Evolution of Fairness and Coalition Formation in Three-Person Ultimatum Games
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Author’s Accepted Manuscript Evolution of fairness and coalition formation in three-person ultimatum games Takeshi Nishimura, Akira Okada, Yasuhiro Shirata www.elsevier.com/locate/yjtbi PII: S0022-5193(17)30097-8 DOI: http://dx.doi.org/10.1016/j.jtbi.2017.02.033 Reference: YJTBI8989 To appear in: Journal of Theoretical Biology Received date: 24 September 2016 Revised date: 23 February 2017 Accepted date: 27 February 2017 Cite this article as: Takeshi Nishimura, Akira Okada and Yasuhiro Shirata, Evolution of fairness and coalition formation in three-person ultimatum games, Journal of Theoretical Biology, http://dx.doi.org/10.1016/j.jtbi.2017.02.033 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Evolution of Fairness and Coalition Formation in Three-Person Ultimatum Games Takeshi Nishimuraa,∗, Akira Okadab,c, Yasuhiro Shiratad aFaculty of Economics, Komazawa University, Tokyo 154-8525, Japan bInstitute of Economic Research, Kyoto University, Kyoto 606-8501, Japan cGraduate School of Economics, Hitotsubashi University, Tokyo 186-8601, Japan dDepartment of Economics, Otaru University of Commerce, Hokkaido 047-8501, Japan Abstract We consider the evolution of fairness and coalition formation in a three-person ultima- tum game in which the coalition value depends on its size. Traditional game theory, which assumes selfish and rational players, predicts the largest and efficient coalition with a proposer exploiting most of the total value. In a stochastic evolutionary model (the frequency-dependent Moran process with mutations) where players make errors in estimating the payoffs and strategies of others, evolutionary selection favors the forma- tion of a two-person subcoalition under weak selection and in the low mutation limit if and only if its coalition value exceeds a high proportion (0.7) of that of the largest coalition. Proposers offer 30% to 35% of the subcoalition value to a coalition mem- ber, excluding a non-member. Multilateral bargaining is critically different from the bilateral one. Coalition-forming behavior may cause economic inefficiency and so- cial exclusion. Stochastic evolutionary game theory thus provides theoretical support to explain the behavior of human subjects in economic experiments of a three-person ultimatum game. Keywords: Coalition formation, Evolutionary game theory, Fairness, Finite populations, Resource allocation ∗Corresponding author: Faculty of Economics, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo 154-8525, Japan Email address: [email protected] (Takeshi Nishimura) Preprint submitted to Journal of Theoretical Biology February 27, 2017 .