games
Nash equilibrium
A pair of choices neither person wants to leave alone.
A Nash equilibrium is a pair of choices where neither person wants to change their own choice, once they know what the other person is doing. In this grid each of you picks Left or Right. The green number is yours. The red number is theirs. A higher number is better for that person.
Pick a cell. See whether either player would want to switch.
In a Nash equilibrium, each person's choice is their best reply to what the other person is doing.
Neither person gains by switching alone.
A game can have one Nash equilibrium, more than one, or none among plain choices. This grid has two.
It names a result that stays put. That result is not always best for the pair: both Left pays 2 each, and both Right pays 1 each.