Comparison of Oracles

Abstract: We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Distinct characterizations are provided for deterministic and stochastic signaling functions, based on information matching, partition refinements, and common knowledge components. This study extends Blackwell (1951) to games and expands the work of Aumann (1976) on common knowledge by developing a theory of information loops.