Heterogenous allocation of chips promotes fairness in the Ultimatum Game

¹ School of Electro-Mechanical Engineering, Xidian University - Xi'an 710071, China
² Institute of Systems Engineering, Macau University of Science and Technology - Taipa, Macau
³ Faculty of Mathematics, King Abdulaziz University - Jeddah 21589, Saudi Arabia
⁴ Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University - Beijing 100871, China

Received: 24 January 2015
Accepted: 13 March 2015

Abstract

In an economic Ultimatum Game, two players interact to decide how to split a certain amount of money. The proposer formulates an allocation scheme to divide the sum, and the responder's decision is, either adoption, in which case both players are rewarded in accordance with the scheme, or rejection, in which case neither player is benefited. The economic theory and game theory predict that a rational proposer will offer his opponent a minimal but nonzero share and the responder will admit this scheme. However, this prediction is impractical in real situations and abundant experiments and theories are presented to resolve the discrepancy. Here, we concentrate on investigating the impact of heterogenous allocation of the chips on the evolution of fairness in the framework of the evolutionary game theory. The proposer has the privilege to offer the amount of the chips and make the allocation resolution to the responder. Interestingly, it is found that fairness prevails when the proposer is courageous enough to offer more chips to unsuccessful opponents. Moreover, we find that an amplifying group interaction enlarges the effects of heterogenous allocation of the chips on the evolution of fairness.