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Non-Cooperative And Axiomatic Characterizations Of The Average Lexicographic Value

Author

Listed:
  • TAKUMI KONGO

    (Faculty of Political Science and Economics, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo 169-8050, Japan)

  • YUKIHIKO FUNAKI

    (Faculty of Political Science and Economics, Waseda University, Japan)

  • RODICA BRANZEI

    (Faculty of Computer Science, "Alexandru Ioan Cuza" University, Iasi, Romania)

  • STEF TIJS

    (Center for Economic Research and Department of Econometrics and Operations Research, Tilburg University, The Netherlands)

Abstract

We give a non-cooperative and an axiomatic characterization of the Average Lexicographic value (AL-value) on the class of balanced games. The AL-value is a single-valued solution for balanced TU-games. It is defined as the average of lexicographic maximum of the core of the game with respect to all orders on the player set, and it can be seen as a core selection based on the priority orders on the players. In both of our characterizations of the AL-value, a consistency property which we call average consistency plays an important role, and the property is obtained by the consistency property à la Davis and Maschler of the lexicographic vectors with respect to any order of players.

Suggested Citation

  • Takumi Kongo & Yukihiko Funaki & Rodica Branzei & Stef Tijs, 2010. "Non-Cooperative And Axiomatic Characterizations Of The Average Lexicographic Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 417-435.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002751
    DOI: 10.1142/S0219198910002751
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    References listed on IDEAS

    as
    1. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Discussion Paper 2005-123, Tilburg University, Center for Economic Research.
    2. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, September.
    3. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Other publications TiSEM 0b4f9565-59f7-477f-b8f8-9, Tilburg University, School of Economics and Management.
    4. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Other publications TiSEM 71235183-d284-48b9-84da-c, Tilburg University, School of Economics and Management.
    5. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Discussion Paper 2008-8, Tilburg University, Center for Economic Research.
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    Citations

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    Cited by:

    1. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    2. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.

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    More about this item

    Keywords

    Cooperative games; average lexicographic value; average consistency; characterization; C71; C72;
    All these keywords.

    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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