Social Choice and Welfare

, Volume 28, Issue 4, pp 685–703 | Cite as

The consensus value: a new solution concept for cooperative games

Open Access
Original Paper

Abstract

To generalize the standard solution for 2-person TU games into n-person cases, this paper introduces a recursive two-sided negotiation process to establish cooperation between all players. This leads to a new solution concept for cooperative games: the consensus value. An explicit comparison with the Shapley value is provided, also at the axiomatic level. Moreover, a class of possible generalizations of the consensus value is introduced and axiomatized with the Shapley value at one end and the equal surplus solution at the other. Finally, we discuss a non-cooperative mechanism which implements the consensus value.

Keywords

Cooperative Game Solution Concept Subgame Perfect Equilibrium Unanimity Game Dummy Player 
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.

References

  1. Borm P, van den Brink R, Slikker M (2002) An iterative procedure for evaluating digraph competitions. Ann Oper Res 109:61–75CrossRefGoogle Scholar
  2. van den Brink R, Funaki Y (2004) Axiomatizations of a class of equal surplus sharing solutions for cooperative games with transferable utility. Tinbergen Institute Discussion Paper, TI 2004–136/1, Tinbergen Institute, Amsterdam/Rotterdam, The NetherlandsGoogle Scholar
  3. van den Brink R, Funaki Y, Ju Y (2005) Axiomatizations of the convex combinations of a class of equal surplus solutions and the shapley value, Manuscript. Free University Amsterdam, the NetherlandsGoogle Scholar
  4. Driessen TSH, Funaki Y (1991) coincidence of and collinearity between game theoretic solutions. OR Spektrum 13:15–30CrossRefGoogle Scholar
  5. Dubey P (1975) On the uniqueness of the shapley value. Int J Game Theory 4:229–247CrossRefGoogle Scholar
  6. Feltkamp V (1995) Cooperation in controlled network structures. Ph.D. Dissertation, Tilburg UniversityGoogle Scholar
  7. Ju Y (2004) The consensus value for games in partition function form. CentER Discussion Paper, 2004–60, Tilburg University, The Netherlands. To appear in International Game Theory ReviewGoogle Scholar
  8. Ju Y, Ruys P, Borm P (2004) Compensating losses and sharing surpluses in project-allocation situations. CentER Discussion Paper, 2004–06, Tilburg UniversityGoogle Scholar
  9. Ju Y, Borm P (2005) Externalities and compensation: primeval games and solutions. Keele Economics Research Paper, 2005–05, Keele University, UKGoogle Scholar
  10. Ju Y, Wettstein D (2006) Implementing cooperative solution concepts: a generalized bidding approach. Keele Economics Research Paper, 2006–06, Keele UniversityGoogle Scholar
  11. Maschler M, Owen G (1989) The consistent shapley value for hyperplane games. Int J Game Theory 18:389–407CrossRefGoogle Scholar
  12. Moulin H (2003) Fair division and collective welfare. MIT Press, Cambridge, MAGoogle Scholar
  13. Myerson R (1980) Conference structures and fair allocation rules. Int J Game Theory 9:169–182CrossRefGoogle Scholar
  14. Pérez-Castrillo D, Wettstein D (2001) Bidding for the surplus: a non cooperative interpretation of the shapley value. J Econ Theory 100:274–294CrossRefGoogle Scholar
  15. Quant M, Borm P, Maaten R (2005) A concede-and-divide rule for Bankruptcy problems. CentER Discussion Paper, 2005–20, Tilburg UniversityGoogle Scholar
  16. Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50:97–109CrossRefGoogle Scholar
  17. Shapley LS (1953) A value for n-person games. In: Kuhn H, Tucker AW (eds) Contributions to the theory of games, vol. II. Princeton University Press, Princeton, NJGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.School of Economic and Management StudiesKeele UniversityKeeleUK
  2. 2.CentER and Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands
  3. 3.TILEC, Department of Econometrics and Operations Research, and Tias Business SchoolTilburg UniversityTilburgThe Netherlands

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