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Representation of TU games by coalition production economies

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  • Inoue, Tomoki

    (Center for Mathematical Economics, Bielefeld University)

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.

Suggested Citation

  • Inoue, Tomoki, 2011. "Representation of TU games by coalition production economies," Center for Mathematical Economics Working Papers 430, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:430
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    References listed on IDEAS

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    Cited by:

    1. Inoue, Tomoki, 2013. "Representation of non-transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 141-149.
    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. Brangewitz, Sonja & Gamp, Jan-Philip, 2014. "Competitive outcomes and the core of TU market games," Center for Mathematical Economics Working Papers 454, Center for Mathematical Economics, Bielefeld University.
    4. Inoue, Tomoki, 2012. "Representation of transferable utility games by coalition production economies," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 143-147.

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