What is Nash Equilibrium?
In: 0
Situation where anyone making a move would worsen his own personal outcome.
Take the prisoner dilemna example. Two accomplices committed a crime together and are sentenced to prison for 5 years. Each one is told “if you snitch on your accomplice, your time in prison will be reduced by 5 years, and his will be increased by 10 years”
If they snitch on each other, they both get jailed for 10 years total. If they don’t, they both get 5 years total (which is better). If one does but not the other, the one who snitched gets 0 year and his accomplice gets 15.
The situation where both of them plan to snitch on each other (thus 10 years each) is a Nash equilibrium: because if any of them modifies his decision (and chooses not to snitch on his accomplice), he will worsen his personal outcome by getting 5 more years.
You’d tell me “yeah what if they agree to both not snitch on each other”. Yeah that example is a bit limited indeed, but the point is, there are contexts where that kind of agreement isn’t feasible.
Take the “split or steal” example. It’s a TV game show: [https://en.wikipedia.org/wiki/Golden_Balls#Split_or_Steal](https://en.wikipedia.org/wiki/Golden_Balls#Split_or_Steal)
Well, the case where both contestants choose “steal” is a Nash equilibrium. If one of them changes his decision he’s just shooting himself in the foot with no personal gain from it. Although the case where they’d both choose “split” would be better for everyone.
Latest Answers