Pinning control of social fairness in the Ultimatum game

TL;DR

This paper demonstrates that pinning a small fraction of fair players in the Ultimatum Game can lead the entire population to achieve full fairness, with effectiveness depending on network topology and control strategies.

Contribution

It introduces a pinning control method to promote social fairness in the Ultimatum Game, highlighting its efficiency and robustness across different network structures.

Findings

Small fraction of pinned fair players can induce full fairness.

Network topology influences convergence time and control effectiveness.

Periodic on-off control reduces cost and maintains fairness.

Abstract

Decent social fairness is highly desired both for socio-economic activities and individuals, as it is one of the cornerstones of our social welfare and sustainability. How to effectively promote the level of fairness thus becomes a significant issue to be addressed. Here, by adopting a pinning control procedure, we find that when a very small fraction of individuals are pinned to be fair players in the Ultimatum Game, the whole population unexpectedly evolves into the full fairness level. The basic observations are quite robust in homogeneous networks, but the converging time as a function of the pinning number shows different laws for different underlying topologies. For heterogeneous networks, this leverage effect is even more pronounced that one hub node is sufficient for the aim, and a periodic on-off control procedure can be applied to further save the control cost. Intermittent failures are seen when the pinning control is marginally strong, our statistical analysis indicates some sort of criticality. Our work suggests that the pinning control procedure could potentially be a good strategy to promote the social fairness for some real scenarios when necessary.