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

2. Cheap talk game Two agents: Sender (S) and Receiver (R)
Timing and actions:
Sender observes state , sends message
Receiver observes message , choses action
Preferences: R: S:
Uniform prior distribution of types
Equilibrium in C-S?

3. K=2 replica of CS problem
identical issues (2 dimensional type space)
Preferences
No agenda on such set (incentive compatibility automatically holds)
Partition of a state space with R-choices on such indifference curve?

4. Today: Comparative cheap talk
Partitions generated by messages in the form
Comparative cheap talk equilibria
exist under general assumptions on preferences
require symmetry of different issues
partly (but not fully) informative
welfare predictions ambiguous

5. Relative cheap talk (rankings)
Assume
Consider two messages
Optimal response of R?
S choice

6. More generally
Assume
By denote distributions of the first and second order statistic
Let
Response of R:
Utility of S:
Symmetry and additivity!

7. Welfare (Example)
Assume
Bubbling vs comparative cheap talk

8. Ex ante s welfare (Example)
Assume
Bubbling vs comparative cheap talk

9. More generally
Assume
P: Sender is better off (is worse off) in partly informative equilibrium if his preferences are strictly quasiconvex (quasiconcave)
For quasiconcave, why relative cheap talk is an equilibrium?

10. Extensions Type dependent (supermodular) preferences K issues
Partial rankings
Asymmetric issues

11. Type dependent preferences
Supermodularity

12. Supermodular preferences
Order statistics
Conditional distributions (=order statistic distributions)
Optimal R actions (Topkis, Theorem )
Best response of R

13. Incentive compatibility
R Equilibrium strategy
Which types prefer

14. Supermodular preferences
Strict supermodularity = strict incentives to reveal
Welfare benefit for S in more informative equilibrium
Simple ``quasiconvex’’ preference rule need not hold