Mostly summarized from Gregory Mankiw’s Principles of Economics, 5^th Ed.

PART 5  Firm Behavior and the Organization of Industry

Chapter 17 of 36  Oligopoly

Section 9 of 25

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Figure 1 here

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Figure 1 - The Prisoners' Dilemma

In this game between two criminals 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

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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.

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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.

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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

· we'll give you immunity and you can go free

· your partner will get 20 years in jail”

Both partners confess:

· “if you both confess to the crime

· we won't need your testimony

· we can avoid the cost of a trial

· so you will each get an intermediate sentence of 8 years”

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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

· if he confesses, my best strategy still is to confess, since then I'll spend 8 years in jail rather than 20

· so, regardless of what Clyde does, I’m better off confessing”

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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.

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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.

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.

But because each pursues their own interests, the two together reach an outcome that is worse for each of them.

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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.