Students' Contributions: Prisoner's Dilemma (by 9B Edward Shia)

Prisoner’s Dilemma

The game theory is applied mathematics used it strategic situations that range in many fields, such as: politics, economics, biology, philosophy, and international relations. The game theory basically explains that individual choice is affected by the choice of others. Prisoner’s Dilemma, or PD, provides a counterexample to the game theory. Prisoner’s Dilemma explains how individual choice is not affected by the choice of others.

Formulated by Merill Flood and Melvin Dresher, and later introduced with prison sentence payoffs by Albert W. Tucker, the prisoner’s dilemma is a problem in game theory that explains simply that individual choice is not based on the choice of others, regardless of what the others choose. In a typical PD scenario two people might not cooperate, even if cooperating gives the best penalties, because both people are angling for privileges. In a typical example of PD, two prisoners are caught by the police after a bank theft. They are put into separate cells, and obviously cannot communicate with each other. Since the police do not have enough evidence to convict them, the police cleverly offer the two prisoners the same deal. Each prisoner gets two choices, to confess or to remain silent. The police explain to both prisoners (in separate cells), that if both remain silent, their penalties would be shortened to a sentence of one year in jail. If both confess, both prisoners would have to serve a jail sentence of 5 years, but if either one of them confesses or the other remains silent, the prisoner that confessed can go free. The prisoner who remained silent will serve 10 years of jail sentence. The prisoner sentence payoffs are listed more clearly in the table below:

Prisoner A(Column) / B(Rows)	Confess	Remain Silent
Confess	5 years in jail for both prisoners	A: 10 years sentence, B: Freed
Remain Silent	A: Freed, B: 10 years sentence	1 year in jail for both prisoners

The prisoner’s dilemma explains the “self-profiting” choice in which a person would choose when presented with a two person conflict. Suppose prisoner A was given the two choices, being a rational thinker, prisoner A would think that if prisoner B confessed, it is better to confess so he would have to only serve 5 years in jail instead of 10 years, that is, if he didn’t confess. Similarly, prisoner A would think that if prisoner B did not confess, he could go free if he confessed. So overall, it is better to confess than to remain silent, still given that remaining silent would lessen the jail sentence for both prisoners. The same thinking applies on prisoner B. In this case, the prisoners are at a stage called the “dominant strategy equilibrium.” This means that both prisoners have a dominant strategy (to confess), and when dominant strategies are combined, this is the state called the “dominant strategy equilibrium.”

The prisoner’s dilemma successful presents the human instinct of “self-profiting” in practical real life situations. In one instance, 2 countries are given a choice, military expansion or reduction of weaponry. Both countries would profit if they choose military expansion, but if one country chooses to reduce weaponry, only one country would benefit (the one that choose military expansion). Regardless of what the other country chose, military expansion would be beneficial. So the countries would be more likely to choose to expand the military. In another practical example, countries are given to choice to reduce CO2 emissions, individual countries would benefit far greater to not reduce CO2 emissions than to other countries. Although it is beneficial to all countries if they cut the emissions all together, regardless of the choice the other countries chose, angling for profit, the countries are more likely to not alter the emission of CO2. Overall, the Prisoner’s Dilemma is both practical, and presents natural human responses in a realistic way when given two strategic choices, unaffected by the choice of others. 

Bibliography
1.    Wikipedia. Prisoner’s Dilemma. 5.16.2010. http://en.wikipedia.org/wiki/Prisoner's_dilemma
2.    Wikipedia. Game Theory. 5.16.2010. http://en.wikipedia.org/wiki/Game_theory
3.    Unknown. The Prisoner’s Dilemma. 5.16.2010. http://faculty.lebow.drexel.edu/McCainR//top/eco/game/dilemma.html