Pseudo polynomial size LP formulation for calculating the least core value of weighted voting games

Masato Tanaka and Tomomi Matsui

Mathematical Social Sciences, 2022, vol. 115, issue C, 47-51

Abstract: In this paper, we propose a pseudo polynomial size LP formulation for finding a payoff vector in the least core of a weighted voting game. The numbers of variables and constraints in our formulation are both bounded by O(nW+), where n is the number of players and W+ is the total sum of (integer) voting weights. When we employ our formulation, a commercial LP solver calculates a payoff vector in the least core of practical weighted voting games in a few seconds. We also extend our approach to vector weighted voting games.

Keywords: Weighted voting games; Least core; Linear programming (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:115:y:2022:i:c:p:47-51

DOI: 10.1016/j.mathsocsci.2021.12.002

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