A Necessary and Sufficient Condition for Partial Monotonicity of Noncooperative Games

Naoki Matsumoto ()
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Naoki Matsumoto: Research Institute for Digital Media and Content, Keio University, Hiyoshi Campus West Annex 1, 2-1-1 Hiyoshihoncho, Kouhoku-ku, Yokohama, Kanagawa 223-8523, Japan

International Game Theory Review (IGTR), 2020, vol. 22, issue 04, 1-5

Abstract: It is a classical and interesting problem to find a Nash equilibrium of noncooperative games in the strategic form. It is well known that the game always has a mixed-strategy Nash equilibrium, but it does not necessarily have a pure-strategy Nash equilibrium. Takeshita and Kawasaki proved that every noncooperative partially monotone game has a pure-strategy Nash equilibrium, that is, the partial monotonicity is a sufficient condition for a noncooperative game to have a pure-strategy Nash equilibrium. In this paper, we prove the necessary and sufficient condition for a noncooperative n-person game with n ≥ 2 to be partially monotone. This result is an improvement of Takeshita and Kawasaki’s result.

Keywords: Noncooperative game; pure strategy; Nash equilibrium; partially monotone (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219198920500061

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