  From a perspective of designing or engineering for opinion formation games in
social networks, the "opinion maximization (or minimization)" problem has been
studied mainly for designing subset selecting algorithms. We define a
two-player zero-sum Stackelberg game of competitive opinion optimization by
letting the player under study as the leader minimize the sum of expressed
opinions by doing so-called "internal opinion design", knowing that the other
adversarial player as the follower is to maximize the same objective by also
conducting her own internal opinion design. We furthermore consider multiagent
learning, specifically using the Optimistic Gradient Descent Ascent, and
analyze its convergence to equilibria in the simultaneous version of
competitive opinion optimization.
