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Robustness of Full Revelation in Multisender Cheap Talk

Author

Listed:
  • Margaret Meyer

    (Nuffield College and Dept. of Economics, Oxford University)

  • Inés Moreno de Barreda

    (Dept of Economics, Oxford University)

  • Julia Nafziger

    (Dept. of Economics and Business, Aarhus University)

Abstract
This paper studies information transmission in a two-sender, multidimensional cheap talk setting where there are exogenous restrictions on the feasible set of policies for the receiver. Such restrictions, which are present in most applications, can, by limiting the punishments available to the receiver, prevent the existence of fully revealing equilibria (FRE). We focus on FRE that are i) robust to small mistakes by the senders, in that small differences between the senders’ messages result in only small punishments by the receiver, and ii) independent of the magnitudes of the senders’ bias vectors. For convex policy spaces in an arbitrary number of dimensions, we prove that if there exists a FRE satisfying property ii), then there exists one satisfying both i) and ii). Thus the requirement of robustness is, under these assumptions, not restrictive. For convex policy spaces in two dimensions, we provide a simple geometric condition, the Local Deterrence Condition, on the directions of the senders’ biases relative to the frontier of the policy space, that is necessary and sufficient for the existence of a FRE satisfying i) and ii). We also provide a specific policy rule, the Min Rule, for the receiver that supports a FRE satisfying i) and ii) whenever one exists. The Min Rule is the anonymous rule that punishes incompatible reports in the least severe way, subject to maintaining the senders’ incentives for truthtelling, no matter how large their biases. We characterize necessary and sufficient conditions for collusion-proofness of a FRE supported by the receiver using the Min Rule and show that if such a FRE is not collusion-proof, then no other FRE satisfying ii) can be collusion-proof. We extend our existence results to convex policy spaces in more than two dimensions and to non-convex two-dimensional spaces. Finally, our necessary and sufficient condition, as well as our specific policy rule, can be easily adapted if the receiver is uncertain about the directions of the biases and/or if the biases vary with the state of the world.

Suggested Citation

  • Margaret Meyer & Inés Moreno de Barreda & Julia Nafziger, 2016. "Robustness of Full Revelation in Multisender Cheap Talk," Economics Papers 2016-W02, Economics Group, Nuffield College, University of Oxford.
    • Handle: RePEc:nuf:econwp:1602
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    References listed on IDEAS

    as
    1. Marco Battaglini, 2002. "Multiple Referrals and Multidimensional Cheap Talk," Econometrica, Econometric Society, vol. 70(4), pages 1379-1401, July.
    2. Friedman James W. & Samuelson Larry, 1994. "Continuous Reaction Functions in Duopolies," Games and Economic Behavior, Elsevier, vol. 6(1), pages 55-82, January.
    3. Meyer, Margaret & Moreno de Barreda, Inés & Nafziger, Julia, 2019. "Robustness of full revelation in multisender cheap talk," Theoretical Economics, Econometric Society, vol. 14(4), November.
    4. Vijay Krishna & John Morgan, 2001. "A Model of Expertise," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 747-775.
    5. , & ,, 2008. "Multi-sender cheap talk with restricted state spaces," Theoretical Economics, Econometric Society, vol. 3(1), March.
    6. Lai, Ernest K. & Lim, Wooyoung & Wang, Joseph Tao-yi, 2015. "An experimental analysis of multidimensional cheap talk," Games and Economic Behavior, Elsevier, vol. 91(C), pages 114-144.
    7. Friedman, James W. & Samuelson, Larry, 1990. "Subgame perfect equilibrium with continuous reaction functions," Games and Economic Behavior, Elsevier, vol. 2(4), pages 304-324, December.
    8. Gilat Levy & Ronny Razin, 2007. "On the Limits of Communication in Multidimensional Cheap Talk: A Comment," Econometrica, Econometric Society, vol. 75(3), pages 885-893, May.
    9. Ambrus, Attila & Lu, Shih En, 2014. "Almost fully revealing cheap talk with imperfectly informed senders," Games and Economic Behavior, Elsevier, vol. 88(C), pages 174-189.
    10. Krishna, Vijay, 2001. "Asymmetric Information and Legislative Rules: Some Amendments," American Political Science Review, Cambridge University Press, vol. 95(2), pages 435-452, June.
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    Cited by:

    1. Meyer, Margaret & Moreno de Barreda, Inés & Nafziger, Julia, 2019. "Robustness of full revelation in multisender cheap talk," Theoretical Economics, Econometric Society, vol. 14(4), November.
    2. Szalay, Dezső & Deimen, Inga, 2015. "Information, authority, and smooth communication in organizations," CEPR Discussion Papers 10969, C.E.P.R. Discussion Papers.
    3. Lu, Shih En, 2017. "Coordination-free equilibria in cheap talk games," Journal of Economic Theory, Elsevier, vol. 168(C), pages 177-208.
    4. Deimen, Inga & Szalay, Dezsö, 2014. "Smooth, strategic communication," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100333, Verein für Socialpolitik / German Economic Association.
    5. Feddersen, Timothy & Gradwohl, Ronen, 2020. "Decentralized advice," European Journal of Political Economy, Elsevier, vol. 63(C).

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    More about this item

    JEL classification:

    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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