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Comparison of information structures


  • GOSSNER, Olivier

    () (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)


Several authors have observed that in interactive decision frameworks, welfare is not monotonic with information in the sense that more information can make agents worse off. This contrasts with Blackwell’s comparison of statistical experiments in which more information can only make the statistician better off. We introduce the notion of an information structure L as being richer than another J when for every game G, all correlated equilibrium distributions of G induced by J are also induced by L. If L is richer than J, L can always make all agents as well off than J. We also define J to be faithfully reproducible from L when all the players can compute from their information in L “new information” that reproduces what they could have received from J . Our main result is that L is richer than J if and only if J is faithfully reproducible from L.

Suggested Citation

  • GOSSNER, Olivier, 1997. "Comparison of information structures," CORE Discussion Papers 1997091, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1997091

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    References listed on IDEAS

    1. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
    2. repec:dau:papers:123456789/6244 is not listed on IDEAS
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
    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 561-574, September.
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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.
    6. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    7. 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.
    8. Vida, Péter & Āzacis, Helmuts, 2013. "A detail-free mediator," Games and Economic Behavior, Elsevier, vol. 81(C), pages 101-115.
    9. Olivier Gossner, 1997. "Protocoles de communication robustes," Revue Économique, Programme National Persée, vol. 48(3), pages 685-695.
    10. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2017. "A normalized value for information purchases," Working Papers 2017-51, Center for Research in Economics and Statistics, revised 05 Jan 2017.
    11. 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.
    12. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, EconWPA.
    13. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
    14. 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.
    15. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    16. Kloosterman, Andrew, 2015. "Public information in Markov games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 28-48.

    More about this item


    Information structure; correlated equilibrium; statistical experiment; value of in- formation;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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