Abstract:
The alteration of opinions of individuals in groups over time is a
particular common phenomenon in social life. Taking into account the
influence of homogeneous members and some special influential
persons, an opinion dynamics game is established. In a social
network, two special influence nodes pursuing their certain goals
with the process of influencing the opinions of other normal nodes
in discrete time is considered. From the perspective of
non-cooperation, Stackelberg equilibrium is selected as the solution
of the opinion dynamics game. Given distinct information knowledge,
players will derive different equilibrium strategies. The open-loop
and feedback information configurations are investigated. In the
two-person non-cooperative dynamic game, techniques of Pontryagin's
minimum principle and dynamic programming are adopted to derive the
equilibrium levels of influence for influence nodes and the
equilibrium opinions for other normal nodes in the network. To
compute and compare the various equilibrium concepts under different
information structures, numerical results are presented for
different scenarios.
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