Semi-Infinite Assignment and Transportation Games

  • Joaquín Sánchez-Soriano
  • Natividad Llorca
  • Stef Tijs
  • Judith Timmer
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 57)

Abstract

Games corresponding to semi-infinite transportation and related assignment situations are studied. In a semi-infinite transportation situation, one aims at maximizing the profit from the transportation of a certain good from a finite number of suppliers to an infinite number of demanders. An assignment situation is a special kind of transportation situation where the supplies and demands for the good all equal one unit. It is shown that the special structure of these situations implies that the underlying infinite programs have no duality gap and that the core of the corresponding game is nonempty.

Keywords

Assignment Problem Transportation Problem Demand Point Transportation Plan Cooperative Game Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    I. Curiel, Cooperative Game Theory and Applications, Kluwer, 1997.CrossRefGoogle Scholar
  2. [2]
    F.Y. Edgeworth, Mathematical Psychics, Kegan, London, 1981.Google Scholar
  3. [3]
    V. Fragnelli, F. Patrone, E. Sideri, and S. Tijs. Balanced games arising from infinite linear models, Mathematical Methods of Operations Research, 50:385–397, 1999.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    J.R.G. van Gellekom, J.A.M. Potters, J.H. Reijnierse, S.H. Tijs, and M.C. Engel. Characterization of the Owen set of linear production processes, games and economic behavior, 32:139–156, 2000.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    D.B. Gillies. Some theorems on N-person games. Dissertation, Princenton University, 1953.Google Scholar
  6. [6]
    K. Glashoff, and S-A. Gustafson. Linear Optimization andApproximation, Springer-Verlag, 1983.CrossRefGoogle Scholar
  7. [7]
    M. A. Goberna and M.A. López. LinearSemi-Infintite Optimization, Wiley, 1998.Google Scholar
  8. [8]
    N. Llorca, S. Tijs, and J. Timmer. Semi-infinite assignment problems and related games, International Garne Theory Review, 2:97–106, 2000.MathSciNetMATHGoogle Scholar
  9. [9]
    K.G. Murty. Linear Programming, Wiley, 1983.MATHGoogle Scholar
  10. [10]
    G. Owen. On the Core of Linear Production Games, Mathematical Programming, 9:358–370, 1975.MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    G. Owen. Garme Theory, Academic Press, 1995.Google Scholar
  12. [12]
    J. Sánchez-Soriano, M.A. López, and I. García-Jurado. On the Core of Transportation Games, Mathematical Social Sciences, 2000.Google Scholar
  13. [13]
    A. Schrijver. Theory of Linear and Integer Prograrmrming, Wiley, 1986.Google Scholar
  14. [14]
    L.S. Shapley and S. Shubik. The Assignment Game I: The Core, International Journal of Garme Theory, 1:111–130, 1972.MathSciNetCrossRefGoogle Scholar
  15. [15]
    J. Timmer, N. Llorca and S. Tijs. Games Arasing from Infinite Production Situations, International Gamne Theory Review, 2:97–106, 2000.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Joaquín Sánchez-Soriano
    • 1
  • Natividad Llorca
    • 1
  • Stef Tijs
    • 2
  • Judith Timmer
    • 2
  1. 1.Department of Statistics and Applied MathematicsMiguel Hernández UniversityElcheSpain
  2. 2.CentER and Department of Econometrics and Operations ResearchTilburg UniversityLE TilburgThe Netherlands

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