We study how information affects equilibria and welfare in games. For an agent, more precise information about an unknown state of the world leads to a mean-preserving spread of beliefs. We provide necessary and sufficient conditions to obtain either a non-increasing mean or a...

We study information design with multiple privately informed agents who interact in a game. Each agent's utility is linear in a real-valued state. We show that there always exists an optimal mechanism that is laminar partitional and bound its “complexity.” For each type profile, such a...

Consider a family of zero-sum games indexed by a parameter that determines each player's payoff function and feasible strategies. Our first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium value and strategies depend...