1. 1

2. problem set 14 from Osborne’s Introd. To G.T. p.332 Ex. 332.1

3. 3 Separating Equilibrium e Envy Envy Beliefs: H LL Payoffs for education The firm’s action plan

4. 4 The structure of equilibrium

5. 5 Separating Equilibrium e Beliefs: H LL Can the firm have these beliefs??? It is a strictly dominated (inferior) strategy for type L to send a signal in this interval Whatever action the firm takes, (even if it pays him as if he were H ) he is better off sending e*(L). L (An H is better off in this interval if he is identified as H. ) Any signal above e* s is dominated for both types, so the firm is allowed to believe something.

6. 6 Separating Equilibrium e Beliefs: H LL If we accept this argument then the firm ‘s belief in this interval should be H. The only separating equilibrium is when e S * is at the left of this interval The Intuitive Criterion This argument is known as The Intuitive Criterion of In-Koo Cho & David Kreps L

7. 7 Beer or Quiche

8. 8 Beer or Quiche Nature chooses the type of player 1 : Weak, Strong with probability r, 1-r The Weak type likes Quiche for his breakfast, the Strong likes Beer. Player 1 chooses his breakfast Player 2 does not know the type of player 1 but observes what he had for breakfast. He then decides whether to pick up a fight with player 1. Player 1 gets 1 point if he had his favorite meal, and gets additional 2 points if there was no fight. Player 2 gets 1 point if he fought the Weak type or if he did not fight the Strong all other payoffs are 0

9. 9 Beer or Quiche N S W r 1-r beer quiche fight III fight II 0, 1 3, 1 1, 0 2, 0 1, 1 2, 1 0, 0 3, 0 Is there a separating equilibrium ? pq 1-p1-q

10. 10 Beer or Quiche N S W r 1-r beer quiche fight III fight II 0, 1 1, 0 1, 1 2, 1 3, 0 Is there a separating equilibrium ? 01 10 3, 1 not an equilibrium 2, 0 0, 0

11. 11 Beer or Quiche N S W r 1-r beer quiche fight III fight II 2, 0 1, 1 0, 0 Is there a separating equilibrium ? 10 01 3, 1 0, 1 2, 1 not an equilibrium 3, 0 1, 0

12. 12 Beer or Quiche N S W r 1-r beer quiche fight III fight II 2, 0 1, 1 0, 0 3, 0 Is there a pooling equilibrium ? rq 1-r1-q 3, 1 0, 1 2, 1 If r > ½ then fight 1, 0 not an equilibrium

13. 13 Beer or Quiche N S W r 1-r beer quiche fight III fight II 2, 0 3, 0 Is there a pooling equilibrium ? pr 1-p1-r 3, 12, 1 If r > ½ then fight r > ½ 0, 0 1, 10, 1 1, 0 not an equilibrium

14. 14 Beer or Quiche N S W r 1-r beer quiche fight III fight II 3, 0 Is there a pooling equilibrium ? rq 1-r1-q 0, 1 2, 1 If r < ½ then not fight 1, 0 r < ½ 2, 0 3, 1 If q > ½ then fight 0, 0 1, 1 an equilibrium

15. 15 Beer or Quiche N S W r 1-r beer quiche fight III fight II 2, 0 Is there a pooling equilibrium ? pr 1-p1-r 3, 1 If r < ½ then not fight r < ½ 0, 0 1, 1 If p > ½ then fight 0, 1 1, 0 p > ½ an equilibrium 3, 0 2, 1 but …..

16. 16 Beer or Quiche N S W r 1-r beer quiche fight III fight II 2, 0 Is there a pooling equilibrium ? pr 1-p1-r 3, 1 r < ½ 0, 0 1, 10, 1 1, 0 p > ½ 3, 0 2, 1 Is it reasonable for player 2 to believe that W w ill drink beer when all his possible payoffs (after beer) are less than 3 ? 0 0, 1 2 2, 0 3 3, 0