B.6 Prisoner Dilemmas
Review Questions
Lesson Topics
The Prisoners’ Dilemma shows why people
might not cooperate even if it is profitable. Cournot
duopoly is a prisoners’ dilemma. Lower output by all
is profitable but lower output by you is unprofitable.
Duopoly with Substitutes (1) is a prisoners’
dilemma with firms simultaneously choosing prices
and producing gross substitutes. Profitable
cooperation raises prices.
Duopoly with Complements is a prisoners’
dilemma with firms simultaneously choosing prices
and producing gross substitutes. Profitable
cooperation lowers prices.
Advertising is a prisoners’ dilemma when
advertising mostly transfers customers between firms
rather than generating new customers. Profitable
cooperation reduces advertising.
Cleaning and Other Public Goods are prisoner
dilemmas when public good purchases by all is
profitable but purchases by you are unprofitable.
Profitable cooperation increases good purchases.
Noise and Other Externalities (1) can be
prisoner dilemmas. Profitable cooperation decreases
the negative externalities (like noise) and increases
the positive externalities (like entertainment).
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B.6 Prisoner Dilemmas
Review Questions
Duopoly with Substitutes
Question. MillerCoors and Anheuser-Busch control
a large share of the U.S. Domestic beer market. The
unit cost of a keg to both retailers is $75. The retailers
compete on price but consumers do not find the goods
to be perfect substitutes. Suppose MillerCoors and
Anheuser-Busch consider prices $85 and $95. If both choose price $85,
each has demand 50; if both $95, each has 40; and if one chooses $85 and
the other $95, the lower price has demand 85 and the higher price 5.
Are the two goods gross substitutes or gross complements? What price
should MillerCoors choose in this Price Competition Game?
Are there mutual gains from cooperation? Can MillerCoors trust AnheuserBusch to cooperate? Can Anheuser-Busch trust MillerCoors to cooperate?
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B.6 Prisoner Dilemmas
Review Questions
Answer to Question:
To begin, fill out the normal form for this game of simultaneous moves. For
example, at Miller price $95 and Busch price $85, Miller’s demand is 5 and
Busch’s is 85, so Miller profits $(95-75)x5 = $100 and Busch profits $(8575)x85 = $850.
Busch
Miller
$85
500,500
100,850
$85
$95
$95
850,100
800,800
Goods are gross substitutes because a higher price for one means higher
demand for the other.
Each player should choose $85 since it is the dominate strategy for each
player: $85 it gives better payoffs for that player compared with $95, no
matter whether the other player chooses $85 or $95.
Busch
Miller
$85
500,500
100,850
$85
$95
3
$95
850,100
800,800
B.6 Prisoner Dilemmas
Review Questions
There are mutual gains if both MillerCoors and Anheuser-Busch cooperate
and charge $95. But MillerCoors cannot trust Anheuser-Busch to
cooperate because Anheuser-Busch cooperating and choosing $95 is not a
best response to MillerCoors cooperating and choosing $95.
Likewise, Anheuser-Busch cannot trust MillerCoors to cooperate because
MillerCoors cooperating and choosing $95 is not a best response to
Anheuser-Busch cooperating and choosing $95.
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B.6 Prisoner Dilemmas
Review Questions
Noise and Other Externalities
Question. Consider a downtown Fullerton street on
which 8 bars are run, and which suffers from a
serious drunkenness problem that detracts
customers because of the violence and smell. It
costs $200 daily in foregone profit for each bar to enforce moderation stop
serving customers before they become drunk. If a bar owner decides to
enforce moderation, all bars on the street will have improved sales and
profits. Suppose every bar on the street will have a $20 increase in daily
profit for each bar that decides to enforce moderation. Should anyone
enforce moderation? Are there mutual gains from cooperation? If so, can
any bar trust other bars to cooperate?
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B.6 Prisoner Dilemmas
Review Questions
Answer to Question:
No one should enforce moderation since Not Enforce Moderation is a
dominate strategy. For any strategies by each of the other 7 bars, the extra
payoff to Bar X from enforcing moderation is a $20 increase minus a $200
cost, which makes the payoff $180 less than for Not Enforce Moderation.
When each of the 8 bars follows their dominate strategy, no one enforces
moderation, and the payoff to each bar is 0. And if each of the 8 bars
enforce moderation, each receives a $20x8 increase minus a $200 cost,
which makes the payoff $40 less than in the dominance solution. So
mutual gains are not possible.
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