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Maximally Informative Decision Rules In a Two-Person Decision Problem

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  • Kei Kawakami

Abstract

This paper studies how much information can be revealed when agents with private information lack commitment to actions in a given mechanism as well as to the mechanism itself. In a two-person decision problem, agents are allowed to hold on to an outcome in one mechanism while they play another mechanism and learn new information. Formally, decision rule is maximally informative if it is (i) posterior im-plementable and (ii) robust to a posterior proposal of another posterior implementable decision rule. Focusing on a two-person problem, we identify environments where maximally informative decision rules exist. We also show that a maximally informative decision rule must be implemented by a mechanism with a small number of actions (at most 5 for two agents). The result indicates that lack of commitment to a mechanism signi?cantly reduces the amount of information revelation in equilibrium. Keywords: Information aggregation, Limited commitment, Posterior e¢ ciency, Posterior implementation, Renegotiation-proofness.

Suggested Citation

  • 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.
    • Handle: RePEc:mlb:wpaper:1178
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    References listed on IDEAS

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    1. Holmstrom, Bengt & Myerson, Roger B, 1983. "Efficient and Durable Decision Rules with Incomplete Information," Econometrica, Econometric Society, vol. 51(6), pages 1799-1819, November.
    2. 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.
    3. Cramton Peter C. & Palfrey Thomas R., 1995. "Ratifiable Mechanisms: Learning from Disagreement," Games and Economic Behavior, Elsevier, vol. 10(2), pages 255-283, August.
    4. Maskin, Eric & Tirole, Jean, 1992. "The Principal-Agent Relationship with an Informed Principal, II: Common Values," Econometrica, Econometric Society, vol. 60(1), pages 1-42, January.
    5. Neeman, Zvika & Pavlov, Gregory, 2013. "Ex post renegotiation-proof mechanism design," Journal of Economic Theory, Elsevier, vol. 148(2), pages 473-501.
    6. Watson, Joel, 1999. "Starting Small and Renegotiation," Journal of Economic Theory, Elsevier, vol. 85(1), pages 52-90, March.
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    Keywords

    Information aggregation; Limited commitment; Posterior effeciency; Posterior implementation; Renegotiation-proofness.;
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