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Computing Superdifferentials of Lovász Extension with Application to Coalitional Game
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SYSNO ASEP 0467447 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Computing Superdifferentials of Lovász Extension with Application to Coalitional Game Author(s) Adam, Lukáš (UTIA-B)
Kroupa, T. (CZ)Number of authors 2 Source Title Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016). - Cham : Springer International, 2016 - ISBN 978-3-319-40595-7 Pages s. 35-45 Series Communications in Computer and Information Science Series number 610 Number of pages 11 s. Publication form Print - P Action International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU) 2016 /16./ Event date 20.06.2016 - 24.06.2016 VEvent location Eindhoven Country NL - Netherlands Event type WRD Language eng - English Country CH - Switzerland Keywords Coalitional game ; Lovász extension ; Choquet integral ; Core ; Weber set ; Superdifferential Subject RIV BA - General Mathematics R&D Projects GA15-00735S GA ČR - Czech Science Foundation (CSF) Institutional support UTIA-B - RVO:67985556 UT WOS 000389515800004 EID SCOPUS 84977137654 DOI https://doi.org/10.1007/978-3-319-40596-4_4 Annotation 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. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2017
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