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Information Transmission in Nested Sender-Receiver Games

  • Sidartha Gordon

    (Département d'économie)

  • Ying Chen

    (Department of Economics (Johns Hopkins University))

We introduce a “nestedness” relation for a general class of sender-receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game is nested in game if the players’s optimal actions are closer in game. We show that under some conditions, more information is transmitted in the nested game in the sense that the receiver’s expected equilibrium payoff is higher. The results generalize the comparative statics and welfare comparisons with respect to preferences in the seminal paper of Crawford and Sobel (1982). We also derive new results with respect to changes in priors in addition to changes in preferences. We illustrate the usefulness of the results in three applications: (i) delegation to an intermediary with a different prior, the choice between centralization and delegation, and two-way communication with an informed principal.

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Paper provided by Sciences Po Departement of Economics in its series Sciences Po Economics Discussion Papers with number 2014-04.

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Date of creation: Apr 2014
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Handle: RePEc:spo:wpecon:info:hdl:2441/5adcidkke9omt0s9p6m01j1rh
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  1. V. Crawford & J. Sobel, 2010. "Strategic Information Transmission," Levine's Working Paper Archive 544, David K. Levine.
  2. Ivanov, Maxim, 2010. "Communication via a strategic mediator," Journal of Economic Theory, Elsevier, vol. 145(2), pages 869-884, March.
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  13. Jerry R. Green & Nancy L. Stokey, 1980. "A Two-Person Game of Information Transmission," Discussion Papers 418, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Paul R. Milgrom, 1979. "Good Nevs and Bad News: Representation Theorems and Applications," Discussion Papers 407R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Chen, Ying, 2012. "Value of public information in sender–receiver games," Economics Letters, Elsevier, vol. 114(3), pages 343-345.
  16. Watson, Joel, 1996. "Information Transmission When the Informed Party Is Confused," Games and Economic Behavior, Elsevier, vol. 12(1), pages 143-161, January.
  17. Natalia Lazzati, 2013. "Comparison of equilibrium actions and payoffs across players in games of strategic complements," Economic Theory, Springer, vol. 54(3), pages 777-788, November.
  18. Wei Li, 2010. "Peddling Influence through Intermediaries," American Economic Review, American Economic Association, vol. 100(3), pages 1136-62, June.
  19. Szalay, Dezsö, 2012. "Strategic information transmission and stochastic orders," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 386, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  20. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, 09.
  21. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
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