Balancedness conditions for exact games

Péter Csóka, P. Jean-Jacques Herings and László Kóczy ()

Mathematical Methods of Operations Research, 2011, vol. 74, issue 1, 52 pages

Abstract: 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. Copyright The Author(s) 2011

Keywords: Totally balanced games; Exact games; Convex games; C71; C61 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (4)

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Related works:
Working Paper: Balancedness Conditions for Exact Games (2008)
Working Paper: Balancedness conditions for exact games (2007)
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DOI: 10.1007/s00186-011-0348-3

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