Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity of Hong Kong

Strategic Choice in Oligopoly, Monopolistic Competition,

and Everyday Life

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Games and Strategic Behavior

Thus far, we have viewed economic decision makers as confronting an environment that is essentially passive.

But there exist many cases in which relevant costs and benefits depend not only on the behavior of the decision makers themselves but also on the behavior of others.

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Example 11.1. Should the prisoners confess?

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Two prisoners, X and Y, are held in separate cells for a serious crime that they did, in fact, commit.

The prosecutor, however, has only enough hard evidence to convict them of a minor offense, for which the penalty is, say, a year in jail.

Each prisoner is told that if one confesses while the other remains silent, the confessor will go free while the other spends 20 years in prison.

If both confess, they will get an intermediate sentence, say five years.

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It is often convenient to summarize the elements of a game in the form of a payoff matrix.

Three elements:1. Players (2 prisoners)2. Strategies (confess, remain silent)3. Payoffs (jail sentences)

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Prisoner X

Prisoner YConfess Remain Silent

5 yearsfor each

1 yearfor each

20 years for X0 years for Y

0 years for X20 years for YConfess

RemainSilent

The two prisoners are not allowed to communicate with one another. If the prisoners are rational and narrowly self-interested, what will they do?

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Prisoner X

Prisoner YConfess Remain Silent

5 yearsfor each

1 yearfor each

20 years for X0 years for Y

0 years for X20 years for YConfess

RemainSilent

Their dominant strategy is to confess.

No matter what Y does, X gets a lighter sentence by speaking out.1. If Y too confesses, X gets five years instead of 20. 2. And if Y remains silent, X goes free instead of spending a year in jail.

The payoffs are perfectly symmetric, so Y also does better to confess, no matter what X does.

Dominant Strategy: One that yields a higher payoff no matter what the other players in a game choose.

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The difficulty is that when each behaves in a self-interested way, both do worse than if each had shown restraint.

Thus, when both confess, they get five years, instead of the one year they could have gotten by remaining silent.

And hence the name of this game, prisoner's dilemma.

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Example 11.2.

Why did students have to wait in line overnight to buy Cornell hockey tickets?

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Example 11.2.

Each year Cornell announced a time at which its ticket window would open for the sale of a limited number of hockey tickets for students.

Students showed up more than 24 hours in advance to wait in line for these tickets, even though no more tickets were available that way than if everyone had shown up only 1 hour in advance.

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Example 11.2.

Suppose that if everyone shows up one hour in advance, everyone has a 50-50 chance of getting a ticket, and that the odds of getting a ticket are the same if everyone shows up 24 hours in advance.

If you show up 24 hours in advance and everyone else shows up one hour in advance, you are sure to get a ticket.

But if you show up 1 hour in advance and others show up 24 hours in advance, you have no chance to get a ticket.

The same applies to other students.

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Example 11.2.

Waiting only one hour has no cost to you. But you would be willing to pay $40 to avoid having to wait 24 hours.

A 50-50 chance of getting a ticket is worth $50 to you and a 100 percent chance of getting a ticket is worth $100.

Other students value these outcomes just as you do.

What will happen?

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Example 11.2.

Your payoff if you and others arrive 24 hours early:

0.50 ($100) - $40 = $10(expected value of

ticket)(waiting

cost)

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Example 11.2.

You

OthersArrive 1hour early

$10 foreveryone

$50 foreveryone

0 for you$60 for others

$60 for you0 for others

Arrive 1hour early

Arrive 24hours early

Arrive 24hours early

Everyone's dominant strategy is to come 24 hours early, and so this is the equilibrium outcome of the game. But it would be better if everyone came one hour early.

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Example 11.3.

Why do hockey players vote in secret ballots for helmet rules, even though they choose not to wear helmets when there is no rule?

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Example 11.3.

Consider two hockey teams-- say, the Bruins and Rangers-- each of whose players can choose to wear helmets or not.

Not wearing a helmet increases the odds of winning, perhaps by making it slightly easier to see and hear, or perhaps by intimidating opposing players (on the view that it is not safe to challenge someone who is crazy enough to go without a helmet).

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Example 11.3.

If players value the higher odds of winning more than they value the extra safety, explain why they will choose not to wear helmets, even though the odds of winning when players on both sides wear helmets are no different from the odds when no one wears helmets.

At the same time, not wearing a helmet increases the odds of getting hurt.

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Example 11.3.The dominant strategy for each team is to go without helmets, even though this combination of choices is worse for both teams than the alternative in which each team wears helmets. Bruins

Rangers

Wear Helmets

Don't Wear Helmets

Second best for each

Third best for each

Best for Bruins Worst for Rangers

Best for Rangers Worst for Bruins

Don't Wear Helmets

Wear Helmets

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Example 11.4. Why do people shout at cocktail parties?

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Whenever large numbers of people gather for conversation in a closed space, the ambient noise level rises sharply.

After attending such gatherings, people often complain of sore throats and hoarse voices from having to speak so loudly to be heard.

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If everyone instead spoke at a normal voice level at cocktail parties, they would avoid these symptoms.

And because the overall noise level would be lower, they would hear just as well as when they all shout at one another.

So why shout?

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The dominant strategy for everyone is to speak more loudly.

But when all follow their dominant strategies, we get a worse outcome than if everyone had continued speaking normally.

Other Conversation Pairs

You and your partner

Speak more loudly

Second best for you and others

Best for others Worst for you

Best for you Worst for others

Speak normally

Speak normally

Speak more loudly Third best for you and others

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Nash Equilibrium

Nash equilibrium:a combination of strategies such that each player's strategy is the best he/she can choose given the strategy chosen by the other player.

John F. Nash Jr.The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1994

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Nash equilibrium in prisoner’s dilemmas

In prisoner's dilemmas, the Nash equilibrium occurs when each player plays his dominant strategy. Many games have a Nash equilibrium, even though not every player has a dominant strategy. Other Conversation Pairs

You and your partner

Speak more loudly

Second best for you and others

Best for others Worst for you

Best for you Worst for others

Speak normally

Speak normally

Speak more loudly Third best for you and others

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Example 11.5. Should American spend more on advertising?

Suppose that United Airlines and American are the only carriers that serve the Chicago-St. Louis market.

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If the relevant payoffs are as shown, does United have a dominant strategy? Does American?

American

United

Leave spendingthe same

$3000 for U$8000 for A

Raise adspending

Raise adspending


$8000 for U$4000 for A

$4000 for U$5000 for A

$5000 for U$2000 for A

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American 's dominant strategy is to raise its ad spending. United, however, does not have a dominant strategy.

American

United


$3000 for U$8000 for A

Raise adspending

Raise adspending


$8000 for U$4000 for A

$4000 for U$5000 for A

$5000 for U$2000 for A

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If each firm does the best it can, given what it knows about the incentives facing the other, what will happen in this game? American

United


$3000 for U$8000 for A

Raise adspending

Raise adspending


$8000 for U$4000 for A

$4000 for U$5000 for A

$5000 for U$2000 for A

Since United can predict that American will follow its dominant strategy, United's best move is to leave its own ad spending the same.The Nash equilibrium is that American will Raise ad spending and United will leave spending the same.

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Example 11.6. Should Michael accept Tom's offer?

Tom and Michael are subjects in an experiment. The experimenter begins by giving $100 to Tom, who must

then propose how to divide the money between himself and Michael.

He can propose any division he chooses, provided the proposed amounts are integers and he offers Michael at least one dollar.

Suppose he proposes $X for himself and $(100-X) for Michael. Michael must then say whether he accepts the proposal.

If he does, they each get the amounts proposed. But if Michael rejects the proposal, each player gets zero, and

the $100 reverts to the experimenter. It is common knowledge that Tom and Michael will play this

game only once and that each has the goal of making as much money for himself as possible.

What should Tom propose?

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Unlike earlier games, the timing of each player’s decision in this game is important.

The payoffs for this game are better represented in a game tree, rather than a payoff matrix.

Tom proposes$X for himself,$(100-X) forMichael

A B

$X for Tom$(100-X) forMichael

Michael accepts

$0 for Tom$0 for Michael

Michael refuses

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Suppose Tom proposes $99 for himself, $1 for Michael.

Tom proposes$99 for himself,$1 for Michael

A B



Michael accepts

Michael refuses

This is the most advantageous offer Tom can make, and at point B, Michael's best bet is to accept it.Michael's problem is that he cannot make a credible threat to refuse Tom's one-sided offer.

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Example 11.7. Should the business owner open a distant branch?

The owner of a thriving local business wants to start up a satellite outlet in a distant city.

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If the outlet is managed honestly, the owner can pay the manager $1000 per week and still earn an economic profit of $1000 per week from the outlet.

The manager’s best alternative employment pays $500 per week. The owner's concern is that she will not be able to monitor the

behavior of the outlet manager, and that this person would therefore be in a position to embezzle heavily from the business.

The owner knows that if the distant outlet is managed dishonestly, the manager can earn $1500 per week, while causing the owner a financial loss of $500 per week.

If the owner believes that all managers are selfish income-maximizers, will she open the new outlet?

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First step: Construct the game tree for the distant-outlet game .

Managerialcandidatepromises tomanagehonestly

A B

$1000 for owner$1000 for manager

Owner gets $0Manager gets $500for working elsewhere

Open distant outlet

Don’t open outlet

C

manage honestly

manage dishonestly-$500 for owner$1500 for manager

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To predict how game will play out, work backward from end of the tree.


A B



Open distant outlet

Don’t open outlet

C

manage honestly


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If the outlet is opened, the manager must decide at C whether to manage honestly.


Open distant outlet

C

manage honestly


If his only goal is to make as much money for himself as he can, he will manage dishonestly (bottom branch at C), since that way he earns $500 more than by managing honestly (top branch at C). So if the owner opens the new office, she will end up with a financial loss of $500.

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If instead she had chosen not to open the office (bottom branch at point B), she would have ended up with a financial return of zero.


Don’t open outlet

B

Owner gets -$500Manager gets $1500

Open outlet

And since zero is better than -$500, she will choose not to open the satellite office.

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A B



Open distant outlet

Don’t open outlet

C

manage honestly


Even though opening the outlet and managing it honestly would be better for both the owner and manager, purely self-interested persons cannot achieve this outcome.

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A Thought Experiment

I have just gotten home from a crowded concert and discover I have lost $1000 in cash. The cash had been in my coat pocket in a plain envelope with my name and address written on it.

Do you know anyone who you feel certain would return it to me if he or she found it?

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Resolving Prisoner's Dilemmas and Other Commitment Problems

In games like the prisoner's dilemma, the hockey helmet game, the ultimatum bargaining game, and the satellite office game, players have trouble arriving at the outcomes they desire because they are unable to make credible commitments.

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For example, if both players in the prisoner's dilemma could somehow reach a binding agreement to remain silent, each would be assured of getting a shorter sentence.

Hence the logic of the underworld code of Omerta, under which the family of anyone who provided evidence against a fellow mob member would be killed.

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Likewise, the helmet rule results in a better outcome for hockey players by committing them to wear helmets in circumstances in which they would otherwise choose not to do so.

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Example 11.8. Will the restaurateur pay the waiter extra to provide good service?

The restaurateur wants his waiter to provide good service so that customers will enjoy their meals and come back in the future.

If the waiter provides good service, the owner can pay him $100 per day.

But if the waiter provides bad service, the most he can pay the waiter is $60 per day.

The waiter is willing to provide bad service for $60 per day, and for $30 extra would be willing to provide good service.

The owner's problem is that he cannot tell whether the waiter has provided good service.

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Example 11.8. Will the restaurateur pay the waiter extra to provide good service?

Restaurateur

Waiter

Pay waiter $100/day

Pay waiter $60/day

Provide bad service

Provide good service


Third best for each

Best for owner Worst for waiter

Best for waiter Worst for owner

Each side has a dominant strategy:Restaurateur- pay $60/day; waiter- provide bad service. Outcome is lower-right cell and that is inefficient.The tip is a solution to this commitment problem.

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Changing material incentive as a solution to commitment problem

The Mafia's code of silence, hockey helmet rules, tips for waiters -- all work by changing the material incentives facing the relevant decision makers.

But it is not always practical to changes material incentives in precisely the desired ways.

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Example 11.9. Tipping

What if the restaurant is located in a distant city the diner doesn’t expect to visit again?

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Example 11.9. Tipping

Unlike case of restaurant with local patrons, this waiter has no way to penalize the diner in the future if he leaves no tip. Diner

Waiter

Leave 15% tip

Leave no tip

Provide bad service

Provide good service


Third best for each

Best for diner Worst for waiter

Best for waiter Worst for diner

Dominant strategy for the waiter: provide bad service. Dominant strategy for diner: leave no tip. Again a worse outcome for each than if waiter had provided good service and diner had tipped.

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Moral Sentiments as Commitment Devices

If commitment problems cannot be solved by altering the relevant material incentives, it may nonetheless be possible to solve them by altering people's psychological incentives.

For example, feelings of guilt when they cause harm to others, feelings of sympathy for the interests of their trading partners, feelings of outrage when they are treated unjustly, and so on.

These feelings may lessen the incentive to behave in opportunistic and mutually destructive ways.

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Two Standards of Rationality

1. The Self-interest Standard: A person is rational if she is efficient in

pursuit of her own interests. The self-interest model is often not

descriptive.

Return wallets Rescues Bone marrow donation

Blood donation

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Two Standards of Rationality

2. The Adaptive Rationality Standard: A taste can be added to the self-interest

model, but only upon a plausible showing that someone motivated by that taste would not be handicapped in the quest to acquire the resources needed for survival and reproduction..

Return wallets Rescues Bone marrow donation

Blood donation

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The Possibility of Honest Managers

If the owner believes that the managerial candidate comes from a society whose members have been strongly conditioned to behave honestly, will she open the new office?

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Suppose that the effect of the conditioning is to cause the managerial candidate to be willing to pay $10,000 to avoid the guilt he would feel if he managed dishonestly.

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Managerial candidate promises to manage honestly

Owner opens satellite office

Owner does not open satellite office

Manager manages honestly. Owner gets $1000, manager gets $1000

Owner gets $0, Manager gets $500 by working elsewhere

Manager manages dishonestly. Owner gets -$500, manager gets -$8500

C

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A taste

A taste for actions that result in avoidable costs cannot be favored by natural selection unless others can infer the presence of that taste.

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Who are more likely to be honest (i.e. , to have a taste of honesty)?

The person is very religious, e.g., buddhist, christian, etc.

The person listens to classical music. The person belongs to some hiking club. The person is more educated, e.g., holds higher

degree, such as PhD in Economics. The person has gotten a written

recommendation from Mr. Li Ka Shing.

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End

Ka-fu Wong University of Hong Kong

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