  Consensus formation in a social network is modeled by a dynamic game of a
prescribed duration played by members of the network. Each member independently
minimizes a cost function that represents his/her motive. An integral cost
function penalizes a member's differences of opinion from the others as well as
from his/her own initial opinion, weighted by influence and stubbornness
parameters. Each member uses its rate of change of opinion as a control input.
This defines a dynamic non-cooperative game that turns out to have a unique
Nash equilibrium. Analytic explicit expressions are derived for the opinion
trajectory of each member for two representative cases obtained by suitable
assumptions on the graph topology of the network. These trajectories are then
examined under different assumptions on the relative sizes of the influence and
stubbornness parameters that appear in the cost functions.
