Comparison of Information Structures.

Several authors have observed that in interactive decision frameworks, welfare is not monotonic with information in the sense that more information can make agents worse off. This contrats with Blackwell's comparison of statistical experiments in which more informationcan only make the statistician betteroff. We introduce the notion of an information structure 'I' as being richer than another 'J' when for every game G, all correlated equilibrium distributions of G induced by 'J' are also induced by 'I'. If 'I' is richer than 'J', 'I' can always make all agents as well of than 'J'.