Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games

Carles Rafels and Neus Ybern

International Journal of Game Theory, 1995, vol. 24, issue 2, 113-26

Abstract: In this paper we characterize convex games by means of Owen's multilinear extension and the marginal worth vectors associated with even or odd permutations. Therefore we have obtained a refinement of the classic theorem; Shapley (1971), Ichiishi (1981) in order to characterize the convexity of a game by its marginal worth vectors. We also give new expressions for the marginal worth vectors in relation to unanimity coordinates and the first partial derivatives of Owen's multilinear extension. A sufficient condition for the convexity is given and also one application to the integer part of a convex game.

Date: 1995
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