  This article studies the evolution of opinions and interpersonal influence
structures in a group of agents as they discuss a sequence of issues, each of
which follows an opinion dynamics model. In this work, we propose a general
opinion dynamics model and an evolution of interpersonal influence structures
based on the model of reflected appraisals proposed by Friedkin. Our
contributions can be summarized as follows: (i) we introduce a model of opinion
dynamics and evolution of interpersonal influence structures between issues
viewed as a best response cost minimization to the neighbor's actions, (ii) we
show that DeGroot's and Friedkin-Johnsen's models of opinion dynamics and their
evolution of interpersonal influence structures are particular cases of our
proposed model, and (iii) we prove the existence of an equilibrium. This work
is a step towards providing a solid formulation of the evolution of opinions
and interpersonal influence structures over a sequence of issues.
