We introduce the notion of an information structure T as bring richer than another F when for every game G, all correlated equilibrium distributions of G induced by F are also induced by T. In particular, if T is richer than F then T can make all agents as well off as a in any game. Ws also define a to be faithfully reproducible from T when all the players can compute from their information in T "new information" that reproduces what they could have received from F. Our main result is that T is richer than F if and only if F is faithfully reproducible from T. Classification Number: C72. (C) 2000 Academic Press.
Gossner, O. (2000). Comparison of information structures. Games and Economic Behavior, 30(1), 44-63. https://doi.org/10.1006/game.1998.0706 (Original work published 2000)