A New Solution Concept for the Ultimatum Game leading to the Golden Ratio

Abstract The Ultimatum Game is a paradigmatic two-player game. A proposer can offer a certain fraction of some valuable good. A responder can accept the offer or reject it, implying that the two players receive nothing. The only subgame-perfect Nash equilibrium is to only offer an infinitesimal amou...

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Autor principal:	Stefan Schuster
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/9eaf34473cbd4f7590f224e767382838
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spelling	oai:doaj.org-article:9eaf34473cbd4f7590f224e7673828382021-12-02T11:51:13ZA New Solution Concept for the Ultimatum Game leading to the Golden Ratio10.1038/s41598-017-05122-52045-2322https://doaj.org/article/9eaf34473cbd4f7590f224e7673828382017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-05122-5https://doaj.org/toc/2045-2322Abstract The Ultimatum Game is a paradigmatic two-player game. A proposer can offer a certain fraction of some valuable good. A responder can accept the offer or reject it, implying that the two players receive nothing. The only subgame-perfect Nash equilibrium is to only offer an infinitesimal amount and to accept this. However, this equilibrium is not in agreement with experimental observations, which show varying accepted offers around 40%. While some authors suggest that the fairest split of 50% vs. 50% would be explainable on theoretical grounds or by computer simulation, a few authors (including myself) have recently suggested that the Golden Ratio, about 0.618 vs. about 0.382, would be the solution, in striking agreement with observations. Here we propose a solution concept, based on an optimality approach and epistemic arguments, leading to that suggested solution. The optimality principle is explained both in an axiomatic way and by bargaining arguments, and the relation to Fibonacci numbers is outlined. Our presentation complements the Economic Harmony theory proposed by R. Suleiman and is based on infinite continued fractions. The results are likely to be important for the theory of fair salaries, justice theory and the predictive value of game theory.Stefan SchusterNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-11 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Stefan Schuster A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
description	Abstract The Ultimatum Game is a paradigmatic two-player game. A proposer can offer a certain fraction of some valuable good. A responder can accept the offer or reject it, implying that the two players receive nothing. The only subgame-perfect Nash equilibrium is to only offer an infinitesimal amount and to accept this. However, this equilibrium is not in agreement with experimental observations, which show varying accepted offers around 40%. While some authors suggest that the fairest split of 50% vs. 50% would be explainable on theoretical grounds or by computer simulation, a few authors (including myself) have recently suggested that the Golden Ratio, about 0.618 vs. about 0.382, would be the solution, in striking agreement with observations. Here we propose a solution concept, based on an optimality approach and epistemic arguments, leading to that suggested solution. The optimality principle is explained both in an axiomatic way and by bargaining arguments, and the relation to Fibonacci numbers is outlined. Our presentation complements the Economic Harmony theory proposed by R. Suleiman and is based on infinite continued fractions. The results are likely to be important for the theory of fair salaries, justice theory and the predictive value of game theory.
format	article
author	Stefan Schuster
author_facet	Stefan Schuster
author_sort	Stefan Schuster
title	A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
title_short	A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
title_full	A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
title_fullStr	A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
title_full_unstemmed	A New Solution Concept for the Ultimatum Game leading to the Golden Ratio
title_sort	new solution concept for the ultimatum game leading to the golden ratio
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/9eaf34473cbd4f7590f224e767382838
work_keys_str_mv	AT stefanschuster anewsolutionconceptfortheultimatumgameleadingtothegoldenratio AT stefanschuster newsolutionconceptfortheultimatumgameleadingtothegoldenratio
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A New Solution Concept for the Ultimatum Game leading to the Golden Ratio

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