Comparison of Information Structures

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. In particular, if I is richer than J then I can make all agents as well off as J in any game. We also define J to be faithfully reproducible from I when all the players can compute from their information in I "new information" that reproduces what they could have received from J. Our main result is that I is richer than J if and only if J is faithfully reproducible from I. Journal of Economic Literature Classification Number: C72.