View source for Battaglini, M. (2002), Multiple Referrals and Multidimensional Cheap Talk

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[http://www.edegan.com/pdfs/Battaglini%20(2002)%20-%20Multiple%20Referrals%20and%20Multidimensional%20Cheap%20Talk.pdf Full-text PDF]

==Abstract==

In previous work on  cheap  talk, uncertainty has  almost  always been  modeled  using  a  single-dimensional  state  variable.  In  this  paper we  prove  that  the  dimensionality  of  the uncertain  variable  has  an  important  qualitative impact  on  results  and  yields  interesting insights into the  "mechanics" of information transmission. Contrary to  the unidimensional case, if there is more than one  sender, full revelation of information in all states of nature is  generically possible,  even  when  the  conflict  of  interest is  arbitrarily large. What really matters in transmission of information is the local behavior of  senders' indifference curves at the ideal point of  the  receiver, not  the proximity of  players' ideal point.

==Rui's Intro points==
* Departure point is the Gilligan/Krehbeil paper or 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\in 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.