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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 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.

SUBMITTER: Schuster S

PROVIDER: S-EPMC5514050 | biostudies-literature | 2017 Jul

REPOSITORIES: biostudies-literature

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

Schuster Stefan S

Scientific reports 20170717 1

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. ...[more]

PMID: 28717242

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Project description:Preference for beauty is human nature, as previous behavior studies have supported the notion of "beauty premium" in which attractive people were more easily to get promoted and receive higher salaries. In the present study, 29 males were recruited to participate in a three-person ultimatum game (UG) including a proposer, a responder and a powerless third player. Each subject, playing as the responder, had to decide whether to accept an offer from the allocator both for himself and a female third person. We aimed to elucidate how the facial attractiveness of the female subject affected the male subjects' fairness and decision-making in social exchanges. Frontal feedback-related negativity (FRN) in response to four offers in an attractive-face condition revealed no significant differences between offers; however, when the companion was an unattractive female, an "unfair/fair" offer, which assigned a lower share to the responder and a fair share to the third player, elicited the largest FRN. Furthermore, when the third player was offered the smallest amount ("fair/unfair" offer), a larger FRN was generated in an attractive-face condition than unattractive-face condition. In the "unfair/fair" offer condition in which subjects received a smaller allocation than the third person, the beauty of their female counterparts attenuated subjects' aversion to inequality, resulting in a less negative FRN in the frontal region and an increased acceptance ratio. However, the influence of the third player's facial attractiveness only affected the early evaluation stage: late P300 was found to be immune to the "beauty premium". Under the two face conditions, P300 was smallest following an "unfair/fair" offer, whereas the amplitudes in the other three offer conditions exhibited no significant differences. In addition, the differentiated neural features of processing facial attractiveness were also determined and indexed by four event-related potentials (ERP) components: N170, frontal N1, N2 and late positive potentials (LPPs).

Dataset Information

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

Publications

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

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