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Comparative cooperative game theory

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Abstract

Given two side-payment gamesv andw, both defined for the same finite player-setN, the following three welfare criteria are characterized in terms of the datav andw: (A) For everyy ∃ C(w) there existsx ∃ C(v) such thaty≤x; (A′) For everyx∃C(v) there existsyεC(w) such thaty≤x; and (B) There existyεC(w) andxεC(v) such thaty≤x. (HereC(v) denotes the core ofv.) Given two non-side-payment gamesv andw, sufficient conditions for the criteria (A′) and (B) are established, by observing that an ordinal convex game has a large core.

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Authors and Affiliations

  1. Department of Economics, The Ohio State University, Arps Hall, 1945 N. High St., 43210-1172, Columbus, OH, USA

    T. Ichiishi

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  1. T. Ichiishi
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In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986.

A substantially revised version of Ichiishi (1987a). A part of this paper was written during the author's visit to CORE in early June 1987. The hospitality and the financial support of CORE as well as support from the Ohio State University are gratefully acknowledged. The author thanks Van Kolpin, Jean-FranÇois Mertens, Shmuel Zamir and two anonymous referees for their comments and suggestions on the earlier versions. Any possible deficiency in this paper is the author's responsibility.

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Ichiishi, T. Comparative cooperative game theory. Int J Game Theory 19, 139–152 (1990). https://doi.org/10.1007/BF01761073

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  • DOI: https://doi.org/10.1007/BF01761073

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