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### 041713

1. 1. More on Games April 17, 2013
2. 2. Announcements• I have homework 1 and 2: come get at end of class.• Homework 3 is now posted on website.• Due at the beginning of class on Monday.
3. 3. Last Class• Began our discussion about game theory.• Introduced the concepts of (1) players, (2) strategies, and (3) payoffs
4. 4. Learning Goals• Recreate prisoner’s dilemma• Set penalties to enforce Nash equilibria.• (Time permitting) Conceptualize how games change when players move sequentially
5. 5. Prisoner’s Dilemma Redux• Players: Jake and Lisa• Strategies: Confess or Deny.• Payoffs: – Both confess: 2 years each – Both deny: 1 year each – Jake confesses, Lisa denies: Jake 0 years, Lisa 5 years – Lisa confesses, Jake denies: Jake 5 years, Lisa 0 years
6. 6. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years (J) 1 year (J) Deny 0 years (L) 1 year(L)
7. 7. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years(J) 1 year (J) Deny 0 years (L) 1 year(L) Confess is a dominant strategy for Jake. How about Lisa?
8. 8. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years(J) 1 year (J) Deny 0 years (L) 1 year(L) Confess is a dominant strategy for Jake. How about Lisa?
9. 9. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years(J) 1 year (J) Deny 0 years (L) 1 year(L) Confess is a dominant strategy for Jake. How about Lisa?
10. 10. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years(J) 1 year (J) Deny 0 years (L) 1 year(L) Confess is a dominant strategy for Jake. How about Lisa?
11. 11. The Prisoner’s Dilemma Remember: Payoffs are sentences; lower is better! Lisa Confess Deny 2 years (J) 0 years (J) Confess 2 years (L) 5 years (L)Jake 5 years (J) 1 year (J) Deny 0 years (L) 1 year(L)
12. 12. Payoff Matrix for Advertising Game AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 2 million (Vz) Spending 1 million (ATT) 0.5 million (ATT)Verizon Leave 0.5 million (Vz) 1.5 million (Vz) Spending 2 million (ATT) 1.5 million (ATT) Unchanged
13. 13. Payoff Matrix for Advertising Game AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 2 million (Vz) Spending 1 million (ATT) 0.5 million (ATT)Verizon Leave 0.5 million (Vz) 1.5 million (Vz) Spending 2 million (ATT) 1.5 million (ATT) Unchanged
14. 14. Payoff Matrix for Advertising Game Obviously both are better off at (Unchanged,Unchanged). How to get there? AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 2 million (Vz) Spending 1 million (ATT) 0.5 million (ATT)Verizon Leave 0.5 million (Vz) 1.5 million (Vz) Spending 2 million (ATT) 1.5 million (ATT) Unchanged Contract: I will play ``unchanged.’’ If I cheat, I pay the other no less than X dollars. What X makes (Unchanged, Unchanged) a Nash Equilibrium?
15. 15. Last class: What X makes (No Chg, No Chg) a Nash Equilibrium?A. 0 millionB. 0.5 million (~30% of class)C. 1 million (~50% of class)D. 1.5 millionE. 2 million
16. 16. Payoff Matrix for Advertising Game AT&T Leave Spending Increase Spending Unchanged Increase 1 million+X-X(Vz) 2 million-X(Vz) Spending 1 million+X-X(ATT) 0.5million+X(ATT)Verizon Leave 0.5 million+X(Vz) 1.5 million (Vz) Spending 2 million-X(ATT) 1.5 million (ATT) Unchanged Contract: I will play ``unchanged.’’ If I cheat, I pay the other no less than X dollars. What X makes (Unchanged, Unchanged) a Nash Equilibrium?
17. 17. Payoff Matrix for Advertising Game: X=1 million. AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 1 million (Vz) Spending 1 million (ATT) 1.5million (ATT)Verizon Leave 1.5 million (Vz) 1.5 million (Vz) Spending 1 million (ATT) 1.5 million (ATT) Unchanged
18. 18. Payoff Matrix for Advertising Game: X=1 million. AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 1 million (Vz) Spending 1 million (ATT) 1.5million (ATT)Verizon Leave 1.5 million (Vz) 1.5 million (Vz) Spending 1 million (ATT) 1.5 million (ATT) Unchanged
19. 19. OK, this is technically correct.• But why use a sledgehammer when you can use a chisel?• Note, with a 1 million penalty, (Unch,Unch) is Nash, but also dominant.• What is the smallest penaltynecessary?
20. 20. Payoff Matrix for Advertising Game AT&T Leave Spending Increase Spending Unchanged Increase 1 million+X-X(Vz) 2 million-X(Vz) Spending 1 million+X-X(ATT) 0.5million+X(ATT)Verizon Leave 0.5 million+X(Vz) 1.5 million (Vz) Spending 2 million-X(ATT) 1.5 million (ATT) Unchanged Contract: I will play ``unchanged.’’ If I cheat, I pay the other no less than X dollars. What X makes (Unchanged, Unchanged) a Nash Equilibrium?
21. 21. Payoff Matrix for Advertising Game: X=0.5 million. AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 1.5 million (Vz) Spending 1 million (ATT) 1million (ATT)Verizon Leave 1 million (Vz) 1.5 million (Vz) Spending 1.5 million (ATT) 1.5 million (ATT) Unchanged
22. 22. Payoff Matrix for Advertising Game: X=0.5 million. AT&T Leave Spending Increase Spending Unchanged Increase 1 million (Vz) 1.5 million (Vz) Spending 1 million (ATT) 1million (ATT)Verizon Leave 1 million (Vz) 1.5 million (Vz) Spending 1.5 million (ATT) 1.5 million (ATT) Unchanged Whoa! cool!
23. 23. The Economics of Cartels• Cartel: any group of firms that agree to restrict output for the purpose of earning an economic profit.• But cartels are notoriously hard to maintain. Why?• Example: oligopolists Boeing and Airbus P \$1 million Profit MC=ATC \$600 million MR D 1000 Q (in thousands)
24. 24. Payoff Matrix for a Cartel Agreement Boeing P=\$1 million P=\$999,999 (Cooperate) (Defect) P=\$1 million \$300 million (A) 0 (A) (Cooperate) \$300 million (B) ≈\$600 million (B)Airbus P=\$999,999 ≈\$600 million (A) ˂\$300million (A) (Defect) 0 (B) ˂\$300 million (B) Contract for at least how much of a penalty for defecting?
25. 25. Let’s Play a Game• I need 10 volunteers.• Each person: Write your name and a number between 0 and 100. The cards will be collected and the numbers averaged. The number closest to exactly half of the average is the winner.• I predict the winner is near ___. Am I right?
26. 26. Second Round• I need 10 volunteers.• Each person: Write your name and a number between 0 and 100. The cards will be collected and the numbers averaged. The number closest to exactly half of the average is the winner.• I predict the winner is near ___. Am I right?
27. 27. Third Round• I need 10 volunteers.• Each person: Write your name and a number between 0 and 100. The cards will be collected and the numbers averaged. The number closest to exactly half of the average is the winner.• I predict the winner is near ___. Am I right?
28. 28. What is the Nash Equilibrium?Can someone give an answer and explain?
29. 29. Games in Which Timing Matters Opening a New RestaurantAlice and Bill are each considering opening a restaurant intheir local neighborhood . . . But what kind? Bill Dinner Breakfast \$1000 (A) \$1600 (A) Dinner \$1000 (B) \$1400 (B) Alice \$1400 (A) \$800 (A) Breakfast \$1600 (B) \$800 (B)
30. 30. Decision Tree \$1000 (A) D \$1000 (B) D B \$1400 (A) \$1600 (B) \$1600 (A) D \$1400 (B) B B \$800 (A) \$800 (B) Bill Alice OutcomeDecides Decides