0467447 20240103213159.120161217235959.9 84977137654 000389515800004 10.1007/978-3-319-40596-4_4 11 s. P Communications in Computer and Information Science 610 cav_un_epca*0468640978-3-319-40595-735-45ChamSpringer International2016 Coalitional game Lovász extension Choquet integral Core Weber set Superdifferential cav_un_auth*0309054 Adam Lukáš Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0015063 Kroupa T. CZ http://library.utia.cas.cz/separaty/2016/MTR/adam-0467447.pdf cav_un_auth*0321507 GA15-00735S GA ČR Every coalitional game can be extended from the powerset onto the real unit cube. One of possible approaches is the Lovász extension, which is the same as the discrete Choquet integral with respect to the coalitional game. We will study some solution concepts for coalitional games (core, Weber set) using superdifferentials developed in non-smooth analysis. It has been shown that the core coincides with Fréchet superdifferential and the Weber set with Clarke superdifferential for the Lovász extension, respectively. We introduce the intermediate set as the limiting superdifferential and show that it always lies between the core and the Weber set. From the game-theoretic point of view, the intermediate set is a non-convex solution containing the Pareto optimal payoff vectors, which depend on some ordered partition of the players and the marginal coalitional contributions with respect to the order. cav_un_auth*0340759 International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU) 2016 /16./ 20160620 20160624 Eindhoven NL BA 2017 2 PR RVO:67985556 http://hdl.handle.net/11104/0266447 S 3+4 Proceedings Paper Computer Science Artificial Intelligence|Computer Science Theory Methods 2016 978-3-319-40595-7 84977137654 SCOPUS PUBMED 000389515800004 WOS cav_un_epca*0468640 Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016) 978-3-319-40595-7 35 45 Cham Springer International 2016 Communications in Computer and Information Science 610