Interactive Information Design

We study the interaction between multiple information designers who try to influence the behavior of a set of agents. When the set of messages available to each designer is finite, such games always admit subgame perfect equilibria. When designers produce public information about independent pieces of information, every equilibrium of the direct game (in which the set of messages coincides with the set of states) is an equilibrium with larger (possibly infinite) message sets. The converse is true for a class of Markovian equilibria only. When designers produce information for their own corporation of agents, pure strategy equilibria exist and are characterized via an auxiliary normal form game. In an infinite-horizon multi-period extension of information design games, a feasible outcome which Pareto dominates a more informative equilibrium of the one-period game is supported by an equilibrium of the multi-period game.