Nash Equilibrium Essentials

A combination of strategies where no player can improve their own payoff by changing only their own move, given what everyone else does.

If you froze the game and revealed all choices, every player would say they wouldn't change their move.

That the outcome is good, fair, fun, or socially optimal — only that it's stable.

1) Circle Row's best payoff for each Column choice, 2) circle Column's best payoff for each Row choice, 3) cells with both circles are Nash equilibria.

(Stag, Stag) — great for both — and (Hare, Hare) — mediocre but stable.

(Defect, Defect), giving each player 1 when cooperation would have given 3 — stable but terrible.

Whatever you pick, if the opponent knew it they'd switch, so no cell is regret-free; it needs a mixed (randomized) strategy.

Every game has at least one equilibrium if mixed (randomizing) strategies are allowed.

A solved, boring game — fix by lowering the dominant line's payoff or raising rewards for cooperation.

A communication/social game — good for co-op, negotiation, alliances; play happens between the equilibria.