A consensus opinion model based on the evolutionary game

TL;DR

This paper introduces a novel consensus opinion model based on evolutionary game theory, analyzing how network structure, cost-benefit ratios, and noise influence the speed of reaching consensus.

Contribution

It presents a new opinion dynamics model integrating evolutionary game principles and explores its behavior on scale-free networks with various parameters.

Findings

Existence of an optimal cost-benefit ratio for fastest consensus

Consensus time decreases with higher average degree and increases with noise

Power-law relationship between network size and consensus time

Abstract

We propose a consensus opinion model based on the evolutionary game. In our model, both of the two connected agents receive a benefit if they have the same opinion, otherwise they both pay a cost. Agents update their opinions by comparing payoffs with neighbors. The opinion of an agent with higher payoff is more likely to be imitated. We apply this model in scale-free networks with tunable degree distribution. Interestingly, we find that there exists an optimal ratio of cost to benefit, leading to the shortest consensus time. Qualitative analysis is obtained by examining the evolution of the opinion clusters. Moreover, we find that the consensus time decreases as the average degree of the network increases, but increases with the noise introduced to permit irrational choices. The dependence of the consensus time on the network size is found to be a power-law form. For small or larger ratio of cost to benefit, the consensus time decreases as the degree exponent increases. However, for moderate ratio of cost to benefit, the consensus time increases with the degree exponent. Our results may provide new insights into opinion dynamics driven by the evolutionary game theory.