Prisoners' Dilemma: To confess or not to confess?

This post is about Game Theory, which is

"a mathematical method for analyzing calculated circumstances where a person's success is based upon the choices of others". (http://en.wikipedia.org/wiki/Game_theory)

For background on the game of prisoners' dilemma, please view the following video:

 http://www.youtube.com/watch?v=uX4CkBlXoxo

 Here is a matrix representation of this situation:

Bob\ Jack	Confess	Not confess
Confess	(3, 3)	(0.5, 5)
Not confess	(5, 0.5)	(1, 1)

The entries in the cells are the prison terms. For example, the entry that corresponds to (Confess, Not confess)- the entry in the first row second column- is the length of sentence to Bob (0.5) and Jack (5), respectively, when Bob confesses but Jack does not.
Now how do we determine the outcome of this game? What are the dominant strategies for each player?

Notice, if Jack plays "Confess", Bob will play "Confess" (since he prefers spending 3 years in prison rather than 5(if he does not confess)). Similarly, if Jack plays "Not confess", then Bob's best response is to "Confess". So, no matter what Jack plays, Bob's best reply is always "Confess". By the same logic, no matter what Bob plays, Jack's best reply is always "Confess" too.

     http://thebsreport.files.wordpress.com/2009/06/prisoner3.gif?w=875&h=580

Hence, (confess, confess) is a dominant strategy equilibrium in this game (Dutta, 1999).

However, this is not the most efficient outcome, since by not confessing, both players can simultaneously reduce their prison terms. But due to a lack of trust, the outcome (not confess, not confess) is not sustainable.

So next time, if you want two people to confess to their crime, you know what to offer them!!!

The game of prisoners dilemma has many real life applications especially in economics. A classic case is that of advertising where say two firms, A and B compete with each other. The profits each derive from advertising depends on the advertising conducted by the other firm. If both spend the same large amount in advertising, then their costs increase and no one benefits at the expense of the other. So both could reduce their costs (and increase their profits) by reducing advertising expenditure simultaneously. However, suppose if firm B decides not to spend on advertising, then firm A can benefit immensely by advertising. Since both firms cannot trust each other to advertise less, both end up advertising large equal amounts and making lesser profits.                                                       (http://en.wikipedia.org/wiki/Game_theory)

Reference:

• Game Theory                                                                                                                     http://en.wikipedia.org/wiki/Game_theory
• Dutta, Prajit K. (1999) Strategies and Games: Theory and Practice. The MIT Press: Cambridge, Massachusetts.
• Prisoner's Dilemma                                                                                                                            http://www.youtube.com/watch?v=uX4CkBlXoxo