Skip to main content
SpringerLink
Log in

Proportional share analysis

  • Original Paper
  • Published:
TOP Aims and scope Submit manuscript

Abstract

The purpose of this paper is to generalize the theory of “equal share analysis”, developed by Selten in 1972, to the one in which every player has a positive weight. We show that for any positive vector of weights, α∈R N++ , it is always possible to find a coalition structure and a payoff vector forming a proportional regular configuration.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Branzei R, Dimitrov D, Tijs S (2004) Egalitarism in convex fuzzy games. Math Soc Sci 47:313–325

    Article  Google Scholar 

  • Bhattacharya A (2004) On the equal division core. Soc Choice Welf 22:391–399

    Article  Google Scholar 

  • Crott HW, Albers W (1981) The equal division kernel: an equity approach to coalition formation and payoff distribution in N-person games. Eur J Soc Psychol 77:285–305

    Article  Google Scholar 

  • Dutta B, Ray D (1989) A concept of egalitarism under participation constraints. Econometrica 57(3):615–635

    Article  Google Scholar 

  • Izquierdo JM, Rafels C (2001) Average monotonic cooperative games. Games Econ Behav 36:174–192

    Article  Google Scholar 

  • Klijn F, Slikker M, Tijs S, Zarzuelo J (2000) The egalitarian solution for convex games: some characterizations. Math Soc Sci 40:111–121

    Article  Google Scholar 

  • Komorita SS (1979) An equal excess model of coalition formation. Behav Sci 24:369–381

    Article  Google Scholar 

  • Selten R (1972) Equal share analysis of characteristic function experiments. In: Sauermann H (ed) Contributions to experimental economics III. JCB Mohr, Tubingen, pp 130–165

    Google Scholar 

  • Selten R (1978) The equity principle in economic behavior. In: Gottinger WH, Leinfellner W (eds) Decision theory and social ethics: issues in social choice. Reidel, Dordrecht, pp 289–301

    Google Scholar 

  • Vilella C (2004) Coalition structures and proportional share analysis for TU cooperative games. PhD. Dissertation, Rovira i Virgili University, Reus

Download references

Author information

Authors and Affiliations

  1. Dep. de Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Av. Diagonal, 690, 08034, Barcelona, Spain

    Carles Rafels

  2. Dep. de Gestió d’Empreses, Universitat Rovira i Virgili, Av. Universitat, 1, 43204, Reus, Spain

    Cori Vilella

Authors
  1. Carles Rafels
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cori Vilella
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cori Vilella.

Additional information

We want to thank G. Bergantiños, M. Ferré, J.M. Izquierdo, F. Llerena, F.X. Martínez de Albéniz, M. Núñez and two anonymous referees for helpful comments, and the support of the Barcelona Economics Program of CREA. Institutional support from Ministerio de educación y ciencia, under grant SEJ2005-02443, and from Generalitat de Catalunya, under grant 2005SGR-00949, are gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rafels, C., Vilella, C. Proportional share analysis. TOP 15, 341–354 (2007). https://doi.org/10.1007/s11750-007-0024-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11750-007-0024-1

Keywords

Mathematics Subject Classification (2000)

Search

Navigation