Econometrica: Sep 1999, Volume 67, Issue 5
On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games
Philip J. RenyA 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.
Log In To View Full Content