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# Comparison of information structures

## Author

Listed:
• Olivier Gossner

## 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 ${\cal I}$.

## Suggested Citation

• Olivier Gossner, 1996. "Comparison of information structures," Economics Working Papers 169, Department of Economics and Business, Universitat Pompeu Fabra.
• Handle: RePEc:upf:upfgen:169
as

File URL: https://econ-papers.upf.edu/papers/169.pdf
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## References listed on IDEAS

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1. repec:dau:papers:123456789/6244 is not listed on IDEAS
2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
4. 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 561-574, September.
5. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
6. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
Full references (including those not matched with items on IDEAS)

## Citations

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Cited by:

1. Gossner, Olivier, 2010. "Ability and knowledge," Games and Economic Behavior, Elsevier, vol. 69(1), pages 95-106, May.
2. 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..
3. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
4. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
5. Takashi Ui, 2009. "Bayesian potentials and information structures: Team decision problems revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(3), pages 271-291, September.
6. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
7. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
8. 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.
9. Vida, Péter & Āzacis, Helmuts, 2013. "A detail-free mediator," Games and Economic Behavior, Elsevier, vol. 81(C), pages 101-115.
10. repec:eee:gamebe:v:109:y:2018:i:c:p:126-131 is not listed on IDEAS
11. Olivier Gossner, 1997. "Protocoles de communication robustes," Revue Économique, Programme National Persée, vol. 48(3), pages 685-695.
12. Leal Vizcaíno René & Mekonnen Teddy, 2019. "Bayesian Comparative Statics," Working Papers 2019-03, Banco de México.
13. 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.
14. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, University Library of Munich, Germany.
15. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
16. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2003. "Positive value of information in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 17-31, December.
17. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
18. repec:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9646-z is not listed on IDEAS
19. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.

### Keywords

Game--theory; information; correlation;

### 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

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