We consider the models of average-oriented opinion dynamics. An opinion about an event is distributed among the agents of a social network. There are an optimization problem and two game-theoretical models when players as centers of influence aim to make the opinions of the agents closer to the target ones in a finite time horizon minimizing their costs. The optimization problem and the games of competition for the agents’ opinion are linear-quadratic and solved using the Euler-equation approach. The optimal strategies for optimization problem and the Nash equilibria in the open-loop strategies for the games are found. Numerical simulations demonstrate theoretical results.