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arXiv · 2101.11180

Pseudo Polynomial Size LP Formulation for Calculating the Least Core Value of Weighted Voting Games

Masato Tanaka·Tomomi Matsui
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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 $\mbox{O}(n W_+)$, 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.

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Masato Tanaka, Tomomi Matsui. 2021-01-27. Pseudo Polynomial Size LP Formulation for Calculating the Least Core Value of Weighted Voting Games. https://doi.org/10.1016/j.mathsocsci.2021.12.002

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