Computing the nucleolus of weighted voting games

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Computing the nucleolus of weighted voting games

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Title: Computing the nucleolus of weighted voting games
Author: Elkind, Edith; Pasechnik, Dmitrii V.
Copyright year: 2009
Abstract: Weighted voting games (WVG) are coalitional games in which an agent’s contribution to a coalition is given by his weight, and a coalition wins if its total weight meets or exceeds a given quota. These games model decision-making in political bodies as well as collaboration and surplus division in multiagent domains. The computational complexity of various solution concepts for weighted voting games received a lot of attention in recent years. In particular, Elkind et al.(2007) studied the complexity of stability related solution concepts in WVGs, namely, of the core, the least core, and the nucleolus. While they have completely characterized the algorithmic complexity of the core and the least core, for the nucleolus they have only provided an NP-hardness result. In this paper, we solve an open problem posed by Elkind et al. by showing that the nucleolus of WVGs, and, more generally, kvector weighted voting games with fixed k, can be computed in pseudopolynomial time, i.e., there exists an algorithm that correctly computes the nucleolus and runs in time polynomial in the number of players n and the maximum weight W. In doing so, we propose a general framework for computing the nucleolus, which may be applicable to a wider of class of games.
Subject: DRNTU::Science::Mathematics::Applied mathematics
Type: Conference Paper
Conference name: Symposium on Discrete Algorithms (2009 : New York, USA)
School: School of Physical and Mathematical Sciences
Rights: © 2009 SIAM This paper was published in SODA’ 09 and is made available as an electronic reprint (preprint) with permission of Society for Industrial and Applied Mathematics. The paper can be found at the following official publisher’s URL: [http://siam.org/proceedings/soda/2009/soda09.php.] One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.
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