A game is if for every nonequilibrium strategy and every payoff vector limit resulting from strategies approaching , some player has a strategy yielding a payoff strictly above even if the others deviate slightly from . If strategy spaces are compact and convex, payoffs are quasiconcave in the owner's strategy, and the game is better‐reply secure, then a pure strategy Nash equilibrium exists. Better‐reply security holds in many economic games. It also permits new results on the existence of symmetric and mixed strategy Nash equilibria.