Martínez-Legaz, Juan Enrique 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]. Cited in 3 Documents MSC: 91A12 Cooperative games PDFBibTeX XMLCite \textit{J. E. Martínez-Legaz}, Lect. Notes Econ. Math. Syst. 563, 293--303 (2006; Zbl 1152.91335)