  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.
