, Volume 22, Issue 3, pp 860–874 | Cite as

A constrained egalitarian solution for convex multi-choice games

  • R. Branzei
  • N. Llorca
  • J. Sánchez-Soriano
  • S. Tijs
Original Paper


This paper deals with a constrained egalitarian solution for convex multi-choice games named the d value. It is proved that the d value of a convex multi-choice game belongs to the precore, Lorenz dominates each other element of the precore and possesses a population monotonicity property regarding players’ participation levels. Furthermore, an axiomatic characterization is given where a specific consistency property plays an important role.


Multi-choice games Convex games Lorenz domination Constrained egalitarian solution 

Mathematics Subject Classification (2010)



  1. Branzei R, Dimitrov D, Tijs S (2008) Models in Cooperative Game Theory. Springer, BerlinGoogle Scholar
  2. Branzei R, Llorca N, Sánchez-Soriano J, Tijs S (2007) Egalitarianism in multi-choice games. CentER DP 2007-54, Tilburg University, The NetherlandsGoogle Scholar
  3. Branzei R, Llorca N, Sánchez-Soriano J, Tijs S (2009a) Multichoice total clan games. TOP 17:123–138CrossRefGoogle Scholar
  4. Branzei R, Tijs S, Zarzuelo J (2009b) Convex multi-choice cooperative games: characterizations and monotonic allocation schemes. Eur J Oper Res 198:571–575CrossRefGoogle Scholar
  5. Davis M, Maschler M (1965) The kernel of a cooperative game. Nav Res Logist Q 12:223–259CrossRefGoogle Scholar
  6. Derks J, Peters H (1993) A Shapley value for games with restricted coalitions. Int J Game Theory 21:351–360CrossRefGoogle Scholar
  7. Dutta B, Ray D (1989) A concept of egalitarianism under participation constraints. Econometrica 57:615–635CrossRefGoogle Scholar
  8. Dutta B, Ray D (1991) Constrained egalitarian allocations. Games Econ Behav 3:403–422CrossRefGoogle Scholar
  9. Gillies DB (1953) Some theorems on n-person games, Ph. D. Thesis, Princeton University Press, Princeton, New JerseyGoogle Scholar
  10. Grabisch M, Lange F (2007) Games on lattices, multichoice games and the Shapley value: a new approach. Math Methods Oper Res 65:153–167CrossRefGoogle Scholar
  11. Grabisch M, Xie L (2007) A new investigation about the core and Weber set of multichoice games. Math Methods Oper Res 66:491–512CrossRefGoogle Scholar
  12. Hart S, Mas-Colell A (1989) Potential, value and consistency. Econometrica 57:589–614CrossRefGoogle Scholar
  13. Hsiao C-R, Raghavan TES (1993a) Monotonicity and dummy free property for multi-choice cooperative games. Int J Game Theory 21:301–312CrossRefGoogle Scholar
  14. Hsiao C-R, Raghavan TES (1993b) Shapley value for multi-choice cooperative games (I). Games and Econ Behav 5:240–256CrossRefGoogle Scholar
  15. Hwang Y, Liao Y (2010) The unit-level-core for multi-choice games: the replicated core for TU games. J Glob Optim 47:161–171CrossRefGoogle Scholar
  16. Hwang Y, Liao Y (2011) The multi-core, balancedness and axiomatizations for multi-choice games. Int J Game Theory 40:677–689CrossRefGoogle Scholar
  17. Klijn F, Slikker M, Zarzuelo J (2000) The egalitarian solution for convex games: some characterizations. Math Soc Sci 40:111–121CrossRefGoogle Scholar
  18. Nouweland van den A, Potters J, Tijs S, Zarzuelo J (1995) Cores and related solution concepts for multi-choice games. Math Methods Oper Res 41:289–311CrossRefGoogle Scholar
  19. Peters H, Zank H (2005) The egalitarian solution for multi-choice games. Ann Oper Res 137:399–409CrossRefGoogle Scholar
  20. Sánchez-Soriano J, Branzei R, Llorca N, Tijs S (2010) A technical note on Lorenz dominance in cooperative games. CentER DP 2010-101. Tilburg University, The NetherlandsGoogle Scholar
  21. Shapley LS (1953) A value for n-person games. Ann Math Stud 28:307–317Google Scholar
  22. Sprumont Y (1990) Population monotonic allocation schemes for cooperative games with transferable utility. Games Econ Behav 2:378–394CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2013

Authors and Affiliations

  • R. Branzei
    • 1
  • N. Llorca
    • 2
  • J. Sánchez-Soriano
    • 2
  • S. Tijs
    • 3
  1. 1.Faculty of Computer Science“Alexandru Ioan Cuza” UniversityIasiRomania
  2. 2.CIO and Department of Statistics, Mathematics and Computer ScienceUniversity Miguel Hernández of ElcheElcheSpain
  3. 3.CentER and Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands

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