A Game of Influence on Opinion Formation - Precision Targeting in the Modern Information Space

We introduce a dynamic zero-sum game called a targeting game, where two strategic players exert influence on the opinion formation inside a network of nonstrategic agents. The nonstrategic agents have exogenously given initial opinions and update their opinions throughout an infinite discrete time horizon as in the DeGroot model. The two strategic players have fixed and opposite opinions. They can target specific agents in specific time periods. As a result of their targets, the convergence state of the opinion dynamics is affected, which the players aim to bring as close as possible to their own opinion. In order to derive Nash equilibria, we first study the one-sided optimization problem and provide sufficient conditions under which an optimal target exists and is found in the initial period. Moreover, we provide an instance where no optimal targets exist. Then, in the two-sided context, we provide necessary and sufficient conditions for the existence of a Nash equilibrium where both players select their one-sided optimal target. Also, we provide an instance where no Nash equilibria exist. An important role is played by the property of attractiveness, which encapsulates an agent’s openness to external information and their position in the network.