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Posterior Implementability in a Two-Person Decision Problem


  • Green, Jerry R
  • Laffont, Jean-Jacques


When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publically obser vable, the players' information is augmented by their observation of each others' strategies. In this paper the authors study the set of Bayesian implementable decision rules which have the further property that the information c onveyed in the process of thier implementation does not invalidate the optimality of the players' strategies. Such rules are called posterior implementable. The authors concentrate on a two-person problem with two possible decisions and, for this problem, they obtain a complete characterization of the set of posterior implementable decision rules. Copyright 1987 by The Econometric Society.

Suggested Citation

  • Green, Jerry R & Laffont, Jean-Jacques, 1987. "Posterior Implementability in a Two-Person Decision Problem," Econometrica, Econometric Society, vol. 55(1), pages 69-94, January.
  • Handle: RePEc:ecm:emetrp:v:55:y:1987:i:1:p:69-94

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    Cited by:

    1. Bernard Lebrun, 2008. "First-Price, Second-Price, and English Auctions with Resale," Working Papers 2008_06, York University, Department of Economics.
    2. Lopomo, Giuseppe, 2001. "Optimality and Robustness of the English Auction," Games and Economic Behavior, Elsevier, vol. 36(2), pages 219-240, August.
    3. Edward Cartwright & Myrna Wooders, 2009. "On purification of equilibrium in Bayesian games and expost Nash equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 127-136, March.
    4. Hao Li & Sherwin Rosen & Wing Suen, 2001. "Conflicts and Common Interests in Committees," American Economic Review, American Economic Association, vol. 91(5), pages 1478-1497, December.
    5. Olivier Compte & Philippe Jehiel, 2009. "Veto Constraint in Mechanism Design: Inefficiency with Correlated Types," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 182-206, February.
    6. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    7. Ehud Kalai, 2006. "Structural Robustness of Large Games," Discussion Papers 1431, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "Posterior Implementation versus Ex-Post Implementation," Levine's Bibliography 666156000000000556, UCLA Department of Economics.
    9. Bikhchandani, Sushil & Haile, Philip A. & Riley, John G., 2002. "Symmetric Separating Equilibria in English Auctions," Games and Economic Behavior, Elsevier, vol. 38(1), pages 19-27, January.
    10. Johannes Hörner & Massimo Morelli & Francesco Squintani, 2015. "Mediation and Peace," Review of Economic Studies, Oxford University Press, vol. 82(4), pages 1483-1501.
    11. Kei Kawakami, 2016. "Posterior renegotiation-proofness in a two-person decision problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 893-931, November.
    12. Minehart, Deborah & Scotchmer, Suzanne, 1999. "Ex Post Regret and the Decentralized Sharing of Information," Games and Economic Behavior, Elsevier, vol. 27(1), pages 114-131, April.
    13. Jehiel, Philippe & Meyer-ter-Vehn, Moritz & Moldovanu, Benny & Zame, William R., 2007. "Posterior implementation vs ex-post implementation," Economics Letters, Elsevier, vol. 97(1), pages 70-73, October.
    14. Krasa, Stefan, 1999. "Unimprovable Allocations in Economies with Incomplete Information," Journal of Economic Theory, Elsevier, vol. 87(1), pages 144-168, July.
    15. Lebrun, Bernard, 2012. "Optimality and the English and second-price auctions with resale," Games and Economic Behavior, Elsevier, vol. 75(2), pages 731-751.
    16. Alejandro Francetich, 2013. "Becoming the Neighbor Bidder: Endogenous Winner’s Curse in Dynamic Mechanisms," Working Papers 501, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Bergemann, Dirk & Wambach, Achim, 2015. "Sequential information disclosure in auctions," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 1074-1095.
    18. Grüner, Hans Peter, 2007. "Protocol Design and (De-)Centralization," CEPR Discussion Papers 6357, C.E.P.R. Discussion Papers.
    19. Kei Kawakami, 2013. "Maximally Informative Decision Rules In a Two-Person Decision Problem," Department of Economics - Working Papers Series 1178, The University of Melbourne, revised 2014.
    20. Deb, Joyee & Kalai, Ehud, 2015. "Stability in large Bayesian games with heterogeneous players," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1041-1055.
    21. Evans, Robert & Reiche, Sönje, 2015. "Contract design and non-cooperative renegotiation," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1159-1187.
    22. Cramton Peter C. & Palfrey Thomas R., 1995. "Ratifiable Mechanisms: Learning from Disagreement," Games and Economic Behavior, Elsevier, vol. 10(2), pages 255-283, August.
    23. Helmut Bester & Roland Strausz, "undated". "Imperfect Commitment and the Revelation Principle," Papers 004, Departmental Working Papers.
    24. Robert Evans & Sonje Reiche, 2013. "Mechanism Design and Non-Cooperative Renegotiation," Cambridge Working Papers in Economics 1331, Faculty of Economics, University of Cambridge.
    25. Ehud Kalai, 2005. "Partially-Specified Large Games," Levine's Bibliography 784828000000000565, UCLA Department of Economics.

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