Mathematical Methods of Operations Research

, Volume 74, Issue 1, pp 41–52

Balancedness conditions for exact games

  • Péter Csóka
  • P. Jean-Jacques Herings
  • László Á. Kóczy
Open Access


We provide two new characterizations of exact games. First, a game is exact if and only if it is exactly balanced; and second, a game is exact if and only if it is totally balanced and overbalanced. The condition of exact balancedness is identical to the one of balancedness, except that one of the balancing weights may be negative, while for overbalancedness one of the balancing weights is required to be non-positive and no weight is put on the grand coalition. Exact balancedness and overbalancedness are both easy to formulate conditions with a natural game-theoretic interpretation and are shown to be useful in applications. Using exact balancedness we show that exact games are convex for the grand coalition and we provide an alternative proof that the classes of convex and totally exact games coincide. We provide an example of a game that is totally balanced and convex for the grand coalition, but not exact. Finally we relate classes of balanced, totally balanced, convex for the grand coalition, exact, totally exact, and convex games to one another.


Totally balanced games Exact games Convex games 

JEL Classification

C71 C61 

Copyright information

© The Author(s) 2011

Authors and Affiliations

  • Péter Csóka
    • 1
  • P. Jean-Jacques Herings
    • 2
  • László Á. Kóczy
    • 3
  1. 1.Department of FinanceCorvinus University of BudapestBudapestHungary
  2. 2.Department of EconomicsMaastricht UniversityMaastrichtThe Netherlands
  3. 3.Institute of Economics of the Hungarian Academy of Sciences and Óbuda UniversityBudapestHungary

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