Semi-Infinite Assignment Problems and Related Games

N. Llorca, S.H. Tijs, J.B. Timmer

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Abstract

In 1972 Shapley and Shubik introduced assignment games associated to finite assignment problems in which two types of agents were involved and they proved that these games have a non-empty core. In this paper we look at the situation where the set of one type is infinite and investigatewhen the core of the associated game is non-empty. Two infinite programming problems 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 non-empty. Finally, the existence of optimal assignments is discussed.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages12
Volume1999-74
Publication statusPublished - 1999

Publication series

NameCentER Discussion Paper
Volume1999-74

Keywords

  • Infinite programs
  • assignment
  • cooperative games
  • balancedness

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    Llorca, N., Tijs, S. H., & Timmer, J. B. (1999). Semi-Infinite Assignment Problems and Related Games. (CentER Discussion Paper; Vol. 1999-74). Microeconomics.