  Uni-directional social interactions are ubiquitous in real social networks
whereas undirected interactions are intensively studied. We establish a voter
model in a dynamical directed network. We analytically obtain the degree
distribution of the evolving network at any given time. Furthermore, we find
that the average degree is captured by an emergent game. On the other hand, we
find that the fate of opinions is captured by another emergent game. Beyond
expectation, the two emergent games are typically different due to the
unidirectionality of the evolving networks. The Nash equilibrium analysis of
the two games facilitates us to give the criterion under which the minority
opinion with few disciples initially takes over the population eventually for
in-group bias. Our work fosters the understanding of opinion dynamics ranging
from methodology to research content.
