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Neighbor games and the leximax solution

Author

Listed:
  • Flip Klijn
  • Dries Vermeulen
  • Herbert Hamers
  • Tamás Solymosi
  • Stef Tijs
  • Joan Pere Villar

Abstract

Neighbor games arise from certain matching or sequencing situations in which only some specific pairs of players can obtain a positive gain. As a consequence, the class of neighbor games is the intersection of the class of assignment games (Shapley and Shubik (1972)) and the class of component additive games (Curiel et al. (1994)). We first present some elementary features of neighbor games. After that we provide a polynomially bounded algorithm of order p 3 for calculating the leximax solution (cf. Arin and Iñarra (1997)) of neighbor games, where p is the number of players. Copyright Springer-Verlag 2003

Suggested Citation

  • Flip Klijn & Dries Vermeulen & Herbert Hamers & Tamás Solymosi & Stef Tijs & Joan Pere Villar, 2003. "Neighbor games and the leximax solution," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 191-208, November.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:2:p:191-208
    DOI: 10.1007/s001860300298
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    References listed on IDEAS

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    1. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    2. Arin, J. & Inarra, E., 1997. "Consistency and Egalitarianism: The Egalitarian Set," ASSET - Instituto De Economia Publica 163, ASSET (Association of Southern European Economic Theorists).
    3. Imma Curiel & Jos Potters & Rajendra Prasad & Stef Tijs & Bart Veltman, 1994. "Sequencing and Cooperation," Operations Research, INFORMS, vol. 42(3), pages 566-568, June.
    4. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Other publications TiSEM be67f9e9-7a4a-47f1-9fb9-7, Tilburg University, School of Economics and Management.
    6. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(4), pages 565-580, December.
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    Cited by:

    1. van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 116-139, January.
    2. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    3. Francesc Llerena & Llúcia Mauri, 2016. "Reduced games and egalitarian solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1053-1069, November.
    4. Llerena Garrés, Francesc & Mauri Masdeu, Llúcia, 2014. "On reduced games and the lexmax solution," Working Papers 2072/237591, Universitat Rovira i Virgili, Department of Economics.

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    More about this item

    Keywords

    Neighbor Games; Leximax Solution; Assignment Games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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