Comparison of Oracles

2025-05-21

AI Summary

This paper investigates information dominance relations among oracles (public information sources) in incomplete-information games—specifically, when one oracle can replicate the equilibrium outcome set induced by another across all games. Method: It extends the Blackwell order to multi-player games via three novel characterizations: simultaneous posterior matching, partition refinement, and public-knowledge components; develops an information-cycle theory generalizing Aumann’s framework of common knowledge; and derives necessary and sufficient conditions for deterministic and stochastic oracles to induce equivalent dominance. Contribution/Results: The work establishes a unified ordinal characterization of information structures, bridging decision-theoretic and game-theoretic notions of informativeness. It provides foundational theoretical benchmarks for mechanism design and information-sharing protocols, enabling rigorous comparison of information sources in strategic environments with non-cooperative agents.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

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 by developing a theory of information loops.

Problem

• Analyzes incomplete-information games with public oracles
• Characterizes deterministic and stochastic signaling functions
• Extends Blackwell's and Aumann's work on information theory

Innovation

• Extends Blackwell's work to game theory
• Develops theory of information loops
• Uses deterministic and stochastic signaling functions