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On The Semivalues And The Power Core Of Cooperative Tu Games

Author

Listed:
  • IRINEL DRAGAN

    (University of Texas at Arlington, Department of Mathematics, Arlington, 76019-0408, USA)

  • JUAN ENRIQUE MARTINEZ-LEGAZ

    (University Autonoma of Barcelona, CODE and Department of Economics, 08193 Bellaterra (Barcelona), Spain)

Abstract

A weighted average worth per capita formula is presented for any semivalue of a TU game. Further, this formula is used to derive a characterisation of the class of games with the property that a given semivalue belongs to the power core of the game, by means of a linear system of inequalities. It is shown that for the Shapley value, the only efficient semivalue, this system reduces to the system already obtained by Inarra and Usategui. The potential approach is also used even for the more general case of values possessing a potential. A direct proof shows that for a value possessing a potential, the value of a game is in the power core relative to this value, if and only if the potential game is weak average convex. From this result, it follows that for a game and each of its subgames the value possessing a potential is in the corresponding power cores, if and only if the potential game relative to the value is average convex. This is an extension of the result obtained by Marin–Solano and Rafels for the Shapley value, proved by using the dividend form of the game.

Suggested Citation

  • Irinel Dragan & Juan Enrique Martinez-Legaz, 2001. "On The Semivalues And The Power Core Of Cooperative Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02n03), pages 127-139.
    • Handle: RePEc:wsi:igtrxx:v:03:y:2001:i:02n03:n:s0219198901000324
    DOI: 10.1142/S0219198901000324
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    Cited by:

    1. Carreras, Francesc & Giménez, José Miguel, 2010. "Semivalues: power,potential and multilinear extensions," MPRA Paper 27620, University Library of Munich, Germany.
    2. Carreras, Francesc & Giménez, José Miguel, 2011. "Power and potential maps induced by any semivalue: Some algebraic properties and computation by multilinear extensions," European Journal of Operational Research, Elsevier, vol. 211(1), pages 148-159, May.

    More about this item

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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