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Comparison of information structures

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  • 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 ${\cal I}$.

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 169.

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Date of creation: May 1996
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Handle: RePEc:upf:upfgen:169

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Web page: http://www.econ.upf.edu/

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Keywords: Game--theory; information; correlation;

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References

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  1. Robert J. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Working Paper Archive 661465000000000377, David K. Levine.
  2. 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.
  3. GOSSNER, Olivier, 1997. "Secure protocols or how communication generates correlation," CORE Discussion Papers 1997092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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).
  5. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  6. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
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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. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, EconWPA.
  3. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2003. "Positive value of information in games," International Journal of Game Theory, Springer, vol. 32(1), pages 17-31, December.
  4. Vida, Péter & Azacis, Helmuts, 2012. "A Detail-Free Mediator," Cardiff Economics Working Papers E2012/10, Cardiff University, Cardiff Business School, Economics Section.
  5. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
  6. B. Bassan & O. Gossner & M. Scarsini & S. Zamir., 1999. "A class of games with positive value of information," THEMA Working Papers 99-32, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  7. Ehud Lehrer & Dinah Rosenberg, 2003. "What restrictions do Bayesian games impose on the value of information?," Game Theory and Information 0312005, EconWPA.
  8. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
  9. 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.

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