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Comparison of Oracles: Part II

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Listed:
  • David Lagziel
  • Ehud Lehrer
  • Tao Wang

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.

Suggested Citation

  • David Lagziel & Ehud Lehrer & Tao Wang, 2025. "Comparison of Oracles: Part II," Papers 2511.04449, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2511.04449
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    References listed on IDEAS

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    1. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    2. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    3. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    4. David Lagziel & Ehud Lehrer, 2025. "Constrained Mediation: Bayesian Implementability of Joint Posteriors," Papers 2510.20986, arXiv.org, revised Nov 2025.
    5. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    7. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    8. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
    9. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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