During the last few months, I’ve been reading a lot about “Game theory” and “Rationality” and “Super-Rationality”. It’s really an interesting subject and it has A LOT of applications in real life.
The basic, or elemental brick in the game theory is what we call the “Prisoner’s dilemma”, it is the main and most important model in game theory that can be used to represent lot of different situations in real life. Here we go:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. Oh, yes, there is a catch … If both prisoners testify against each other, both will be sentenced to two years in jail.
So, in another words:
- if both keep silent, they will get one year in jail sentence.
- If one kept silent and the other defects, the one who defects get free, the other one gets three years!
- if both defected, both get 2 years.
Here is the table that represents the situation:
|Prisoner B stays silent (cooperates)||Prisoner B betrays (defects)|
|Prisoner A stays silent (cooperates)||Each serves 1 year||Prisoner A: 3 years
Prisoner B: goes free
|Prisoner A betrays (defects)||Prisoner A: goes free
Prisoner B: 3 years
|Each serves 2 years|
In the rational way of thinking:
The rational way of thinking is the one where each agent tries to maximize his own payoff regardless what the others will do: here, each prisoner will try to minimize his own sentence duration, regardless what the second one does: it is always better to defect. Because, if prisoner A chooses to cooperate, By defecting prisoner B goes free instead of serving 1 year and if prisoner A has chosen to defect, prisoner B has better to choose to defect as well, this way, he will serve 2 years instead of 3.
The rational way of thinking leads both prisoners to defect which is also the only Nash Equilibrium in this game. The dilemma is that by both defecting, prisoners will be sentenced for 2 years while by both collaborating, it would have been better for both of them (just 1 year of prison)! But if we play the game again, they will both prefer to defect again and again in the rational way and will both serve 2 years.
The Nash equilibrium is really very sticky and once reached, it is really hard to escape from it, because each one will be afraid that the second person will defect, so he will feel stupid if he chooses to cooperate while the other one did not. I organized a social game in my town in Lebanon, with teenagers of 15-16 years old, they reached the Nash equilibrium very quickly and couldn’t get away from it for 10 continuous times! Nash equilibrium is a very safe, secure state although it might not be for the best of everyone.
Super-rational way of thinking:
Superrationality is an alternative method of reasoning. First, it is assumed that the answer to a symmetric problem will be the same for all the superrational players. Thus the sameness is taken into account before knowing what the strategy will be. The strategy is found by maximizing the payoff to each player, assuming that they all use the same strategy. Since the superrational player knows that the other superrational player will do the same thing, whatever that might be, there are only two choices for two superrational players. Both will cooperate or both will defect depending on the value of the superrational answer. Thus the two superrational players will both cooperate, since this answer maximizes their payoff.
I find there is a kind of spirituality in the Super-rational way of thinking. It aligns with the Golden rule:
“One should treat others as one would like others to treat oneself”
If I prefer the other players to choose “Cooperate”, I should chose “Cooperate” as well. I can’t say I prefer the others to cooperate and me to defect, because if we scale this up to every player, everyone WILL defect.
- Prisoner’s dilemma with 3 or more players (erik-poupaert.blogspot.com)
- Game Theory 101 MOOC Completed (wjspaniel.wordpress.com)
- The prisoner’s dilemma (businessinsider.com)
- Prisoner’s Dilemma :: An example of the application of Game Theory (designgames12.wordpress.com)
- The prisoner’s dilemma (sgtreport.com)
- Game Theory :: The mathematics of games (designgames12.wordpress.com)
- TTT Game Theory and Law (pirategirl69.wordpress.com)