1. Multidimensional Cheap Talk (Quasiconvex preferences)
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:
Sender observes state , convex, compact, message
Receiver observes message , choses action
R preferences
S preferences
Can we find a partition even if preferences are asymmetric?

3. Spinning argument
Persuasion by Cheap Talk (AER 2010)

4. General argument
compact and convex, absolutely continuous, full support
R preferences
S preferences, type independent, continuous
For any and define
P: For any there exists such that
Borsuk-Ulam theorem

5. Substantive insight Partly revealing (influential) equilibrium Exists!
R prefers revealing equilibrium (Blackwell) to bubbling
S prefers revealing equilibrium if preferences strictly quasiconvex
Finer partitions
linear preferences (straighforward)
strictly quasiconvex preferences (harder)

6. S utility linear in
For N=1,2,.. one can construct 2^N element partition,
Probability mass of each element
Sender essentially reveals all the information in K-1 dimensions
Argument extends for strictly quasivonvex preferences

7. Strictly quasiconvex utility: problem
Argument extends for strictly quasivonvex preferences

8. Strictly quasiconvex utility: solution
Argument extends for strictly quasivonvex preferences

9. 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

10. 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)
- unanimous voting
- second price auction

11. Application 1: Advertising
S: Two-good monopoly, (olive oil, wine) zero cost
Unobserved quality of commodity k
Independent ``linear’’ markets, expected utility
Q: advertise quality in of products or one market?
Argument extends for strictly quasivonvex preferences

12. Advertising: Solution
Profit
S preferences: continuous, strictly quasiconvex
Bubling v.s ranking equilibrium

13. Application 2: 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. students on the market
Dealer charging commission fee
Lobbyist advising a senator on several bill proposals

14. Recommendation game (solution)
S preferences: continuous, strictly quasiconvex

15. Logit model K products Discrete choice Buyers utility
Remark: logit model (McFadden) with extreme value distribution

16. Application 3: Jury trial
Two aspects, evidence observed by defense
R: Jury
two types, each cares bout one aspect
privately observed threshold
probability of voting for conviction
S: defense attorney, utility =probability of acquittal
Unanimous voting:
Defense needs to persuade one of the two

17. Jury trial: Solution
S preferences: continuous, strictly quasiconvex

18. Application 4: Disclosure in SP auction
Second price auction
One objects with two characteristics
R: N buyers
Unobservable independent types
Value of an object
S: utility = sexpected econd highest bid

19. Application 4: Disclosure in SP auction
For