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Semi-infinite assignment problems and related games

Author

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  • Natividad Llorca
  • Stef Tijs
  • Judith Timmer

Abstract

In this paper we look at semi-infinite assignment problems. These are situations where a finite set of agents of one type has to be assigned to an infinite set of agents of another type. This has to be done in such a way that the total profit arising from these assignments is as large as possible. An infinite programming problem and its dual arise here, which we tackle with the aid of finite approximations. We prove that there is no duality gap and we show that the core of the corresponding game is nonempty. Finally, the existence of optimal assignments is discussed. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Natividad Llorca & Stef Tijs & Judith Timmer, 2003. "Semi-infinite assignment problems and related games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(1), pages 67-78, April.
    • Handle: RePEc:spr:mathme:v:57:y:2003:i:1:p:67-78
    DOI: 10.1007/s001860200245
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    Cited by:

    1. C G Lennon & J M McGowan & K Y Lin, 2008. "A game-theoretic model for repeated assignment problem between two selfish agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(12), pages 1652-1658, December.
    2. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.

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