Skip to main content
Log in

Some new results on least square values for TU games

  • Published:
Top Aims and scope Submit manuscript

Abstract

In this paper we present some new results concerning the least square family of values for TU games. We first examine the stability of these values from a dynamic point of view and propose a reinteropretation of them from the standpoint of the propernsity to disrupt approach. In the second part the family of individually rational least square (IRLS) values is introduced and an alternative kernel-like formulation of them is provided. Finally we describe a natural and simple algorithm for calculating any IRLS value of a game.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Banzhaf, J. F. (1965). Weighted Voting doesn't work: A Mathematical Analysis.Rutgers Law Review 19, 317–343.

    Google Scholar 

  • Charnes, A., Rousseau, J. and Seiford, L. (1978). Complements, Mollifiers and the Propensity to Disrupt”.International Journal of Game Theory 7, 37–50.

    Article  Google Scholar 

  • Davis, J. and Maschler, M. (1965). The kernel of a cooperative game.Naval Research Logistics Quarterly 12, 223–259.

    Google Scholar 

  • Gately, D. (1974). Sharing the Gains from Regional Cooperation: a Game Theoretic Application to Planning Investment in Electric Power.International Economic Review 15, 195–208.

    Article  Google Scholar 

  • Grotte, J. H. (1976). Dynamics of Cooperative Games.International Journal of Game Theory 5, 27–64.

    Article  Google Scholar 

  • Littlechid, S. C. and Vaidya, K. G. (1976). The Propensity to Disrupt and the Disruption Nucleolus of a Characteristic Function Game.International Journal of Game Theory 5, 151–161.

    Article  Google Scholar 

  • Maschler, M., Peleg, B. S. and Shapley, L. S. (1979). Geometric Properties of the Kernel, Nucleolus and related Solutions Concepts.Mathematics of Operations Research 4, 303–338.

    Article  Google Scholar 

  • Ruiz, L. M. (1994)El Enfoque Mìnimo Cuadrático en los Juegos con Utilidad Transferible, (in Spanish), Thesis. Departamento de Economía Aplicada I, Basque Country University, Bilbao.

    Google Scholar 

  • Ruiz, L. M., Valenciano, F. and Zarzuelo, J. M. (1996). The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector.International Journal of Game Theory 25, 113–134.

    Article  Google Scholar 

  • Ruiz, L. M., Valenciano, F. and Zarzuelo, J. M. (1998). The Family of Least Square Values for Tranferable Utility Games.Games and Economic Behavior 24, N1, 109–130.

    Article  Google Scholar 

  • Shapley, L. S. (1953). A Value forn-Person Games.Annals of Mathematics Studies 28, 307–317.

    Google Scholar 

  • Spinetto, R. D. (1971). Solution concepts of n-person cooporative games as points in the game space. Technical report No 138, Department of Operations Research, College of Engineering, Cornell University, Ithaca, NY.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We gratefully acknowledge financial support from the Basque Government (Project PI95/101) and from the D.G.E.S. of the Ministerio de Educatión y Cultura (Project PB96-0247).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruiz, L.M., Valenciano, F. & Zarzuelo, J.M. Some new results on least square values for TU games. Top 6, 139–158 (1998). https://doi.org/10.1007/BF02564802

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02564802

Key Words

AMS subject classification

Navigation