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Some characterizations of convex games. (English) Zbl 1152.91335
Seeger, Alberto (ed.), Recent advances in optimization. Proceedings of the twelfth French-German-Spanish conference on optimization, Avignon, France, September 20–24, 2004. Berlin: Springer (ISBN 3-540-28257-2/pbk). Lecture Notes in Economics and Mathematical Systems 563, 293-303 (2006).
Several characterizations of convexity for totally balanced games are presented. As a preliminary result, it is first shown that the core of any subgame of a nonnegative totally balanced game can be easily obtained from the maximum average value (MAV) function of the game. This result is then used to get a characterization of convex games in terms of MAV functions. It is also proved that a game is convex if and only if all of its marginal games are totally balanced.
For the entire collection see [Zbl 1079.90002].

91A12 Cooperative games