We consider n-person games with quasi-concave payoffs that depend on a player's own
action and the sum of all players' actions. We show that a discrete-time, stochastic process in
which players move towards better replies—the better-reply dynamics—converges globally
to a Nash equilibrium if actions are either strategic substitutes or strategic complements for
all players around each Nash equilibrium that is asymptotically stable under a deterministic,
adjusted best-reply dynamics. We present an example of a 2-person game with a unique …