1. Multidimensional Cheap Talk
Persuasion by Cheap Talk (AER 2010)
Comparative cheap talk (JET 2007)
Chakraborty an Harbaugh

2. Multidimensional Cheap Talk
Two agents: Sender (S) and Receiver (R)
Timing and actions: for each k=1,….K
Sender observes state , sends message
Receiver observes message , choses action
k=1,…K potential issues
R preferences
S preferences
Examples: professor with K students, biased media outlet

3. Type independent preferences, 1 issue (dimension)
Type independent monotonic preferences
Large biases in CS model
Type independent utilities
One dimension: only non influential equilibrium
Argument:
Example: media outlet (S) and voter (R)
Type measure of honesty
Action voting effort
Communication impossible to sustain

4. Bubbling equilibrium issues (uniform distribution) S preferences
Next: 3 key lessons

5. Influential equilibrium (lesson 1)
issues (uniform distribution), receiver
S preferences (change to symmetric)
Messages could be interpreted as ``rankings’’ (Comparative cheap talk)
With strict preference

6. Welfare Rankings (lesson 2)
R (always) prefers informative equilibrium to bubbling (Blackwell)
S preferences (quasiconvex, quasiconcave, linear)
How comes that S might strictly prefer bubbling equilibrium?
Examples of quasiconvex preferences

7. Fragility to asymmetries (lesson 3)
issues (uniform distribution)
Asymmetric preferences (change to symmetric)
What if
Influential equilibrium disappears

8. P1: Comparative Cheap Talk (JET 2007)
K symmetric issues:
Separable S utilities, symmetric across issues
Symmetric prior distribution
Weak supermodularity (e.g., type independent)
Results (K alternatives)
Complete or partial rankings (``top 3’’) supported in equilibriu
Almost fully revealing equilibrium with
Asymmetric issues:
Example: type independent utilities (weak supermodularity)
Strict supermodularity (strict incentives in symmetric settings)
Influential equilibrium exist with sufficiently small perturbations
Levy and Razin (ECMA 2007) – non-existence of R equilibrium with large asymmetries

9. Persuasion by Cheap Talk (AER 2010)
Assumption: Type independent, possibly non-additive utility of S
Arbitrary asymmetries with respect to
utilities
distributions
Main Results:
informative equilibrium exists with ``sophisticated messages’’
Full revelation along K-1 dimensions)

10. Asymmetry in utilities
Spinning argument

11. Problem issues (uniform distribution), receiver
Asymmetric S preferences
Exists partition for which expected values fall on the same indifference curve

12. General ``spinning’’ argument
Sphere
Function is odd if
P: Continuous and odd function has an origin.
(Borsuk-Ulam)

13. General ``spinning’’ argument
compact and convex, absolutely continuous, full support
R preferences
S preferences, type independent, continuous
Observation: function is continuous and odd

14. General argument
compact and convex, absolutely continuous, full support
R preferences
S preferences, type independent, continuous
Borsuk-Ulam imply that for any there exists
s.t.
P: There exists an influential equilibrium
Constructive argument
How large is the set of PBN

15. Finer partition (lesson 4)
Linear utility function
For N=1,2,.. one can construct 2^N element partition,
Probability mass of each element goes to zero
Sender reveals all the information in K-1 dimensions

16. Nonlinear preferences: problem and solution
Argument extends for strictly quasivonvex preferences

17. Substantive insight Partly revealing (influential) equilibrium Exists!
R prefers revealing equilibrium to bubbling
S prefers revealing equilibrium if preferences strictly quasiconvex

18. Quasiconvex preferences:
Desirability of quasiconvex preferences:
Partly revealing equilibria improve S (ex ante) welfare
For such preferences infinite partitions exist
Former property important given easy commitment to ``not to talk’’
Argument extends for strictly quasivonvex preferences

19. Benefits from randomness of ?
Which economic settings give rise to quasiconvex preferences
Let ,
When variation in is good?
Four settings:
1. Separable convex utility per each issue (advertising)
2. Settings in which determines the outcome
- unit demand (recommendation game)

20. Application : Recommendation game
2 objects, quality observed by a seller
R: buyer, unit demand, outside option
S: salesperson maximizes probability of selling
Interpretation:
Professor with Ph.D. two students on the market, one position
Dealer charging a commission fee
Lobbyist advising a senator on several bill proposals