title: Evolution of fairness and coalition formation in three-person ultimatum games.
abstract: We consider the evolution of fairness and coalition formation in a three-person ultimatum 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 formation 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 30-35% of the subcoalition value to a coalition member, excluding a non-member. Multilateral bargaining is critically different from the bilateral one. Coalition-forming behavior may cause economic inefficiency and social 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.
authors.affiliation: Faculty of Economics, Komazawa University, 1-23-1 Komazawa, Setagaya-ku, Tokyo 154-8525, Japan. Electronic address: tnishi@komazawa-u.ac.jp.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Nishimura
authors.affiliation: Institute of Economic Research, Kyoto University, Kyoto 606-8501, Japan; Graduate School of Economics, Hitotsubashi University, Tokyo 186-8601, Japan.
authors.forename: Akira
authors.initials: A
authors.lastname: Okada
authors.affiliation: Department of Economics, Otaru University of Commerce, Hokkaido 047-8501, Japan.
authors.forename: Yasuhiro
authors.initials: Y
authors.lastname: Shirata
mesh_terms: D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D006801:Humans; D009154:Mutation; D012919:Social Behavior; D012945:Social Values; D013269:Stochastic Processes
keywords: Coalition formation; Evolutionary game theory; Fairness; Finite populations; Resource allocation