Comparison of Oracles

TL;DR

This paper studies the power of different oracles in incomplete-information games, characterizing when one oracle can replicate another's equilibrium outcomes through various signaling strategies.

Contribution

It provides new characterizations of oracle dominance in games, extending classical results on information and common knowledge to strategic settings.

Findings

Deterministic and stochastic signaling functions are characterized by posterior matching and partition refinements.

Dominance relations between oracles are formally defined and analyzed.

The work extends Blackwell's and Aumann's classical theories to game-theoretic contexts.

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 simultaneous posterior matching, partition refinements, and common knowledge components. This study extends the work of Blackwell (1951) to games, and expands the study of Aumann (1976) on common knowledge, along with the companion Part II, which develops a theory of information loops.