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A Simple Procedure to Obtain the Extreme Core Allocations of an Assignment Market

Author

Listed:
  • Josep M. Izquierdo
  • Marina Núñez
  • Carles Rafels

Abstract

Given an assignment market, we introduce a set of vectors, one for each possible ordering on the player set, which we name the max-payoff vectors. Each one of these vectors is obtained recursively only making use of the assignment matrix. Those max-payoff vectors that are efficient turn up to give the extreme core allocations of the market. When the assignment market has large core (that is to say, the assignment matrix is dominant diagonal and doubly dominant diagonal) all the max-payoff vectors are extreme core allocations.

Suggested Citation

  • Josep M. Izquierdo & Marina Núñez & Carles Rafels, 2006. "A Simple Procedure to Obtain the Extreme Core Allocations of an Assignment Market," Working Papers 275, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:275
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    References listed on IDEAS

    as
    1. 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.
    2. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    3. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    4. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
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    Cited by:

    1. Michel Grabisch & Peter Sudhölter, 2016. "On a class of vertices of the core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01411947, HAL.
    2. Marina Núñez, 2016. "Comments on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 327-329, July.
    3. Michel Grabisch, 2016. "Rejoinder on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 335-337, July.
    4. 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.
    5. Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
    6. Núñez, Marina & Rafels, Carles, 2009. "A glove-market partitioned matrix related to the assignment game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 598-610, November.

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