Effects of coupling strength and coupling schemes between interdependent lattices on the evolutionary ultimatum game

Abstract

Inspired by the fact that interdependent networks are more apt to describe real-world systems than isolated networks, this paper is devoted to the evolutionary ultimatum game on interdependent lattices. In particular, we aim to study the effects of the coupling strengths (denoted by α) on the emergence of fairness behaviours with two kinds of coupling schemes (i.e., symmetric coupling scheme and asymmetric coupling scheme). Here, the coupling strength determines the interdependency of utility between corresponding partners of the two interdependent lattices. By Monte Carlo simulations and the two-way analysis of variance, we quantitatively confirm that the coupling strength has a significant influence on the emergence of fairness. More specifically, the fairness level can be raised and facilitated when the coupling strength is introduced and increased (less than 1, i.e., with α<1) compared with the traditional case. By comparison, the symmetric coupling case with mutual information communication performs better than the asymmetric case with unidirectional information communication. Under the symmetric coupling scheme, we find some counterintuitive but interesting phenomena when the coupling strength is set to 1: the greedy strategy (p<q) may occur in a few simulations, but the altruistic strategy (p≫q) emerges in most other simulations. In addition, we also investigate the evolution of strategies under the asymmetric coupling scheme and find quite different results compared to those of the symmetric coupling scheme. It is further demonstrated that both the coupling schemes and the coupling strength contribute to the successful promotion of fairness. Furthermore, temporal and spatial distributions and characteristic snapshots are provided to clarify the roles of the coupling strength and coupling scheme in the evolution of fairness.