  Opinion dynamics, aiming to understand the evolution of collective behavior
through various interaction mechanisms of opinions, represents one of the most
challenges in natural and social science. To elucidate this issue clearly,
binary opinion model becomes a useful framework, where agents can take an
independent opinion. Inspired by the realistic observations, here we propose
two basic interaction mechanisms of binary opinion model: one is the so-called
BSO model in which players benefit from holding the same opinion; the other is
called BDO model in which players benefit from taking different opinions. In
terms of these two basic models, the synthetical effect of opinion preference
and equivocators on the evolution of binary opinion is studied under the
framework of evolutionary game theory (EGT), where the replicator equation (RE)
is employed to mimick the evolution of opinions. By means of numerous
simulations, we show the theoretical equilibrium states of binary opinion
dynamics, and mathematically analyze the stability of each equilibrium state as
well.
