Game Theory

Often in economics, we think of individuals and firms as acting individually without concern for other economic agents. However, there are instances where strategic interaction models are a better option for understanding real world phenomena.

An introduction to game theory tends to begin with what is called a ‘Prisoners’ Dilemma’ [PD] game. Generally, it is assumed that the self-interested actions of individuals will lead to optimal outcomes for society. However, there are instances where this does not happen. PD games are excellent examples on how to illustrate these results.

The story goes along these lines. It starts with two individuals who have committed two crimes. Let’s call them Al and Bob. The police arrest the pair and place them in separate rooms. There is enough evidence to convict the pair of the minor offence even if the two do not confess. However, the only way to convict the pair of the major crime is if one of the two confesses. As we have all seen in countless television crime dramas, the police decide to offer Al and Bob a deal.

In the first room is Al. A police officer comes in and makes Al the following offer:

• If Al confesses to the major crime, and Bob does not, Al will not have to go to jail on either the major or minor crime- he gets zero jail time.

• If Al does not confess to the major crime, but Bob does, Al will go to jail for 20 years, and Bob gets to go free!

• If both Al and Bob confess to the major crime, they each go to jail for 10 years.

• If neither Al nor Bob confess to the major crime, they each do one year in jail for the minor crime.

Of course, in the other room, the same deal is being offered to Bob.

If you were Al, what would you do? Game theory can show us the answer.

Al not only has to think about what he should do, but also needs to consider that Bob is part of this deal.

Assume that Al thinks that Bob will not confess to the major crime.

• If Al confesses to the major crime, he...