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Neighbour Games and the Leximax Solution

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  • Klijn, F.
  • Vermeulen, D.
  • Hamers, H.J.M.
  • Solymosi, T.
  • Tijs, S.H.
  • Pere Villar, J.

    (Tilburg University, Center for Economic Research)

Abstract

Neighbour 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 neighbour 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 neighbour games. After that we provide a polynomially bounded algorithm of order p3 for calculating the leximax solution (cf. Arin and I˜narra (1997)) of neighbour games, where p is the number of players.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1999-110.

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Date of creation: 1999
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Handle: RePEc:dgr:kubcen:1999110

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Keywords: Neighbour games; Leximax solution; assignment games;

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References

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  1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
  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. Hamers, H.J.M. & Klijn, F. & Solymosi, T. & Tijs, S.H. & Vermeulen, D., 1999. "On the Nucleolus of Neighbour Games," Discussion Paper 1999-111, Tilburg University, Center for Economic Research.
  4. Javier Arin & Jeroen Kuipers & Dries Vermeulen, 2008. "An axiomatic approach to egalitarianism in TU-games," International Journal of Game Theory, Springer, vol. 37(4), pages 565-580, December.
  5. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585.
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Cited by:
  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. Velzen, S. van & Hamers, H.J.M. & Solymosi, T., 2004. "Core Stability in Chain-Component Additive Games," Discussion Paper 2004-101, Tilburg University, Center for Economic Research.
  3. 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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