A Note on the Owen Value for Glove Games

Abstract

A well-known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, different concepts, like the Shapley value, the component restricted Shapley value or the Owen value, yield different distributions of worth. While the Shapley value does not distinguish between productive and unproductive agents in the market and the component restricted Shapley value does not consider imbalancedness of the market, the Owen value accounts for both. As computational effort for Shapley-based allocation rules is generally high, this note provides a computationally efficient formula for the Owen value (and the component restricted Shapley value) for glove games in case of minimal winning coalitions. A comparison of the efficient formulas highlights the above-mentioned differences.