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Battaglini, M. (2002), Multiple Referrals and Multidimensional Cheap Talk (view source)
Revision as of 19:14, 29 September 2020
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|Has article title=Multiple Referrals and Multidimensional Cheap Talk
|Has author=Battaglini, M.
|Has year=2002
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[http://www.edegan.com/pdfs/Battaglini%20(2002)%20-%20Multiple%20Referrals%20and%20Multidimensional%20Cheap%20Talk.pdf Full-text PDF]
==Rui's Intro points==
* Departure point is the Gilligan/Krehbeil paperor Crawford/Sobel.
* Focused NOT on the open/closed rule angle, but more generally on the conflict (difference in ideal points) between commitee/floor or agent/principle.
* Basic idea: "As someone listening to multiple biased experts, I can ask pointed questions to fully reveal the information that the biased experts have." -- Rui, who says this is a loose, intuitive way of understanding the point.
==Model==
* Choice space: <math>x\inRin R^{2]}</math>, a pair of reals.
* Outcomes: <math>y=x+\theta, \theta\in R^{2}</math>. Note that here, <math>\theta</math> is akin to <math>\omega</math> in Gilligan and Krehbeilh.
* Preferences: Single peaked. Ideal point of receiver is <math>x^{R}=(0,0</math>.
*Equilibrium strategy: Perfect Bayesian Equilibrium. * Equilibrium strategies: # Experts reveal truthfully (<math>s^{i}(\theta)=\theta=(m^{i}_{1},m^{i}_{2})</math>). # R only believes <math>(m_{1}^{i},m_{2}^{2})</math>. Meaning: He believes the report of expert 1 on one dimension, and the report of expert 2 on the other dimension. * ==Rui's closing comments ;)==* Slight change in assumptions leads to different answers. * "Degrees of freedom": More dimensions allows more revelation? * Is this robust? People saying no: # Levy and Razin: Study Battaglini model with noise. Think about it this way: Crawford/Sobel show no 1 dimension, 1 sender, no full revelation. Battaglini shows: 2 dims, 2 senders, full revelation. Levy and Razin show: 2 dims, 2 senders, no full revelation. # Ambrose and Takahashi: 2 senders, 2 dimensions plus constraints on choice space -- answer is no full revelation. Even if you choose an interval, full revelation breaks down.
