, Volume 12, Issue 2, pp 331–350 | Cite as

The core and related solution concepts for infinite assignment games

  • Natividad Llorca
  • Joaquín Sánchez-Soriano
  • Stef Tijs
  • Judith Timmer


Assignment problems where both sets of agents that have to be matched are countably infinite, the so-called infinite assignment problems, are studied as well as the related cooperative assignment games. Further, several solution concepts for these assignment games are studied. The first one is the utopia payoff for games with an infinite value. In this solution each player receives the maximal amount he can think of with respect to the underlying assignment problem. This solution is contained in the core of the game.

Second, we study two solutions for assignment games with a finite value. Our main result is the existence of core-elements of these games, although they are hard to calculate. Therefore another solution, the f-strong ε-core is studied. This particular solution takes into account that due to organisational limitations it seems reasonable that only finite groups of agents will eventually protest against unfair proposals of profit distributions. The f-strong ε-core is shown to be nonempty.

Key Words

Cooperative games assignment problems infinite programs solutions 

AMS subject classification



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Copyright information

© Sociedad de Estadística e Investigación Operativa 2004

Authors and Affiliations

  • Natividad Llorca
    • 1
  • Joaquín Sánchez-Soriano
    • 1
  • Stef Tijs
    • 2
  • Judith Timmer
    • 3
  1. 1.CIO and Department of Statistics and Applied MathematicsMiguel Hernández University Elche CampusElcheSpain
  2. 2.CentER and Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands
  3. 3.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands

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