Chapter 9 - Game theory and strategic thinking. In this chapter you will learn: What strategic behavior is and what the components of a strategic game are, why noncooperation is a dominant strategy in the prisoners’ dilemma, how repeated play can enable cooperation,...
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Chapter 9
Game Theory and Strategic Thinking
What will you learn in this chapter?
components of a strategic game are
prisoners’ dilemma
decisions
achieve their goals by limiting their options
Games and strategic behavior
trade‐offs they face and pursue their goals in the
most effective way possible
strategically under different circumstances
people that requires those involved to think
strategically
by anticipating the interplay between your own and
others’ decisions
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Rules, strategies, and payoffs
• All games share three features: rules,
strategies, and payoffs.
game
follow to achieve their goals.
actions
The prisoners’ dilemma
You
3rd choice
10 years
3rd choice
20 years 4th choice
1 year
1st choice
1st choice
20 years
4th choice
2 years 2nd choice
2 years
2nd choice
• Payoff depends on actions of both players:
– Both confess.
– One player confesses.
– Neither player confesses.
• Solve game by finding what the other player would do if you choose a specific action and vice‐versa.
• Because of strategic behavior, the realized outcome is not the best possible outcome available.
which two people in isolation make the choice to
‘confess’ or ‘don’t confess’ that together they committed
a crime
The prisoners’ dilemma
Kerry
Bad reputation
3rd choice
Tight race
Bad reputation
3rd choice
Lose 4th choice
Win
1st choice
iv Win
1st choice
Lose
Tight race Good reputation 2nd choice
Tight race
Good reputation
dominant strategy– an action that they always choose?
the game.
the best possible outcome
The prisoners’ dilemma can be extended to other
applications, such as the Bush‐Kerry presidential election
and the choice to use negative or positive advertising
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The prisoners’ dilemma
You
Don’t litter
-10
3rd choice
-15 4th choice 0
1st choice
0
1st choice
-15
4th choice
-5 2nd choice -5
2nd choice
Litter
but want to contain their losses.
the game.
when all players choose the best strategy they can given the choices of all other players.
The prisoners’ dilemma can also be extended to whether
you should or should not litter
Dominant strategies
Player B
Rock Paper Scissors
Tie
A wins
B wins
B wins
B wins
A wins
A wins
Tie
Tie
paper, scissors has no Nash equilibrium
outcome where you
or your opponent would wish to change your strategy once you find out what the other player is doing
While dominant strategies can sometimes solve for the
equilibrium
Reaching equilibrium
• The Nash equilibrium is sometimes referred to
as the non‐cooperative equilibrium
pursuing their individual interests
• Sometimes players may collude (or cooperate)
to obtain a better outcome for both.
cooperative equilibrium would make both players
better off
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Active Learning: Finding equilibrium
Suppose Greg and Renee must choose whether or not to
offer a lunch special at their respective restaurants
Greg’s Pizzeria
Don’t offer lunch special
-10
-5
-15 20
30
-10
35 25
Offer lunch special
Avoiding competition through commitment
• Sustaining collusion to obtain the cooperative
equilibrium is extremely difficult, as one player
can typically be made better off by defecting.
• It may require a punishment for defecting that
is larger than the payoff for defecting.
to obtain a certain outcome is an example of a
commitment strategy.
• Often the commitment is non‐binding and
individuals break their agreement.
Promoting competition in the public interest
Exxon
3rd choice
Low profits
3rd choice
No profit 4th choice
High profits 1st choice
1st choice
No profit
4th choice
Moderate profits 2nd choice
Moderate profits 2nd choice
Competition • Suppose a small town has
two gas stations, each setting their price
– If they collude, they will earn moderate profits.
– If they compete, they will earn low profits.
Nash equilibrium is the
While cooperation may serve the best interests of the
players directly involved, it may have societal
consequences
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Repeat play in the prisoners’ dilemma
played more than once.
• The cooperative equilibrium is more likely to
occur because simple commitment
mechanisms exist.
other did in the previous game
Sequential games
players moved simultaneously
move prior to other participants choosing an
action
backward induction, in which the optimal strategy
of the last player to choose is determined,
followed by the second‐to‐last player, and so on
Sequential games
Q. What do you have to do to win the Pulitzer prize?
A. You have to work for a top newspaper.
Q. What do you have to do to get a job at a top newspaper?
A. You have to have a graduate degree in journalism.
Q. What do you have to do to get a graduate degree in journalism?
A. You have to have an undergraduate degree in English.
Q. What do you have to do to get that degree?
A. You have to take the prerequisite courses in nonfiction writing.
Therefore, you should take introductory nonfiction writing next semester.
determine your sequence of choices
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Deterring market entry: a sequential game
Burger King:
Should we enter?
If so, where?
Bu ger King:
Shoul we e ter?
If so whe e?
Center of town
Outskirts of town
No Outskirts Outskirts
Center
Center
No
Profits
BK: 2%
McD: 12%
BK: 4%
McD: 4%
BK: 10%
McD: 12%
BK: 8%
McD: 8%
BK: 12%
McD: 2%
BK: 10%
McD: 20%
McDonalds:
Where should we
build?
Burger King:
Should we enter?
If so, where?
Burger King:
Should we enter?
If so, where?
• If McD enters in the center of town:
– BK will not enter and earns a 10% return.
– McD earns 12% return.
• If McD enters in outskirts of town:
– BK will enter at center and earns a 12% return.
– McD earns 2% return.
• McD chooses between 12%
return or 2% return.
• McD chooses to locate at the center of town and BK does not enter.
McDonald’s is considering a new store in a small town
and by how many burger joints enter
Sequential games
Company: What
should wepay
employees?
Company: 0%
Union: 0%
1%
Share of surplus
No
Labor Union:
Should we accept the new offer?
Company: 99%
Union: 1%
Company: What
should we pay
employees?
• If this was a one‐round game and the company moved first, it could offer just 1 percent of the
surplus and the union would have to make a choice:
– Accept the offer.
– Reject it by going on strike and shutting down production.
• The union chooses between a 1% pay raise and 0%.
– The union will accept the offer.
• This is an example of an ultimatum game: One player makes an offer and the other player has
the simple choice of whether to accept or reject.
• First‐mover advantage can be extremely important in one‐round sequential
games.
• Consider a bargaining game, in which a company is negotiating with its
employees’ labor union over wages.
Commitment in sequential games
Aztecs:
Advance or
retreat?
Cortés:
Advance or
retreat?
Cortés: fight to death
Cortés: lives
Aztecs: keep land
Cortés: wins land
Aztecs: live
Advance
Retreat
Advance
Retreat
Advance
Result
Cortés:
Advance or
• Both prefer land, lives, and then a fight to the death.
• If all strategies are available:
– If Aztecs advance, Cortes will retreat.
– If Aztecs retreat, Cortes will advance.
• Given these strategies, Aztecs will advance and
outcome
either advance or retreat
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Commitment in sequential games
Cortés: fight to death
Aztecs: fight to death
Cortés: wins land
Aztecs: live
Advance
Retreat
Advance
Retreat
Retreat Advance
Result
Eliminated
Aztecs:
Advance or
retreat?
Cortés:
Advance or
retreat?
Cortés:
Advance or
retreat?
Eliminated
to advancing by burning his ships
• Burning his ships eliminates the choice to retreat.
• Given this limited choice set, Aztecs choose between:
– Advancing, and fighting to the death.
– Retreating, and living.
• Given these strategies, Aztecs will retreat and Cortes will advance.
Active Learning: Commitment in sequential
games
Burger King:
Should we enter?
If so, where?
Bu ger King:
Shoul we e ter?
If so whe e?
Center of town
Outskirts of town
No Outskirts Outskirts
Center
Center
No
Profits
BK: 2%
McD: 12%
BK: 4%
McD: 4%
BK: 10%
McD: 12%
BK: 8%
McD: 8%
BK: 12%
McD: 2%
BK: 10%
McD: 20%
McDonalds:
Where should we
build?
Burger King:
Should we enter?
If so, where?
Burger King:
Should we enter?
If so, where?
In an effort to not lose market share, suppose Burger King commits
to build in every new town that McDonalds does
Summary
• The concept of strategic games was
introduced.
• Many real‐life decisions can be analyzed as if a
strategic game is being played.
• Game theory can explain choices that may
seem unintuitive, such as why people in
custody confess to their crimes.
• Simultaneous move games were examined as
well as sequential move games.