, Volume 17, Issue 1, pp 123–138 | Cite as

Multi-choice clan games and their core

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


In this paper, we consider market situations with two corners. One corner consists of a group of powerful agents with yes-or-no choices and clan behavior. The other corner consists of non-powerful agents with multi-choices regarding the extent at which cooperation with the clan can be achieved. Multi-choice clan games arise from such market situations. The focus is on the analysis of the core of multi-choice clan games. Several characterizations of multi-choice clan games by the shape of the core are given, and the connection between the convexity of a multi-choice clan game and the stability of its core is studied.


Multi-choice games Clan games Core 

Mathematics Subject Classification (2000)



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Branzei R, Tijs S, Timmer J (2001) Information collecting situations and bi-monotonic allocation schemes. Math Methods Oper Res 54:303–313 CrossRefGoogle Scholar
  2. Branzei R, Dimitrov D, Tijs S (2005) Models in cooperative game theory: crisp, fuzzy, and multi-choice games. Springer, Berlin Google Scholar
  3. Branzei R, Tijs S, Zarzuelo JM (2008) Convex multi-choice games: characterizations and monotonic allocation schemes. Eur J Oper Res. doi:10.1016/j.ejor.2008.09.024 Google Scholar
  4. Calvo E, Santos JC (2000) A value for multichoice games. Math Soc Sci 40:341–354 CrossRefGoogle Scholar
  5. Hsiao C-R, Raghavan TES (1992) Monotonicity and dummy free property for multi-choice cooperative games. Int J Game Theory 21:301–312 CrossRefGoogle Scholar
  6. Hsiao C-R, Raghavan TES (1993) Shapley value for multi-choice cooperative games (I). Games Econ Behav 5:240–256 CrossRefGoogle Scholar
  7. Muto S, Nakayama M, Potters J, Tijs S (1988) On big boss games. Econ Stud Q 39:303–321 Google Scholar
  8. Nouweland van den A (1993) Games and graphs in economic situations. PhD thesis, Tilburg University Google Scholar
  9. Nouweland van den A, Tijs S, Potters J, Zarzuelo J (1995) Cores and related solution concepts for multi-choice games. Math Methods Oper Res 41:289–311 CrossRefGoogle Scholar
  10. Peters H, Zank H (2005) The egalitarian solution for multichoice games. Ann Oper Res 137:399–409 CrossRefGoogle Scholar
  11. Potters J, Poos R, Tijs S, Muto S (1989) Clan games. Games Econ Behav 1:275–293 CrossRefGoogle Scholar
  12. Tijs S, Meca A, Lopez MA (2005) Benefit sharing in holding situations. Eur J Oper Res 162:251–269 CrossRefGoogle Scholar
  13. Voorneveld M, Tijs S, Grahn S (2002) Monotonic allocation schemes in clan games. Math Methods Oper Res 56:439–449 CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2009

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” UniversityIaşiRomania
  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

Personalised recommendations