# Comparison of Information Structures

## Author Info

• Gossner, Olivier

## Abstract

We introduce two ways of comparing information structures, say ${\cal I}$ and ${\cal J}$. First we say that ${\cal I}$ is richer than ${\cal J}$ when for every compact game $G$, all correlated equilibrium distributions of $G$ induced by ${\cal J}$ are also induced by ${\cal I}$. Second, we say that ${\cal J}$ is faithfully reproducable from ${\cal I}$ when all the players can compute from their information in ${\cal I}$ new information'' that they could have received from ${\cal J}$. We prove that ${\cal I}$ is richer than ${\cal J}$ if and only if ${\cal J}$ is faithfully reproducable from ${\cal I}$.

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## Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 30 (2000)
Issue (Month): 1 (January)
Pages: 44-63

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Handle: RePEc:eee:gamebe:v:30:y:2000:i:1:p:44-63

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Web page: http://www.elsevier.com/locate/inca/622836

## Related research

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Find related papers by JEL classification:
• C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

## References

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1. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
2. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
3. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
4. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
5. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
6. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-74, September.
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## Citations

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Cited by:
1. 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.
2. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
3. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2001. "Positive value of information in games," Discussion Paper Series dp294, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Jul 2002.
4. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, EconWPA.
5. Lehrer, Ehud & Rosenberg, Dinah, 2006. "What restrictions do Bayesian games impose on the value of information?," Journal of Mathematical Economics, Elsevier, vol. 42(3), pages 343-357, June.
6. Bassan, B. & Gossner, O. & Scarsini, M. & Zamir, S., 1999. "A Class of Games with Positive Value of Information," Papers 99-32, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
7. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
8. Vida, Péter & Āzacis, Helmuts, 2013. "A detail-free mediator," Games and Economic Behavior, Elsevier, vol. 81(C), pages 101-115.
9. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.

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