Comparison of Oracles: Part II

This paper studies incomplete-information games in which an information provider, an oracle, publicly discloses information to the players. One oracle is said to dominate another if, in every game, it can replicate the equilibrium outcomes induced by the latter. The companion Part I characterizes dominance under deterministic signaling and under stochastic signaling with a unique common knowledge component. The present paper extends the analysis to general environments and provides a characterization of equivalence (mutual dominance) among oracles. To this end, we develop a theory of information loops, thereby extending the seminal work of Blackwell (1951) to strategic environments and Aumann (1976)'s theory of common knowledge.