1. 1

2. 2 Strategic Information Transmission A sender observes the true state t in y[0, 1] t is uniformly distributed The sender reports r to the receiver The receiver takes an action y

3. 3 Is truth-telling an equilibrium? If sender sends the true signal r(t) = t then the receiver should believe that the state is t, when r = t. he will choose y = t the sender will get the payoff: -[t – (t +b)] 2 = -b 2 < 0 But he could report t + b, the receiver will play y = t + b and the sender will get the payoff: -[t + b – (t +b)] 2 = 0 So, is not an equilibrium

4. 4 Similarly, if the sender sends a signal r(t), a monotonic function The receiver should believe t when he seen r(t) And the sender would be better off sending the signal r(t + b) So, this cannot be an equilibrium

5. 5 No Information ?? The sender sends a constant signal r(t) = c The receiver must believe `uniform distribution’. As initially. After another report, assume the receiver believes the same. His optimal action is y = 1/2 The sender’s report does not influence the action. This is an equilibrium !! Next

6. 6

7. 7 No Information ?? But for small values of b and some values of t both would be better off if the action was t+b + + > 0 Inefficient equilibrium

8. 8 Partial Information ( K messages) When the receiver hears he must believe `uniform’ over The sender: In interval must prefer signal At must be indifferent between signals

9. 9 If at t, the sender is indifferent between the two actions A,B, then:

10. 10 Check that it is an equilibrium, i.e. that the sender wants to send these signals)

11. 11 The highest K (for a given b ): b

12. 12 Conspicuous Expenditure as a signal of Quality auffällig A firm is of High or Low quality (costs c H,0 ) It may spend E conspicuously (sponsoring something) A consumer observes the price p and the expenditure E When he buys a products he learns its quality (utility H,0 ) The firm sets a new price and the consumer may buy a second unit.

13. 13 N H L f f c buy n.b. f buy n.b. c buy n.b. f buy n.b. c c

14. 14 An Equilibrium Firm H: Firm L: Consumer believes H only iff (p,E) staisfies Otherwise he believes L Consumer buys product in first period only if And in second period only if he knows it is H, or if the price is 0

15. 15 N H L f f c buy n.b. f buy n.b. c buy n.b. f buy n.b. c c

16. 16

17. 17 end