The most rational choice is not always the best, we'll show all did earlier. Much the moral of this story of betrayal could tell us what would La Fontaine but we owe to mathematician Albert Tucker in the 50s and whose implications are significant both in behavioral ecology that economy.
Here's the story:
Two thugs were arrested by the police, they do not know, or little, and are each isolated in a cell. The concern is that investigators do not have enough evidence to charge them. And as they are cunning and manipulative, he develop this market to be proposed separately to each suspect. "If you denounce your accomplice and he does not denounce you, you shall be released and the other sentenced to 10 years in prison. If you denounce him and also you scoop both for 5 years in prison. If nobody complains, you will both have six months in prison. " Let's put our
-one seconds into the skin of one of two thugs and see what solution is it better to consider. Terminate or be silent? Cooperate or betray?
If I denounce, only 5 years old, is already better.
So if he betrays me to betray my interest too. "
Case 2: the other does not denounce me.
"If I am silent, 6 months sheet.
If I denounce, I am free
Again no hesitation treason must! " Here's what it gives in a table: the payoff matrix.
| behavior of other> | shuts | Denounces |
| I am silent | 6 months / 6 months | 10 years / freedom |
| I denounce | freedom / 10 years | 5 years / 5 years |
So the rational choice is still treason, since the strategies are individualistic, which is the more often the case in economics as in nature. Now see the same problem but from the perspective of the "gang" to whom belong these two offenders. The objective is to minimize losses, the ideal is to avoid the mutual termination - the most rational choice at the individual level that leads to 5 years in prison. Indeed in the case where everyone is silent sentence is 6 months, this explains why the law of silence needed in organized crime.
To conclude, in the absence of control, even though both would benefit from thugs cooperate, the incentive to betray the other are so strong that cooperation is never selected by a rational player. QED: the single most rational choice is not the best!
This problem is a famous example of game theory : the mathematical problem strategy. Note that this result of the systematic betrayal, is valid only if the game is played only once (or a number known in advance)! The best strategy if the game is repeated is quite different ... but it will be the subject of a Another article, along with examples of implications in ecology.
to read on this subject: Wikipedia article