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

01/27/2021

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by   Masato Tanaka, et al.

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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. Both the number of variables and number of constraints in our formulation are bounded by (Wn) where W is the total sum of (integer) voting weights and n is the number of players. 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.