Open-Loop Equilibrium Strategies for Dynamic Influence Maximization Game Over Social Networks

We consider the problem of budget allocation for competitive influence maximization over social networks. In this problem, multiple competing parties (players) want to distribute their limited advertising resources over a set of social individuals to maximize their long-run cumulative payoffs. It is assumed that the individuals are connected via a social network and update their opinions based on the classical DeGroot model. The players must decide the budget distribution among the individuals at a finite number of campaign times to maximize their overall payoff given as a function of individuals' opinions. We show that i) the optimal investment strategy for the case of a single-player can be found in polynomial time by solving a concave program, and ii) the open-loop equilibrium strategies for the multiplayer dynamic game can be computed efficiently by following natural regret minimization dynamics. Our results extend the earlier work on the static version of the problem to a dynamic multistage game.