Probabilistic fair behaviors spark its boost in the Ultimatum Game: the strength of good Samaritans
Guozhong Zheng, Jiqiang Zhang, Rizhou Liang, Lin Ma, and Li Chen

TL;DR
This paper models how probabilistic fair behaviors, inspired by good Samaritans, can induce widespread fairness in populations playing the Ultimatum Game, challenging traditional economic assumptions.
Contribution
It introduces a probabilistic model of fairness in the Ultimatum Game and demonstrates phase transitions and the influence of network structure on fairness emergence.
Findings
Fairness levels undergo abrupt transitions with increasing fair behavior probability.
Small proportions of fair acts can lead to full population fairness.
Heterogeneous networks show continuous fairness transition with influential hubs.
Abstract
Behavioral experiments on the Ultimatum Game have shown that we human beings have remarkable preference in fair play, contradicting the predictions by the game theory. Most of the existing models seeking for explanations, however, strictly follow the assumption of \emph{Homo economicus} in orthodox Economics that people are self-interested and fully rational to maximize their earnings. Here we relax this assumption by allowing that people probabilistically choose to be "good Samaritans", acting as fair players from time to time. For well-mixed and homogeneously structured populations, we numerically show that as this probability increases the level of fairness undergoes from the low scenario abruptly to the full fairness state, where occasional fair behaviors () are sufficient to drive the whole population to behave in the half-half split manner. We also develop a mean-field…
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Taxonomy
TopicsEvolutionary Game Theory and Cooperation · Opinion Dynamics and Social Influence · Complex Systems and Time Series Analysis
