Static Games and Nash Equilibrium Session 12 Prof. Amine Ouazad - - PowerPoint PPT Presentation

Prices and Markets Static Games and Nash Equilibrium

Session 12

• Prof. Amine Ouazad

§ 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 We 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)

Games Businesses Play

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??

• 1. Understand the Game
• 2. How Should You Play?
• 3. How Will Your Opponent (s) Play?
• 4. How to Change the Game!

a. The Payoffs b. The Strategies c. The Players d. The Timing

Prisoners’ Dilemma Battle-of-the-Sexes Coordination Game

The Key Insights of Game Theory

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

You Other Students Low effort High effort High effort Low effort 2

• 2
• 2

2

• 1
• 1

• 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. Dominant and Dominated Strategies

Prisoners’ Dilemma: z-scores

Individual Rationality? Group Rationality? You Other Students Low effort High effort High effort Low effort 2

• 2
• 2

2

• 1
• 1

Dominant Strategy Dominant Strategy

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. 3 Golden Rules (Simultaneous move games)

Caveat : Both of you maybe worse off!!!

Cigarette advertising

Ø All US tobacco companies advertised heavily on television Ø Surgeon General issues official warning

• Cigarette smoking may be hazardous

Ø Cigarette companies’ reaction

• Fear of potential liability lawsuits

Ø Companies strike agreement

• Carry the warning label and cease TV advertising in

exchange for immunity from federal lawsuits. 1964 1970

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

Not Advertise Advertise Advertise Not Advertise Lucky Strike Marlboro What may be the right decision for a single firm, may not be the best collective decision of the industry. Individual Rationality ≠ Industry Rationality

§ 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?? Cigarette Advertising: Prisoner’s Dilemma

Abdalla El-Badri, Opec secretary-general, added that the oil cartel, which accounts for 40 per cent of global oil supplies, would probably keep its production stable for the time being, after member countries cut

• utput in November and December.

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

• utput to 9.3m b/d, according to the

International Energy Agency. “no country should exceed their quota”, Mr El-Badri said of the 30m quota. Why?? […] Metering systems are manipulated to conceal outflows – a practice that began when Nigeria was busting its Opec cartel quota in the 1980s.

2 4 2 42 46 44 26 4 22 52 24 32

Iran’s

• utput

Iraq’s output

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:

Why is there an OPEC Cartel?

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

Me My date One Day Captain America Captain America One Day 10 20 20 10 Dominant Strategies?? Dominated Strategies??

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.

Golden Rules

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.

Nash equilibrium

Game #2: Battle of the sexes

Me My date One Day Captain America Captain America One Day 10 20 20 10 Dominant Strategies?? Dominated Strategies??

Not Withdraw Withdraw Withdraw Not Withdraw Others You 50 50 40 40 40 40

Coordination: Bank Runs

Not Withdraw Withdraw Withdraw Not Withdraw Others You 50 50 40 40 … 40 40 …

Coordination

Changing the game??

Coordination: Microsoft & Intel

• Microsoft invests in the development of

new versions of Windows, which rely on more powerful or different Intel processors.

No investment Investment Investment No investment Intel Microsoft 100 100 200 200 80 50 50 80 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

Student 1 Student 2 Go on Weekend Do the Market Power Games Do the Market Power Games Go on Weekend

• 20

100 Credible payoffs? How do you make the other groupmate work??

Game #3: `Chicken’ Game

• 20

100

Chicken

Enter Not Enter Enter

• 20
• 20

100

Not Enter

100

Boeing vs Airbus

Airbus Boeing

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??

Threats & Counter-Threats: Talk is Cheap

Enter Not Enter Enter

• 20
• 20

100

Not Enter

100

How to Change the Game?

Airbus Boeing

Add a player (government): Subsidy of 30 to Boeing if it Enters

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 Theory Take Aways What you need to know after today’s session

Define the game:

• Timing, Players, Strategies, Payoffs.

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 (mutual best responses).

Next Session: Auctions

• The Heyday of the Auction, The Economist, 1999.
• Course Guide Chapter 15
• The Unkindest Cuts.

Next Session: Sequential Games

Looking ahead: Game Theory Topics

Session 12 (Today) – Static Games and Nash equilibrium Basic and Universal tools. Analysis of Auctions Session 13 (Next Session) – Strategic Commitment How timing matters. Session 14 – Imperfect Competition Price and quantity competition Session 15 – Explicit and Implicit Cooperation How – and why – to explicitly or implicitly cooperate.