Abstract
In Section V.3 we presented three characterizations of convex games in terms of the marginal worth vectors and the core. One of those three characterizations expresses that an n-person game v is convex if and only if all n! marginal worth vectors xθ(v), θ ∈ θn, belong to the core C(v) of the game. According to Theorem III.5.4, a slightly analogous characterization is also available for 1-convex games which were introduced in Section III.5. As a matter of fact, an n-person game v is 1-convex if and only if all n adjusted . efficient upper vectors bv — gv(N)ei, i ∈ N, belong to the core C(v) of the game.
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© 1988 Springer Science+Business Media Dordrecht
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Driessen, T. (1988). k-Convex Games and Solution Concepts. In: Cooperative Games, Solutions and Applications. Theory and Decision Library, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7787-8_7
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DOI: https://doi.org/10.1007/978-94-015-7787-8_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8451-4
Online ISBN: 978-94-015-7787-8
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