1. Comparative Cheap Talk
Comparative cheap talk (JET 2007)
Persuasion by Cheap Talk (AER 2010)
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
Each issue k=1,…K is symmetric in terms of
R and S (additive) preferences
type distribution
Important classes of preferences:

3. Previous lecture We assumed K=2,
We have focused on ``ranking’’ equilibria, R-messages
Type independent preferences of S
Revealing R-messages is (weakly) incentive compatible
Ranking equilibrium is partly informative, influential
R-equilibrium dominates B-equilibirum if quasiconvex
Type dependent (supermodual) preferences of S and R
Revealing R-messages is (strictly) incentive compatible
R-equilibrium may dominate B-equilibirum even with quasiconcave

4. Today Many symmetric issues K>2,
Limit of complete ranking equilibrium as K
Partial rankings (sender welfare non-monotonic)
Asymmetric issues (biases)
Small asymmetries (strict supermodularity)
Non-existence of R equilibrium with large asymmetries
Existence of incentive compatible type partitions (not R partitions)
Next lecture: 4 applications

5. K issues K! number of distinct rankings (permutations)
for K=5 this number is 120
for K=10 this number is
Type independent utility of S
indifference curve is a K-1 dimensional manifold
For each individual issue ranking more informative for higher K

6. Limit K be a c.d.f over types For each issue type. i.i.d
P: Ex ante (per issue) welfare of S (R) asymptotically converges to fully informative one as

7. Heuristic argument

8. Quadratic CS model Preferences
(Best) partition equilibrium versus (best) relative cheap talk equilbirium
Ex ante welfare of S (welfare =R –b^2)

9. Partial Rankings
Coarse equivalent classes (top ten students in a class)
Complete ranking and bubbling are two extremes
Partial rankings induce (first order) ranked posteriors, each for one class
Sender’s welfare need not be monotone in completeness of a ranking

10. Example: Recommendation game
Players:
S: professor with 3 students each with quality ,
Message space =rankings
R: future employer, binary action hire, not hire)
Preferences
Equilibria with (complete or partial) rankings exist

11. Example: Recommendation game
Bubbling equilibrium
Complete ranking equilibrium
Partial rankings (my top 2 students are …)

12. Asymmetric issues Asymmetries
- types are drawn from different distributions
- sender may have stronger preferences for some issues
- receiver may have biases too
Asymmetries are common

13. Problem issues (uniform distribution), receiver
Asymmetric S preferences
Incentives to misreport
2 alternative solutions

14. Solution 1 Strict supermodularity of preferences
Strict incentives to reveal rankings in symmetric setting
R equilibrium exist with sufficiently small perturbations
Levy and Razin (ECMA 2007) – non-existence of R equilibrium with large assymetries

15. Solution 2 (idea)
Persuasion by Cheap Talk (AER 2010)

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

17. General argument
compact and convex, absolutely continuous, full support
R preferences
S preferences, type independent, continuous

18. Arbitrary fine partitions (linear S utility)
Argument extends for strictly quasivonvex preferences