The multilinear extension of a cooperative game was introduced by Owen in 1972. In this contribution we study the Lovász extension for cooperative games by using the marginal worth vectors and the dividends. First, we prove a formula for the marginal worth vectors with respect to compatible orderings. Next, we consider the direct market generated by a game. This model of utility function, proposed by Shapley and Shubik in 1969, is the concave biconjugate extension of the game. Then we obtain (...) the following characterization: The utility function of a market game is the Lovász extension of the game if and only if the market game is supermodular. Finally, we present some preliminary problems about the relationship between cooperative games and combinatorial optimization. (shrink)

There have been two main lines in the literature on restricted games: the first line was started by Myerson (1977) that studied graph-restricted games an the second one was initiated by Faigle (1989). The present paper provides a unified way to look on the literature and establishes connections between the two different lines on restricted games. The strength and advantages of this unified approach becomes clear in the study of the inheritance of the convexity from the game to the restricted (...) game where an interesting result by Nouweland and Borm (1991) on the convexity of graph-restricted games is turned into a direct consequence of the corresponding result by Faigle (1989), by means of this relation. (shrink)