We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments á la Blackwell. More specifically, we consider pairs consisting of a game with incomplete information G and an information structure 𝒮 such that the extended game Γ(G,𝒮) has a unique Pareto payoff profile u. We prove that u is a Nash payoff profile of Γ(G,𝒮), and that for any information structure 𝒯 that is coarser than 𝒮, all Nash payoff profiles of Γ(G,𝒯) are dominated by u. We then prove that our condition is also necessary in the following sense: Given any convex compact polyhedron of payoff profiles, whose Pareto frontier is not a singleton, there exists an extended game Γ(G,𝒮) with that polyhedron as the convex hull of feasible payoffs, an information structure 𝒯 coarser than 𝒮 and a player i who strictly prefers a Nash equilibrium in Γ(G,𝒯) to any Nash equilibrium in Γ(G,𝒮).
