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Analyze This

Warner Brothers

Production Budget: $30,000,000

Both major characters in the movie are big funs of Tony Bennett

WB’s initial offer to Tony Bennett for a performance is only $15,000, but they ended up paying $200,000.

Problem: WB determined to buy the performance and had bought it (sunk cost), but forgot to ask the price first!

Chapter 11: Thinking Strategically

Thinking Strategically

- The payoff to many actions will depend on
- The actions themselves.
- When the actions are taken.
- How the actions relate to those taken by others.
- Example: firms in imperfect competitions have to consider the responses of their rivals when they set their own prices or advertisement budget.

Chapter 11: Thinking Strategically

The Theory of Games

- Three Basic Elements of a Game
- The Players
- Their Strategies
- The Payoffs
- Payoffs are different for different combination of strategies of all the players
- Game Theory: Mathematical Theory!

Chapter 11: Thinking Strategically

The Theory of Games

- Example
- Should United Airlines spend more on advertising?
- Players: United Airlines and American Airlines
- Strategies: increase or stand pat
- Same choices for both players
- They choose the move at the same time
- Payoff: listed in the Payoff Matrix

Chapter 11: Thinking Strategically

gets $5,500

American

gets $2,000

United gets

$5,500

United gets

$8,000

American

gets $8,000

American

gets $6,000

United gets

$2,000

United gets

$6,000

The Payoff Matrix for an Advertising GameAmerican’s Choice

Leave ad

spending

the same

Raise ad

spending

Raise ad

spending

United’s Choice

Leave ad

spending

the same

Chapter 11: Thinking Strategically

The Theory of Games

- Best Response – (conditional)
- one that yields the best payoff for a given strategy by the other player(s).
- Dominant Strategy – (unconditional)
- One that yields a higher payoff no matter what the other players in a game choose
- Dominated Strategy
- Any other strategy available to a player who has a dominant strategy

Chapter 11: Thinking Strategically

gets $5,500

American

gets $2,000

United gets

$5,500

United gets

$8,000

American

gets $8,000

American

gets $6,000

United gets

$2,000

United gets

$6,000

The Payoff Matrix for an Advertising GameAmerican’s Choice

American’s dominant strategy

Best Response to United’s “raise ad spending”

Leave ad

spending

the same

Raise ad

spending

United’s dominant strategy

Raise ad

spending

United’s Choice

Leave ad

spending

the same

Chapter 11: Thinking Strategically

The Theory of Games

- Nash Equilibrium
- Any combination of strategies in which each player’s strategy is her or his best choice, given the other player’s strategies
- When each player has a dominant strategy, equilibrium occurs when each player follows that strategy
- When a game is in equilibrium, no player has any incentive to deviate from his current strategy

Chapter 11: Thinking Strategically

gets $5,500

American

gets $2,000

United gets

$5,500

United gets

$8,000

American

gets $8,000

American

gets $6,000

United gets

$2,000

United gets

$6,000

The Payoff Matrix for an Advertising GameAmerican’s Choice

Leave ad

spending

the same

Raise ad

spending

Raise ad

spending

Nash Equilibrium

United’s Choice

Leave ad

spending

the same

Chapter 11: Thinking Strategically

The Theory of Games

- Nash Equilibrium
- There can be an equilibrium when players do not have a dominant strategy
- Example
- Should United Airlines spend more on advertising?

Chapter 11: Thinking Strategically

gets $4,000

American

gets $3,000

United gets

$3,000

United gets

$8,000

American

gets $5,000

American

gets $2,000

United gets

$4,000

United gets

$5,000

Equilibrium When One Player Lacks a Dominant StrategyAmerican’s Choice

What is the dominant strategy for United Airlines?__________

Leave ad

spending

the same

Raise ad

spending

Which cell is the Nash Equilibrium for the game?__________

Raise ad

spending

United’s Choice

Leave ad

spending

the same

Chapter 11: Thinking Strategically

gets $2,000

American

gets $3,000

United gets

$3,000

United gets

$4,000

American

gets $3,000

American

gets $4,000

United gets

$2,000

United gets

$3,000

What Should United and American Do If Their Payoff Matrix is Modified?American’s Choice

Leave ad

spending

the same

Raise ad

spending

Raise ad

spending

United’s Choice

Leave ad

spending

the same

Chapter 11: Thinking Strategically

RECAP

- The three elements of a game
- Players, strategies and payoffs
- Strategies: best response, dominant and dominated
- Equilibrium: each player chooses the best response respectively – this combination of strategies is called Nash Equilibrium

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Prisoners Dilemma
- A game in which each player has a dominant strategy, and when each plays it, the resulting payoffs are smaller than if each had played a dominated strategy
- If every player is smart on self-interest, all together, the players will achieve a worse outcome than everyone was naïve in playing games.

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Example
- Should the prisoners confess?
- Two prisoners: held in separate cells
- caught with minor crime: 1 year
- They did commit a serious crime, but the prosecutor doesn’t have enough hard evidence to convict them.
- If one confesses and the other remains silent
- Confessor: 0 year; the other: 20 years
- If both of them confess, 5 years for both.

Chapter 11: Thinking Strategically

5 years

Prisoner 2 gets

20 years

Prisoner 1 gets

5 years

Prisoner 1 gets

0 year

Prisoner 2 gets 0 year

Prisoner 2 gets

1 year

Prisoner 1 gets

20 years

Prisoner 1 gets

1 year

The Payoff Matrix for a Prisoner’s DilemmaPrisoner 2’s Choice

Remain

silent

Confess

Confess

Prisoner 1’s Choice

Remain

silent

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Exercise
- Which of these games is a prisoner’s dilemma?

Chapter 11: Thinking Strategically

Chrysler

12 for

Chrysler

10 for

GM

4 for

GM

4 for

Chrysler

5 for

Chrysler

12 for

GM

5 for

GM

Which of These GamesIs a Prisoner’s Dilemma?Chrysler’s Choice

GAME 1

Don’t Invest

Invest

Don’t

Invest

GM’s Choice

Invest

Chapter 11: Thinking Strategically

Chrysler

5 for

Chrysler

4 for

GM

5 for

GM

10 for

Chrysler

4 for

Chrysler

10 for

GM

12for

GM

Which of These GamesIs a Prisoner’s Dilemma?Chrysler’s Choice

GAME 2

Don’t Invest

Invest

Don’t

Invest

GM’s Choice

Invest

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Common thread
- Conflict between the narrow self-interest of individuals and the broader interests of larger communities
- Countless social/economic interactions with similar payoff structures
- Some may involve more than 2 players.

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Prisoner’s Dilemmas Confronting Imperfectly Competitive Firms
- Cartel
- A coalition of firms that agrees to restrict output for the purpose of earning an economic profit
- Economic Naturalist
- Why are cartel agreements notoriously unstable?

Chapter 11: Thinking Strategically

- Impact of Cartel
- Q = 1,000 bottles/day
- P = $1/bottle
- Each firm makes $500/day

1.00

MR

D

1,000

2,000

The Market Demandfor Mineral Water- Assume
- 2 firms (Aquapure & Mountain Spring)
- MC = 0
- Cartel is formed & agree to split monopolistic output and profits

Price $/bottle)

Bottles/day

Chapter 11: Thinking Strategically

- P = $0.90/bottle
- Q = 1,100 bottles/day
- Mountain Spring: Q = 0!

0.90

1,100

The Temptation to Violate a Cartel Agreement2.00

- Mountains Spring retaliates
- P = $.90/bottle
- Both firms split 1,100 bottles/day @ $.90
- Profit = $495/day

Price $/bottle)

1.00

MR

D

1,000

2,000

Bottles/day

Chapter 11: Thinking Strategically

Mountain Spring

$990/day for

Mountain Spring

$500/day for

Aquapure

$0/day for

Aquapure

$0/day for

Mountain Spring

$495/day for

Mountain Spring

$990/day for

Aquapure

$495/day for

Aquapure

The Payoff Matrix for a Cartel AgreementBoth firms keep cutting price until the price = MC = 0. The Cartel breakdown!

Mountain Spring’s Choice

Charge $1

Charge $0.90

Charge

$1

Aquapure’s Choice

Charge

$0.90

Chapter 11: Thinking Strategically

Cartel and The Prisoner’s Dilemma

- When will the rival firms stop cutting prices? – Never until P = MC
- Cartel may have more than two members, retaliation can hurt all members, not only the price cutter.
- Hard to discover the price cutter.

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Economic Naturalist
- How did Congress unwittingly solve the television advertising dilemma confronting cigarette producers?
- When cigarette companies stopped advertising, their profits were higher.
- Increase in demand from advertising
- Bring in smokers
- Entice smokers switch their brands.

Chapter 11: Thinking Strategically

for Philip Morris

$5 million/year

for Philip Morris

$10 million/

year for RJR

$35 million/

year for RJR

$35 million/year

for Philip Morris

$20 million/year

for Philip Morris

$5 million/

year for RJR

$20 million/

year for RJR

Cigarette Advertising as a Prisoner’s DilemmaPhilip Morris’s Choice

Advertise on TV

Don’t advertise on TV

Advertise

on TV

RJR’s Choice

Don’t

Advertise

on TV

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Economic Naturalist
- Why do people stand at concerts, even though they can see just as well when everyone sits?

Chapter 11: Thinking Strategically

-$3 for others

-$2 for you

$1 for you

$1 for others

$0 for others

-$3 for you

$0 for you

Standing versus Sitting at a Concert as a Prisoner’s DilemmaOther People’s Choice

Stand

Sit

Stand

Your Choice

Sit

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Economic Naturalist
- Why do people shout at parties?

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Tit-for-Tat and the Repeated Prisoner’s Dilemma
- Cooperation between players will increase the payoff in a prisoner’s dilemma.
- There is a motive to enforce cooperation.
- One shot game: hard to enforce cooperation, but possible for repeated encounters.

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Tit-for-tat strategy for repeated games
- Tit-for-tat strategy
- Players cooperate on the first move, then mimic their partner’s last move on each successive move
- Remarkably effective strategy to enforce cooperation in repeated prisoner’s dilemma.

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Tit-for-tat strategy for repeated games
- Tit-for-tat strategy requirements
- Two same players – “a stable set” of players
- Players recall other player’s moves
- Memory is important.
- Players have a stake in future outcomes

Chapter 11: Thinking Strategically

The Prisoner’s Dilemma

- Why is the tit-for-tat strategy unsuccessful in competitive, monopolistically competitive, and oligopolistic markets?
- Many firms: more than 2 players
- Retaliation by cutting price may hurt cooperative firms
- Entry threats for an industry with only 2 firms
- Forming a coalition may induce entrance, then the firms would rather just start to cut price now.
- It is hard to implement tit-for-tat strategy effectively in a cartel.

Chapter 11: Thinking Strategically

RECAP: The Prisoner’s Dilemma

- Payoff to each player is smaller when all the players choose their dominant strategies than all choose their dominated strategies.
- The prisoner’s dilemma can explain a lot of situations.
- The tit-for-tat strategy may support cooperation in repeated prisoner’s dilemma under certain conditions.

Chapter 11: Thinking Strategically

Games in Which Timing Matters

- The Ultimate Bargaining Game
- Should Michael accept Tom’s offer?
- Rules of the game
- Experimenter gives $100 to Tom
- Tom proposes how to divide $100 with Michael
- Tom must give Michael X (X = Tom and $100 - X = Michael)
- Michael must either accept the proposal or reject it
- If he does, Tom and Michael get the money
- If he does not, the money goes to the experimenter

Chapter 11: Thinking Strategically

$X for Tom

$(100 – X) for Michael

Michael

accepts

A

B

Michael

refuses

Tom proposes

$X for himself,

$(100 – X) for

Michael

$0 for Tom

$0 for Michael

Decision Tree for TomChapter 11: Thinking Strategically

$1 for Michael

Michael

accepts

A

B

Michael

refuses

Tom proposes

$99 for himself,

$1 for Michael

$0 for Tom

$0 for Michael

Tom’s Best Strategy in an Ultimatum Bargaining Game- Tom can give Michael a take-it-or-leave-it offer
- Tom will propose $1
- Michael will accept
- The outcome is a Nash Equilibrium

Chapter 11: Thinking Strategically

$(100 – X) for Michael

Tom proposes

$X < $(100 - Y) for himself

$(100 - X) > Y for Michael

A

B

Michael announces

that he will reject any

offer less than $Y

Tom proposes

$X > $(100 - Y) for himself

$(100 - X) < Y for Michael

$0 for Tom

$0 for Michael

The Ultimatum Bargaining Gamewith an Acceptance ThresholdNew Rule: Michael can specify in advance

the minimum offer (Y) he will accept

Michael’s best bet Y = 99!

Chapter 11: Thinking Strategically

Games in Which Timing Matters

- Credible Threats and Promises
- Credible Threat
- A threat to take an action that is in the threatener’s interest to carry out
- Will Michael credibly threaten to refuse the $1 offer from Tom?
- Could Warner Brothers credibly threaten to change the singer in the movie?
- Could Chevy credibly threaten to offer a hybrid no matter what Dodge did?

Chapter 11: Thinking Strategically

Games in Which Timing Matters

- Credible threat may be impossible to make so as …
- Credible Promise
- A promise to take action that is in the promiser’s interest to keep

Chapter 11: Thinking Strategically

Decision Tree for the Kidnapper Game

Victim is safe,

kidnapper executed

Victim goes

to police

C

Kidnapper sets

victim free

Victim remains

silent

Victim remains

in danger,

kidnapper survives

A

B

Kidnapper

kills victim

Victim promises

to remain silent

Victim dies,

kidnapper survives

Will the kidnapper release his victim?

Chapter 11: Thinking Strategically

owner gets $1,000,

manager gets $1,000

C

Owner opens

remote office

Manager manages dishonestly;

owner gets -$500,

manager gets $1,500

A

B

Managerial candidate

promises to manage

honestly

Owner does not

open remote office

Owner gets $0,

manager gets $500 by

working elsewhere

Should a business owner

open a remote office?

Decision Tree for the Remote Office GameChapter 11: Thinking Strategically

Games in Which Timing Matters

- Commitment Problem
- A situation in which people cannot achieve their goals because of an inability to make credible threats or promises

Chapter 11: Thinking Strategically

Games in Which Timing Matters

- Commitment Device
- A way of changing incentives so as to make otherwise empty threats or promises credible
- Prisoner’s dilemma – Underworld code of omerta
- kidnapping – blackmailable acts by the victim
- Remote office
- Tips from customers for the waiters
- Share of profit in the remote business

Chapter 11: Thinking Strategically

Games in Which Timing Matters

- RECAP
- Decision tree is used for dynamic games
- Impossibility of credible threat: undesirable outcomes in games – commitment problem
- Commitment devices may help

Chapter 11: Thinking Strategically

The Strategic Roleof Preferences

- Game theory assumes that the goal of the players is to maximize their outcome.
- In most games, players do not attain the best outcomes.
- Altering psychological incentives may also improve the outcome of a game.

Chapter 11: Thinking Strategically

The Strategic Roleof Preferences

- Question
- In a moral society, will the business owner open a remote office?

Chapter 11: Thinking Strategically

owner gets $1,000,

manager gets $1,000

C

Owner opens

remote office

Manager manages dishonestly;

owner gets -$500,

manager gets -$8,500

A

B

Managerial candidate

promises to manage

honestly

Owner does not

open remote office

Owner gets $0,

manager gets $500 by

working elsewhere

The Remote Office Game with an Honest ManagerThe value of dishonesty to the

manager is $10,000

Chapter 11: Thinking Strategically

The Strategic Roleof Preferences

- Are People Fundamentally Selfish?
- Do you tip at out-of town restaurants?
- What would be your first offer in the ultimatum bargaining game?
- Would you refuse a lopsided offer?
- Researchers’ answer is “NO”.

Chapter 11: Thinking Strategically

The Strategic Roleof Preferences

- Are People Fundamentally Selfish?
- If narrow self-interest is not the only motive for making choices
- Revenge for unjustly treatment with ruinous costs.
- Other motives must be understood to predict and explain human behavior.
- How preferences works to solve the commitment problems?

Chapter 11: Thinking Strategically

The Strategic Roleof Preferences

- Preferences as Solutions to Commitment Problems
- Concerns about fairness, guilt, humor, sympathy, etc. do influence the choices people make in strategic interactions.
- Having the preferences alone doesn’t work
- Commitment to these preferences must be communicated for them to influence choices. The preferences must be identifiable to the other party.

Chapter 11: Thinking Strategically

Chapter

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