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On the nucleolus of neighbor games

Author

Listed:
  • Hamers, Herbert
  • Klijn, Flip
  • Solymosi, Tamas
  • Tijs, Stef
  • Vermeulen, Dries

Abstract

The class of neighbour games is the intersection of the class of assignment games (cf. Shapley and Shubik (1972)) and the class of component additive games (cf. Curiel et al. (1994)). For assignment games and component additive games there exist polynomially bounded algorithms of order p4 for calculating the nucleolus, where p is the number of players. In this paper we present a polynomially bounded algorithm of order p2 for calculating the nucleolus of neighbour games.
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Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:146:y:2003:i:1:p:1-18
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    References listed on IDEAS

    as
    1. 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.
    2. Imma Curiel & Jos Potters & Rajendra Prasad & Stef Tijs & Bart Veltman, 1994. "Sequencing and Cooperation," Operations Research, INFORMS, vol. 42(3), pages 566-568, June.
    3. Tamás Solymosi & Harry Aarts & Theo Driessen, 1998. "On Computing the Nucleolus of a Balanced Connected Game," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 983-1009, November.
    4. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    5. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
    6. 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.
    7. repec:fth:tilbur:99110 is not listed on IDEAS
    8. repec:spr:compst:v:58:y:2003:i:2:p:191-208 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. 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.
    3. Nguyen, Tri-Dung & Thomas, Lyn, 2016. "Finding the nucleoli of large cooperative games," European Journal of Operational Research, Elsevier, vol. 248(3), pages 1078-1092.
    4. van den Brink, René & Katsev, Ilya & van der Laan, Gerard, 2010. "An algorithm for computing the nucleolus of disjunctive non-negative additive games with an acyclic permission structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 817-826, December.
    5. 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.

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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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