The Lov¶asz extension of market games
نویسندگان
چکیده
We study the Lov¶ asz extension b v for cooperative games v by using the marginal worth vectors and the dividends. First, we prove that the marginal worth vector aC with respect to an x-compatible ordering C satis ̄es, for supermodular games, b v(x) = min fhx; yi : y 2 Core(v)g = x; aC® : Next, we obtain the following characterization of the utility function of a market game: The utility function of a market game is the Lov¶ asz extension of the game if and only if the market game is supermodular. 1991 Mathematics Subject Classi ̄cation: 90C27, 90D12
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