  The Lipschitz constant of a finite normal-form game is the maximal change in
some player's payoff when a single opponent changes his strategy. We prove that
games with small Lipschitz constant admit pure {\epsilon}-equilibria, and
pinpoint the maximal Lipschitz constant that is sufficient to imply existence
of pure {\epsilon}-equilibrium as a function of the number of players in the
game and the number of strategies of each player. Our proofs use the
probabilistic method.
