0467447 - ÚTIA 2017 RIV CH eng C - Conference Paper (international conference)
Adam, Lukáš - Kroupa, T.
Computing Superdifferentials of Lovász Extension with Application to Coalitional Game.
Communications in Computer and Information Science, 610. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016). Cham: Springer International, 2016, s. 35-45. Communications in Computer and Information Science, 610. ISBN 978-3-319-40595-7.
[International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU) 2016 /16./. Eindhoven (NL), 20.06.2016-24.06.2016]
R&D Projects: GA ČR GA15-00735S
Institutional support: RVO:67985556
Keywords : Coalitional game * Lovász extension * Choquet integral * Core * Weber set * Superdifferential
Subject RIV: BA - General Mathematics
Result website:
http://library.utia.cas.cz/separaty/2016/MTR/adam-0467447.pdf

DOI: https://doi.org/10.1007/978-3-319-40596-4_4

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.
Permanent Link: http://hdl.handle.net/11104/0266447