Mathematical Methods of Operations Research

, Volume 64, Issue 1, pp 95–106 | Cite as

The Compromise Value for Cooperative Games with Random Payoffs

  • Judith TimmerEmail author
Original Article


This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.


Compromise value Random payoffs Cooperative games 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bergantiños G, Casas-Méndez B, Vázquez-Brage M (2000) A non-cooperative bargaining procedure generalising the Kalai–Smorodinsky bargaining solution to NTU-games. Int Game Theory Rev 2:273–286CrossRefMathSciNetzbMATHGoogle Scholar
  2. Bergantiños G, Massó J (1996) Notes on a new compromise value: the χ-value. Optimization 38:277–286CrossRefMathSciNetzbMATHGoogle Scholar
  3. Bergantiños G, Massó J (2002) The Chi-compromise value for non-transferable utility games. Math Methods Oper Res 56:269–286CrossRefMathSciNetzbMATHGoogle Scholar
  4. Borm P, Keiding H, McLean RP, Oortwijn S, Tijs SH (1992) The compromise value for NTU games. Int J Game Theory 21:175–189CrossRefMathSciNetzbMATHGoogle Scholar
  5. Myerson RB (1980) Conference structures and fair allocation rules. Int J Game Theory 9:169–182CrossRefMathSciNetzbMATHGoogle Scholar
  6. Tijs SH (1981) Bounds for the core and the τ-value. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North Holland Publishing Company, Amsterdam, pp 123–132Google Scholar
  7. Tijs SH, Lipperts FAS (1982) The hypercube and the core cover of n-person cooperative games. Cahiers du Centre d’Etudes de Recherche Opérationnelle 24:27–37MathSciNetzbMATHGoogle Scholar
  8. Tijs SH, Otten G-J (1993) Compromise values in cooperative game theory. Top 1:1–51CrossRefzbMATHGoogle Scholar
  9. Timmer J, Borm P, Tijs S (2000) On three Shapley-like solutions for cooperative games with random payoffs. CentER Discussion Paper 2000-73, Tilburg University, Tilburg, The NetherlandsGoogle Scholar
  10. Timmer J, Borm P, Tijs S (2003) On three Shapley-like solutions for cooperative games with random payoffs. Int J Game Theory 32:595–613MathSciNetGoogle Scholar
  11. Timmer J, Borm P, Tijs S (2005) Convexity in stochastic cooperative situations. Int Game Theory Rev 7:25–42CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Center and the Department of Econometrics and ORTilburg UniversityTilburgThe Netherlands

Personalised recommendations