  In this paper, we present a network manipulation algorithm based on an
alternating minimization scheme from (Nesterov 2020). In our context, the
latter mimics the natural behavior of agents and organizations operating on a
network. By selecting starting distributions, the organizations determine the
short-term dynamics of the network. While choosing an organization in
accordance with their manipulation goals, agents are prone to errors. This
rational inattentive behavior leads to discrete choice probabilities. We extend
the analysis of our algorithm to the inexact case, where the corresponding
subproblems can only be solved with numerical inaccuracies. The parameters
reflecting the imperfect behavior of agents and the credibility of
organizations, as well as the condition number of the network transition matrix
have a significant impact on the convergence of our algorithm. Namely, they
turn out not only to improve the rate of convergence, but also to reduce the
accumulated errors. From the mathematical perspective, this is due to the
induced strong convexity of an appropriate potential function.
