Economic Theory Bulletin

, Volume 7, Issue 2, pp 221–234 | Cite as

On the properties of the nucleolus of a veto game

  • Eric BahelEmail author
Research Article


We study the nucleolus of veto games (see Bahel in Int J Game Theory 45(3):543–566, 2016), where some players are indispensable for coalitions to achieve a positive value. We first derive some noticeable properties satisfied by the nucleolus of a veto game: for instance, veto players always receive a higher payoff than the others. In the particular case of clan games, Potters et al. (Games Econ Behav 1:275–293, 1989) provided a formula for the nucleolus. We give a condition that is necessary and sufficient for this formula to apply in a general veto game. Building on this result, we describe an intuitive adjustment process allowing to derive a generic formula for the nucleolus of a veto game.


TU game Veto power Weak player Excess Nucleolus 

JEL Classification

C71 C78 


  1. Arin, J., Feltkamp, V.: The nucleolus and kernel of veto-rich transferable utility games. Int. J. Game Theory 26(1), 61–73 (1997)CrossRefGoogle Scholar
  2. Aumann, R.J., Maschler, M.: Game theoretic analysis of a bankruptcy problem from the Talmud. J. Econ. Theory 36, 195–213 (1985)CrossRefGoogle Scholar
  3. Bahel, E.: On the core and bargaining set of a veto game. Int. J. Game Theory 45(3), 543–566 (2016)CrossRefGoogle Scholar
  4. Bahel, E., Trudeau, C.: Stable lexicographic rules for shortest path games. Econ. Lett. 125, 266–269 (2014)CrossRefGoogle Scholar
  5. Chetty, V.K., Dasgupta, D., Raghavan, T.E.S.: Power and distribution of profits. Discussion paper no. 139, Indian Statistical Institute, Delhi Centre (1976)Google Scholar
  6. Muto, S., Nakayama, M., Potters, J., Tijs, S.: On big boss games. Econ. Stud. Q. 39, 303–321 (1988)Google Scholar
  7. Nakamura, K.: The vetoers in a simple game with ordinal preferences. Int. J. Game Theory 8, 55–61 (1979)CrossRefGoogle Scholar
  8. Potters, J., Poos, R., Tijs, S., Muto, S.: Clan games. Games Econ. Behav. 1, 275–293 (1989)CrossRefGoogle Scholar
  9. Schmeidler, D.: The nucleolus of a characteristic function game. SIAM J. Appl. Math. 17, 1163–1170 (1969)CrossRefGoogle Scholar

Copyright information

© Society for the Advancement of Economic Theory 2018

Authors and Affiliations

  1. 1.Department of EconomicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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