Prices and Markets Static Games and Nash Equilibrium Session 12 Prof. Amine Ouazad
Games We Play § Group projects Free-riding § Flat tire Coordination § Soccer Mixed strategies § Dating Information manipulation § Z-score Prisoners ’ dilemma & collusion § Buying on e-Bay Auctions § Waking up Commitment
Games Businesses Play § Windows Intel Coordination § Tax audits Mixed strategies § Price wars Prisoners ’ dilemma § OPEC output choice Collusion & enforcement § Treasury Securities Auctions (next session) § Market entry Commitment (next session)
Strategic thinking Me and 26 of you are playing a card game (52 cards) § I keep 26 black cards and distribute 26 red cards to each of you § Peter Z. feels guilty about all the money you are paying puts up $2600 in prize money § Pays $100 to every pair of black and red cards turned in § Who is in a stronger bargaining position in terms of splitting the $100? § I offer you $10 for your red card. Would you take it? Oops!! I just lost three cards. How does the game change? Real life application??
The Key Insights of Game Theory 1. Understand the Game 2. How Should You Play? Prisoners ’ Dilemma 3. How Will Your Opponent (s) Play? Battle-of-the-Sexes 4. How to Change the Game! Coordination Game a. The Payoffs b. The Strategies c. The Players d. The Timing
Game Theory Concepts Timing • Simultaneous Move Games • Sequential Games Players • the decision makers. Strategies • the actions that the players can take. Payoffs • The outcomes of players’ strategies, for each player. • Maximize own payoffs (don’t care about others’ payoffs). Simplify the world, and be aware there is actually always a larger game!
This Session: Strategic Reasoning 1. Prisoners’ Dilemma: 3 Golden rules of Game Theory (Simultaneous move games) 2. Battle of the Sexes Nash Equilibrium 3. Chicken Game Next Session Auctions, Sequential Games and Strategic Commitment
Game #1: z-scores & Prisoners’ Dilemma Other Students Low effort High effort You 0 2 Low effort 0 -2 -2 -1 High effort 2 -1
Dominant and Dominated Strategies • A strategy is a dominant strategy if it is the best choice regardless of the actions of the other player. • A strategy is a dominated strategy if it is never the best choice for any action of the other player.
Prisoners’ Dilemma: z-scores Dominant Strategy Other Students Low effort High effort You 0 2 Low effort 0 -2 -2 Dominant Strategy -1 High effort 2 -1 Individual Rationality? Group Rationality?
3 Golden Rules (Simultaneous move games) Golden Rule 1 of Game Theory: If you have a dominant strategy use it. Expect your opponent to use his dominant strategy if he has one. Caveat : Both of you maybe worse off!!! Golden Rule 2 of Game Theory: If you have dominated strategies avoid them. Successively eliminate dominated strategies to predict outcome. Golden Rule 3 of Game Theory: Having exhausted the simple avenues of looking for dominant strategies and eliminating dominated strategies, look for a Nash equilibrium.
Cigarette advertising Ø All US tobacco companies advertised heavily on television Ø Surgeon General issues official warning 1964 • Cigarette smoking may be hazardous Ø Cigarette companies’ reaction • Fear of potential liability lawsuits 1970 Ø Companies strike agreement • Carry the warning label and cease TV advertising in exchange for immunity from federal lawsuits.
Cigarette Advertising • Players: Marlboro, Lucky Strike. • Strategies: “ Advertise ” “ Not Advertise ” . • Payoffs: Profits • Each firm earns $50 million from its customers • Advertising costs a firm $20 million • Advertising captures $30 million from competitor What may be the right decision for a single firm, Marlboro Not Advertise Advertise may not be the best collective decision of the Lucky Strike industry. Not Advertise Individual Rationality ≠ Advertise Industry Rationality
Cigarette Advertising: Prisoner ’ s Dilemma § After the 1970 agreement, cigarette advertising decreased by $63 million § Profits rose by $91 million § Resolved the Prisoner ’ s Dilemma § An equilibrium is NOT necessarily efficient… § And Prisoners ’ Dilemma are dangerous games to play Individual rationality Bad outcomes for all World is littered with Prisoner’s Dilemmas MBA Job Search?? Arms Race?? Doping??
Saudi Arabia, Opec’s largest producer, cut production to its lowest in a year in December. The kingdom supplied more than 10m barrels a day in mid-2012 to meet a seasonal increase in demand and offset the loss of Iranian production. But it has since cut “no country should exceed their output to 9.3m b/d, according to the quota”, Mr El-Badri said of the International Energy Agency. 30m quota. Why?? Abdalla El-Badri, Opec secretary-general, […] Metering systems are added that the oil cartel, which accounts for manipulated to conceal outflows 40 per cent of global oil supplies, would – a practice that began when probably keep its production stable for the Nigeria was busting its Opec time being, after member countries cut cartel quota in the 1980s. output in November and December.
Why is there an OPEC Cartel? Strategies: 2m or 4m barrels per day World price: 4m - $25; 6m - $15; 8m - $10 Extraction cost per barrel: $2 for Iran; $4 for Iraq Payoffs: Iraq ’ s output 2 4 42 44 2 46 26 Iran ’ s output 22 24 4 52 32
This Session: Strategic Reasoning 1. Prisoners’ Dilemma: 3 Golden rules of Game Theory (Simultaneous move games) 2. Battle of the Sexes Nash Equilibrium 3. Chicken Game Next Session Auctions, Sequential Games and Strategic Commitment
Game #2: Battle of the sexes Dominant Strategies?? Dominated Strategies?? My date One Day Captain America Me 20 0 One Day 0 10 0 10 Captain America 0 20
Golden Rules Golden Rule 1 of Game Theory: If you have a dominant strategy use it. Expect your opponent to use his dominant strategy if he has one. Golden Rule 2 of Game Theory: If you have dominated strategies avoid them. Successively eliminate dominated strategies to predict outcome. Golden Rule 3 of Game Theory: Having exhausted the simple avenues of looking for dominant strategies and eliminating dominated strategies, look for a Nash equilibrium.
Nash equilibrium In a Nash equilibrium, • Players have no incentive to deviate unilaterally , • Equivalent definition: each player selects his/her best response given the other player’s strategy.
Game #2: Battle of the sexes Dominant Strategies?? Dominated Strategies?? My date One Day Captain America Me 20 0 One Day 0 10 0 10 Captain America 0 20
Coordination: Bank Runs Others Not Withdraw Withdraw You 50 40 Not Withdraw 50 0 0 40 Withdraw 40 40
Coordination Changing the game?? Others Not Withdraw Withdraw You 50 40 Not Withdraw 50 … … 40 Withdraw 40 40
Coordination: Microsoft & Intel • Microsoft invests in the development of new versions of Windows, which rely on more powerful or different Intel processors. Intel No investment Investment Microsoft 100 50 No investment 100 80 80 200 Investment 50 200 Two Possible Outcomes: [Invest, Invest] & [Not Invest, Not Invest] NASH Equilibria
This Session: Strategic Reasoning 1. Prisoners’ Dilemma: 3 Golden rules of Game Theory (Simultaneous move games) 2. Battle of the Sexes Nash Equilibrium 3. Chicken Game Next Session Auctions, Sequential Games and Strategic Commitment
Group Work @ INSEAD Game #3: `Chicken’ Game Student 2 Go on Weekend Do the Market Power Games Student 1 0 -20 Go on Weekend -20 100 100 0 Do the Market 0 0 Power Games Credible payoffs? How do you make the other groupmate work??
Chicken
Boeing vs Airbus Airbus Enter Not Enter -20 0 Enter -20 100 Boeing 100 0 Not Enter 0 0
Threats & Counter-Threats: Talk is Cheap Threats… “ On January 5, Boeing, the world ’ s top aircraft maker, announced it was building a plane with 600 to 800 seats, the biggest and most expensive airliner ever. Some in the industry suggest Boeing ’ s move is a bluff to preempt Airbus from going ahead with a similar plane. ” - Business Week , 1993 But it is cheap talk… Airbus announces commercial launch of the A380, the largest civil aircraft ever built. “ Boeing … has said that there is no market for such a large plane and has decided to modernize its trustworthy 747 family of planes rather than build its own megaseater. ” - Associated Press June 23, 2000 How did Airbus manage to commit credibly and publicly??
How to Change the Game? Add a player (government): Subsidy of 30 to Boeing if it Enters Airbus Enter Not Enter -20 0 Enter -20 100 Boeing 100 0 Not Enter 0 0
This Session: Strategic Reasoning 1. Prisoners’ Dilemma: 3 Golden rules of Game Theory (Simultaneous move games) 2. Battle of the Sexes Nash Equilibrium 3. Chicken Game Next Session Auctions, Sequential Games and Strategic Commitment
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