The weak core of simple games with ordinal preferences: implementation in Nash equilibrium |
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Authors: | Tomoichi Shinotsuka Koji Takamiya |
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Affiliation: | a Department of Economics, Otaru University of Commerce, 3-5-21, Midori, Otaru 047-8501, Japan;b Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki, Osaka 567-0047, Japan |
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Abstract: | In a simple game, coalitions belonging to a given class are “absolutely powerful” while others have no power. We attempt to make this distinction operational. Toward this end, we propose two axioms on social choice correspondences, Strong Non-Discrimination and Exclusion. Strong Non-Discrimination describes circumstances under which certain coalitions, the losing coalitions, have no influence over social choice. Exclusion requires that there are situations in which certain coalitions, the winning coalitions, can exercise their power. We show that the weak core correspondence is the minimal correspondence satisfying Maskin Monotonicity and Strong Non-Discrimination. We also show that the weak core is the unique correspondence satisfying Nash implementability, Strong Non-Discrimination, and Exclusion. |
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Keywords: | JEL classification codes: C71 C72 D71 D78 |
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