Eli5: Why is Prisoners Dilemma considered a Dilemma?

Question

Eli5: Why is Prisoners Dilemma considered a Dilemma?

In: 46

Answer 1

The short answer is because the Nash equilibrium is not the same as the pareto optimal solution. But that requires some knowledge of these terms, so let’s talk about what they mean:

“Nash equilibrium” means a point at which both players would agree not to change their move, even knowing the other player’s move. Imagine you and your opponent are discussing what you will do with each other out loud.

“If you pick scissors, I’ll pick rock.” -> “If you pick rock, I’ll pick paper.”

Games like rock paper scissors have ***no*** Nash equilibrium because you would continue changing your move forever and never settle on one.

In Prisoner’s Dilemma, the Nash equilibrium is for both players to defect. If someone stays silent, their opponent benefits more by defecting. If someone defects, their opponent ALSO benefits more by defecting. It’s never advantageous for a player to choose to stay silent, so you can confidently defect knowing it will give you the better outcome.

“Pareto optimal” means you add how good the outcome is for all of the players and treat them as the outcome for a single player, then pick the best outcome. Because both players serve a heavier prison sentence if they both defect, but a lighter prison sentence if they both stay silent, both players staying silent ends up being the pareto optimal solution because it’s all around better for everyone.

The dilemma is that even though both players know the outcome will be better for both of them if they both stay silent, both are directly incentivized to defect. Even if both players understand the game perfectly and are perfectly logical, they will still collectively select an outcome that is worse for both of them.

Keep in mind this only applies when the game is only played once and there is no way to enforce additional consequences on the players. The entire basis of society is built upon removing anonymity and enforcing accountability so that the prisoner’s dilemma never actually occurs in the first place.