Comparison of Oracles: Part II

TL;DR

This paper extends the theory of information disclosure in incomplete-information games by characterizing oracle equivalence and developing a theory of information loops, building on foundational work by Blackwell and Aumann.

Contribution

It introduces a general framework for understanding oracle equivalence and develops a new theory of information loops in strategic environments.

Findings

Characterization of oracle equivalence in general environments

Development of a theory of information loops

Extension of Blackwell and Aumann's foundational work

Abstract

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.