In Prisoner’s Dilemma, William Poundstone traces the origin and development of game theory and the personal and political lives of the scientists involved in its conception and development (John von Neumann, Oskar Morgenstern, J. Robert Oppenhiemer, John Nash, Bertrand Russell, and all the major figures surrounding the Manhattan Project and the atom bomb). Game theory is a systematic mathematical process for predicting the outcome of a predicament between two or more people or groups who are in a situation where they only have their best interests in mind.
Poundstone presents the following situation as an example of prisoner’s dilemma:
you, your spouse, and your mother are kidnapped by mad scientists and placed in a room with a strange machine. All three of you are bound to immobile to chairs. A machine gun looms in front of your spouse and mother, and a menacing clock ticks away on the wall . . . [A scientist announces that pushing a button on a] mechanism will aim the gun at the mother and shoot her dead. If you don’t push it within sixty seconds it will aim and fire at your spouse. . . . What do you do? (1)I also saw an example of a prisoner’s dilemma in a recent episode of The Good Wife, where a young college-aged couple is arrested for a crime involving drugs and a murder. The male is the son of prominent society family and the female comes from a middle class (or poorer) single-parent family. The couple are in love and each refuses to compromise by the telling the officers the truth. They are then placed in separate rooms and interrogated individually. The officers try to trick them by suggesting that the other person has confessed to the truth, but they both hold their ground despite the temptations offered to them by the officers to escape the situation unscathed because they have faith that their partner will not say anything. In the end, the viewer learns that the female is actually responsible for the murder although the situation itself only arose because the male wanted to buy drugs to stay awake to study for a paper or final exam. The male ends up confessing to the murder and taking the blame for the female for this reason and out of his love for her. The whole situation of the game that the officers played to manipulate the male and female into revealing the truth of the situation falls into the logic of game theory.
Game theory logic is usually presented in the form of logic tables like the following:
| B refuses deal | B turns state’s evidence | |
| A cooperates | 1 yr, 1 yr | 3 yrs, 0 yrs |
| A turns state’s evidence | 0 yrs, 3 yrs | 2 yrs, 2 yrs |
 |
| F.W. Murnau, Faust, 1926. |
Poundstone describes another prisoner’s dilemma situation where police officials may not have enough evidence to convict two individuals, and they are offered a Faustian bargain (118): if one individual testifies against the other, he/she will go free, but the other individual will get three in prison for the main charge. The catch is that if they both “testify against each other, both will get two years in jail.” Each individual knows that the other is being offered the same deal, and each individual is only concerned with his/her own welfare (and the lesser prison sentence). According to game theory, if both players “are rational, both will testify and both will get two years in jail” (118-119).
Game Theory's Working Parts- Zero sum game (A two-player noncoopertive game "where the total winnings or payoffs are fixed" (51), such as in poker).
- N-person game (A game “with an arbitrary number of players" that "involve[] coalitions that change the rules of the game and its logic).
- Non-zero sum game (A game with three or more players where cooperation is a factor in the game logic. Associated with John Nash's work in Game Theory))
- Pure Strategy (always making strategic moves according to a preset plan).
- Mixed Strategy (make strategic moves randomly, so that your opponent(s) can't orient their moves on a fixed pattern and outsmart you)
- Utility (Subjective. The “abstraction that can be thought of as the ‘points’ that players play for” (170))
- Saddle Points:
- When a game has a saddle point, the saddle point is the solution of the game, the expected outcome of rational play.
- “This rational solution . . . is an equilibrium enforced by self-interest and mistrust” (97)
- “When the maximin and the minimax are identical, that outcome is called a ‘saddle point’” (54).
John Nash
· N-person games involve multiple players, but the concept remains in a 2-person zero sum game context because the players form coalitions (63).
o N-person games worked for JVN and Morgenstern’s aim: to treat economic conflicts as n-person games.
· Nash studied ‘noncooperative’ games where coalitions are forbidden” (96) – multiple players over time: non-zero sum games and games with over three players (97).
o Rule: you can’t change another team’s strategy.
· Emphasis on equilibrium points: “outcomes where the players have no regrets” (98)
o Player’s achieve well-being (key point)
· Nash Equilibrium
o Nash proved that every two-person finite game has at least one equilibrium point.
o Nash’s proof says that non-zero-sum games have equilibrium points, too. Which was a new outcome.
o Mutual defection as strategy with best utility payoff in the long run.
· We need non zero sum game for our disaster logic (rather than zero-sum) because we have multiple players with different interests and different strategies that aren’t in effect changed by another player’s strategy.
Game Theory and Disaster
I tried to imagine how I might fit my disaster of the disease cancer into the game theory logic using the Nash's non-zero sum game logic with equilibrium points. I thought that the "player's" in the game would be the government regulators, scientists, and the public, each of which have functional equilibrium points where their needs are being satisfied as best as possible given the social factors that each operate within. In a non-zero sum game the equilibrium point falls into the defect/defect category--Nash argues that this is the common best outcome for a multi-player situation on a long-term basis. However, Poundstone explains that an experiment by Merrill Flood and Melvin Dresher proved that an outcome of cooperation among the players (cooperation/cooperation) was the most common outcome on a short-term basis.
| B cooperates | B defects | |
| A cooperates | cooperate, cooperate (CC) | cooperate, defect (CD) |
| A defects | defect, cooperate (DC) | defect, defect (DD) |
If these outcomes are both valid in their temporal contexts, I thought (incorrectly because of the problematic of multiple players) that I could imagine the transaction of the individual visiting a doctor after noticing something is wrong. In the transaction of the doctor's visit, all the players come together to cooperate in the service they offer to the patient and the service the patient gives back by being an operand in the system that establishes the factors that create the "well-being" of the other "players in the game." In the long-term, however, if the patient has cancer, then the system itself can be seen to buckle in its full cooperation for any number of reasons associated with treatment options, costs, and the stubbornness of some forms of cancer. The defect/defect strategy could be seen to work in this latter situation when the stakes are raised for each party and each must theoretically decide to shift the outcome toward a slight loss for each party to accommodate for positive outcome for a longer duration.
o Players in the game:
§ Government regulators (equilibrium: regulations, policies)
· Government research funds
§ Scientists (equilibrium dependent on funding)
§ Public (equilibrium: healthy)
§ Health Insurers (equilibrium: wealthy)
o Each has equilibrium points.
o Non-zero sum game cooperation/cooperation; defection/defection
o Strategy: short term: CC
o Strategy: long term: DD (to keep progress innovative but also increase opportunity for disaster).
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