k-Convex Games and Solution Concepts

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 x^θ(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 b^v — g^v(N)eⁱ, i ∈ N, belong to the core C(v) of the game.