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The unit-level-core for multi-choice games: the replicated core for TU games

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Abstract

This note extends the solution concept of the core for traditional transferable-utility (TU) games to multi-choice TU games, which we name the unit-level-core. It turns out that the unit-level-core of a multi-choice TU game is a “replicated subset” of the core of a corresponding “replicated” TU game. We propose an extension of the theorem of Bondareva (Probl Kybern 10:119–139, 1963) and Shapley (Nav Res Logist Q 14:453–460, 1967) to multi-choice games. Also, we introduce the reduced games for multi-choice TU games and provide an axiomatization of the unit-level-core on multi-choice TU games by means of consistency and its converse.

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Authors and Affiliations

  1. Department of Applied Mathematics, National Dong Hwa University, Hualien, 974, Taiwan

    Yan-An Hwang

  2. Department of Applied Mathematics, National Pingtung University of Education, Pingtung, 900, Taiwan

    Yu-Hsien Liao

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  1. Yan-An Hwang
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  2. Yu-Hsien Liao
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Correspondence to Yu-Hsien Liao.

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Hwang, YA., Liao, YH. The unit-level-core for multi-choice games: the replicated core for TU games. J Glob Optim 47, 161–171 (2010). https://doi.org/10.1007/s10898-009-9463-6

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  • DOI: https://doi.org/10.1007/s10898-009-9463-6

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