Last school year, I took an upper-division economics class on game theory. Game theory is a topic within economics that analyzes rational decision-making. While Russell Crowe’s “A Beautiful Mind” portrays game theory as a magical science that requires people to write on beautiful stained glass windows, game theory is really a very simple and fascinating subject matter that helps people categorize rationality, payoffs, and decisions.
The prisoner’s dilemma is one of the most popular and most studied examples in game theory. Imagine 2 criminals who have been captured for a crime. The police are interrogating each of these prisoners in isolated rooms. The police only has enough evidence to put each suspect away for 2 years, but if one of the criminals rats the other one out, they can put the other criminal away for 4 years and only keep the rat for 1 year. However, if both prisoners rat each other out, then both will serve 3 years for semi-cooperating in the light of incriminating evidence.
This leaves 4 scenarios; they are reflected below in each of the four boxes.
1) Prisoner 1 is Silent (will receive 2 years in prison); Prisoner 2 is Silent (will receive 2 years in prison).
2) Prisoner 1 will Rat (will receive 1 year in prison); Prisoner 2 is Silent (will receive 4 years in prison).
3) Prisoner 1 is Silent (will receive 4 years in prison); Prisoner 2 will Rat (will receive 1 years in prison).
4) Prisoner 1 is Rat (will receive 3 years in prison); Prisoner 2 will Rat (will receive 3 years in prison).
Notice that when Prisoner 2’s strategy is “Silent” in scenarios 1 and 2, the best thing for Prisoner 1 to do is “Rat.” When Prisoner 2’s strategy is “Rat” in scenarios 3 and 4, the best thing for Prisoner 1 to do is “Rat.”
The payoffs are symmetrical, so the exact same logic occurs from Prisoner 2’s perspective.
In conclusion, Rat is the best response for both players. The dilemma is that the payoff for both is 3 years, while had they both cooperated; they would have both received only 2 years of prison. Yet, this is really the best option because a purely rational player realizes that the actions of the other player are completely out of his/her control. A rational player should look at the best response for every single action of the other player, freeze those actions, and act in a manner that will maximize his/her payoff.
Traffic in Los Angeles
Drivers in Los Angeles act like the rational prisoners in the Prisoner’s Dilemma. For the sake of this example, let’s say there are “2” cars. In reality, Car 1 will represent one car, while Car 2 will represent the presence of other cars. If you were to look from Car 2’s perspective, the exact opposite would apply. Both cars are trying to reach their own destination. If there is no traffic, a car will reach his/her destination in 20 minutes. If there is traffic, it will take 30 minutes. However, if someone keeps cutting that car off, they won’t be able to merge into any of the necessary lanes and may be forced into the wrong streets. They may even get in a crash. This will change the commute into a 40-minute commute. However, if both cars drive aggressively, there is bound to be a collusion elsewhere, and the traffic will eventually cause the average commute to be 30 minutes long for both cars.
Again, This leaves 4 scenarios. Again, they are reflected below in each of the four boxes.
1) Car 1 Drives Nicely (will take 20 minutes to commute); Car 2 Drives Nicely (will take 20 minutes to commute).
2) Car 1 Drives Aggressively (will take 10 minutes to commute); Car 2 Drives Nicely (will take 40 minutes to commute).
3) Car 1 Drives Nicely (will take 40 minutes to commute); Car 2 Drives Aggressively (will take 10 minutes to commute).
4) Car 1 Drives Aggressively (will take 30 minutes to commute); Car 2 Drives Aggressively (will take 30 minutes to commute).
The same logic applies here. The best thing for Car 1 to do is to always drive aggressively and the best thing for Car 2 to do is to always drive aggressively. As a result, traffic in Los Angeles is always terrible.
Rational isn’t always the best.