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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.
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Last Class• Began our discussion about game theory.• Introduced the concepts of (1) players, (2) strategies, and (3) payoffs
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Learning Goals• Recreate prisoner’s dilemma• Set penalties to enforce Nash equilibria.• (Time permitting) Conceptualize how games change when players move sequentially
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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
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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)
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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?
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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?
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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?
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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?
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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)
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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
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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
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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?
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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
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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?
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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
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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
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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?
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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?
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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
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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!
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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)
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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?
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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?
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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?
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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?
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What is the Nash Equilibrium?Can someone give an answer and explain?
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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)
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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
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