff vectors and Walrasian payoff vectors without double-jobbing.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-430.pdf
    File Function: First version, 2010
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 430.

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    Length: 36 pages
    Date of creation: Apr 2010
    Date of revision:
    Handle: RePEc:bie:wpaper:430

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    Related research

    Keywords: Coalition production economy; transferable utility game; core; Walrasian equilibrium; Walrasian equilibrium without double-jobbing; coalition structure;

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    References

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    1. Sun,N. & Trockel,W. & Yang,Z., 2004. "Competitive outcomes and endogenous coalition formation in an n-person game," Working Papers 358, Bielefeld University, Center for Mathematical Economics.
    2. Qin, Cheng-Zhong, 1993. "A Conjecture of Shapley and Shubik on Competitive Outcomes in the Cores of NTU Market Games," International Journal of Game Theory, Springer, vol. 22(4), pages 335-44.
    3. Guesnerie, R. & Oddou, C., 1979. "On economic games which are not necessarily superadditive : Solution concepts and application to a local public good problem with few a agents," Economics Letters, Elsevier, vol. 3(4), pages 301-306.
    4. Qin Cheng-Zhong, 1994. "The Inner Core of an n-Person Game," Games and Economic Behavior, Elsevier, vol. 6(3), pages 431-444, May.
    5. Boehm, Volker, 1974. "The Core of an Economy with Production," Review of Economic Studies, Wiley Blackwell, vol. 41(3), pages 429-36, July.
    6. Shapley, Lloyd S. & Shubik, Martin, 1969. "On market games," Journal of Economic Theory, Elsevier, vol. 1(1), pages 9-25, June.
    7. Billera, Louis J., 1974. "On games without side payments arising from a general class of markets," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 129-139, August.
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    Cited by:
    1. Inoue, Tomoki, 2012. "Representation of transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 143-147.
    2. Bejan, Camelia & Gómez, Juan Camilo, 2012. "A market interpretation of the proportional extended core," Economics Letters, Elsevier, vol. 117(3), pages 636-638.
    3. Sonja Brangewitz & Jan-Philip Gamp, 2011. "Competitive Outcomes and the Core of TU Market Games," Working Papers 454, Bielefeld University, Center for Mathematical Economics.
    4. Inoue, Tomoki, 2013. "Representation of non-transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 141-149.

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