Mostly
summarized from Gregory Mankiw’s Principles of Economics, 5th Ed.
PART 5 Firm Behavior and the Organization of Industry
Chapter 17 of 36 - Oligopoly
Section 9 of 23
…
Figure 1 - The Prisoners' Dilemma
Game Theory
ChatGPT: game theory is the study of how people or
groups make decisions in situations where the outcome depends on the choices of
multiple players.
Each player chooses a strategy, aiming to maximize
their own benefit, while considering what others might do.
A key concept is the Nash Equilibrium, where no
player can do better by changing only their own strategy.
Game theory helps explain competition, cooperation,
and conflict in economics, politics, and everyday life.
…
In this game two criminals are suspected
of committing a crime.
The sentence each receives depends both
on
· his or her decision whether to
confess or remain silent
· the decision made by the other
prisoner
…
Oligopolies would like to reach the monopoly
outcome, where profit is maximized.
Doing so requires cooperation which can
be difficult to establish and maintain.
Game theory helps with analysis of the
economics of cooperation.
People often fail to cooperate even
when cooperation would make them all better off.
The prisoners' dilemma contains a
general lesson that applies to any group trying to maintain cooperation among
its members.
…
Consider the scenario of criminals
Bonnie and Clyde who have been captured by the police.
The police have enough evidence to convict
Bonnie and Clyde of the minor crime of carrying an unregistered gun that would
get them both a year in jail.
The police also suspect the two
criminals have committed a bank robbery together, but they don’t have hard
evidence needed to convict them.
…
The police question Bonnie and Clyde separately
and offer each the following two.
One of the partners confesses:
· "right now, we can lock you up
for 1 year
· if you
confess to the bank robbery and implicate your partner
· your partner will get 20 years in
jail”
Both partners confess:
· “if you
both confess to the crime
· we can avoid the cost of a trial
· so, you will each get an intermediate
sentence of 8 years”
…
If bank robbers Bonnie and Clyde care
only about their own sentences, what is the expected outcome?
Figure 1 shows the four choices and
outcomes.
Each prisoner has two strategies, to
confess or remain silent.
The sentence each gets depends on the
strategy each chooses.
Bonnie reasons
· "I don't know what Clyde is
going to do
· if he
remains silent, my best strategy is to confess, then I'll go free and not spend
any time in jail (Figure 1 square C)
…
In game theory, a strategy is called a
dominant strategy, if it is the best strategy
for a player to follow regardless of the strategies pursued
by other players.
Here,
confessing is a dominant strategy for Bonnie, she spends less time in jail if
she confesses regardless of whether Clyde confesses or
remains silent.
Clyde faces the same choices as Bonnie,
and reasons in the same way.
Regardless of what Bonnie does, Clyde
can reduce his jail time by confessing.
Confessing is also a dominant strategy for
Clyde.
Finally, both Bonnie and Clyde confess,
and both spend 8 years in jail.
This result A is the Nash equilibrium.
…
From their standpoint, this is a
terrible outcome.
If they had both remained silent both would have
been better off, getting only 1 year in jail on the gun charge.
…
Wouldn’t Bonnie and Clyde have foreseen
this situation and planned ahead?
In this example, before the police
captured them consider if they had made a pact not to confess.
This agreement would have made them
both better off if they both
stuck to it
because they would each spend only 1
year in jail.
But the two criminals did not remain
silent, even though they had agreed to.
Once they were being questioned
separately, self-interest took over and they both confessed.
… …
the two criminals remain silent
futari no hanzai-sha wa chinmoku o
mamotte iru
二人の犯罪者は沈黙を守っている
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