Purpose: Demonstrate that self-interested behavior does not always lead to pareto-optimal outcomes.

Motivation:  "Two suspects are arrested and charged with a crime.  The police lack sufficient evidence to convict the suspects, unless at least one confesses.  The police hold the suspects in separate cells and explain the consequences that will follow from the actions the suspects can take.  If neither confesses, then both will be convicted of a minor offese and sentenced to one month in jail.  If both confess, then both will be sentenced for six months.  Finally, if one confesses but the other does not, then the cofessor will be released immediately but the other will be sentenced to nine months in jail -- six for the crime and a further three for obstructing justice."  From Robert Gibbon, Game Theory for Applied Economists, p. 3.

Decision Analysis:
Two determine what each prisoner will do, we construct a matrix showing the payoffs for each prisoner and for each strategy.  This is a very basic introduction into game theory and principles of decision analysis.  By tradition the payoffs are written as (row's payoff, column's payoff) within each cell.  This form of writing a game with strategies and payoffs is called the normal form.

Prisoner 1 makes the following analysis:

• If my partner keeps quiet (column 2), then I will be best off if I turn my partner in (i.e.confess).  I will get no jail time.
• If my partner confesses (column 3), then I will also be better off if I turn my partner in (i.e. confess).
• Therefore, it is in my self-interest to confess no matter what I believe that my parnter will do.

Result:  Both prisoners confess and get 6 months of jail time each.  Thus, they end up significantly worse off than if they both had kept quiet.

Discussion:  The outcome shown here results only when the prisoners do not have an opportunity to communicate and do not have repeated interactions.  When given the opportunity to communicate, the prisoners may collude and choose to keep quiet.  When allowed repeated interations or plays of the game over time, the prisoners may learn from experience.  Once cooperation takes place, it may be reinforced and radom attempts to not cooperate will be met with a return to the non-cooperative outcome where both prisoners confess.

Application 1:  Games similar to the prisoner's dilemma occur in all venues of policy making.  As we have seen in class, one common application is to the investment in community property.  Most people, acting in their self-interests, will not contribute to the development of community property.  They will understate the value of the community property to themselves and will attempt to free-ride on the contributions of others.  Thus, government intervention may be required to promote cooperation and reduce free-ridership.  We demonstated this through the "candy game."  As the government, I could have collected a 1 candy tax from everyone in the class to ensure that the total distribution of candy at the end of the class was maximized.

Application 2:  Setting up policy choices and outcomes in terms of a game structure can help policy analysts clearly specify alternatives and the payoffs from each alternative especially when the payoffs from these alternatives are uncertain or dependent on decisions outside of the analysts or policy makers control.  It requires us to think about the assumptions being made in our arguments and the motivations of each actor in the policy arena.  Moreover, it can help us generalize from one policy problem to another.  In the study of international policy, these types of analyses help us to understand why things happened the way they did.  To demonstrate this, we worked with several case studies regarding historical international conflicts.