Prisoner's Dilemma

Link: http://www.gametheory.net/Web/PDilemma/

Summary: http://www.gametheory.net/dictionary/PrisonersDilemma.html

A game frequently displayed in television police dramas. Two partners in crime are separated into separate rooms at the police station and given a similar deal. If one implicates the other, he may go free while the other receives a life in prison. If neither implicates the other, both are given moderate sentences, and if both implicate the other, the sentences for both are severe. Each player has a dominant strategy to implicate the other, and thus in equilibrium each receives a harsh punishment, but both would be better off if each remained silent. In a repeated or iterated prisoner's dilemma, cooperation may be sustained through trigger strategies such as tit for tat.


If you want to practice online what we learnt in class, this is a great website to play the Prisoner's Dilemma game.

In this game, you will play against five different opponents, each with a different "personality." You will play each opponent for 25 rounds. The statistics will keep track of your average earnings over the 25 rounds. In each round, you simply have to select "collude" or "cheat."

When you are done with all five opponents, a summary screen will appear with your average payoffs for each opponent.

Here's another link for a game to play:
http://serendip.brynmawr.edu/playground/pd.html
And here's what's important and why it matters: http://serendip.brynmawr.edu/playground/pdref.html

Prisoners' Dilemma is a game which has been and continues to be studied by people in a variety of disciplines, ranging from biology through sociology and public policy. Among its interesting characteristics are that it is a "non-zero-sum"game: the best strategy for a given player is often one that increases the payoff to one's partner as well. It has also been shown that there is no single "best" strategy: how to maximize one's own payoff depends on the strategy adopted by one's partner. Serendip uses a particular strategy (called "tit for tat") which is believed to be optimal under the widest possible set of partner strategies.

http://www.taipeitimes.com/News/editorials/archives/2009/05/03/2003442614

This article gives a good example of game theory in government negotiations. The negotiations between Taiwan and China can be viewed of as a game; both sides can choose a zero-sum or non-zero sum approach to diplomacy. This article evaluates the payoffs for both sides in the tactical and strategic level. This situation is compared to the Prisoner's Dilemma but talks about how negotiations become a "part of a system once it is applied to real-world interaction."

"In international relations, however, negotiations simultaneously involve the tactical and the strategic, meaning that the payoff accrued from the outcome of negotiations is not isolated but part of a system.

What this means is that while it is possible to approach negotiations on a specific topic at the tactical level, once we take a step back, they can also be part of a grand strategy. One implication of this duality is that how one assesses payoff at the tactical level may differ from an assessment at the strategic level."

I am assuming that Prisoner's Dilemma is banking on the fact that the criminals do not talk to each other before they are dragged in. But, even if they do collude before they are brought in for questioning, the dominant strategy still exists. If they both know that if they do not talk to the police and deny all allegations they can potentially go free, police can still thwart this possibility. If the criminals both deny allegations, then the police can simply say that the other person is giving him up, and the criminal will be forced to take the safer option and give up his partner-in-crime to ensure a lesser sentence, instead of gambling on the loyalty of a fellow criminal.

Is there another possibility where the dominant strategy can be thwarted?

http://chronicle.uchicago.edu/001005/posner.shtml

This article discusses examples such as the prisoners dillemma to discuss social norms and the effectiveness of the law. While he claims rationally, people in the Prisoners dillema situation choose between cheating or cooperating, in the real world there are so many multiple interactions that the basic structure can not apply. For example, cheating anyone in the community would hurt your ability to cooperate with the community. Instead, he talks about how different people can "signal" whether they are good cooperating citizens or bad cheating citizens and it might be more effective to play off these social cues and norms than to punish the bad to get "good" results through out the community. He basically rules the game theory ideas behind bilateral relationships can not be directly applied to community relationships, although some conclusions can be drawn from its principles.