  We consider finite two-player normal form games with random payoffs. Player
A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any
action profile, player B's payoff coincides with player A's payoff with
probability p and is i.i.d. from the same uniform distribution with probability
1-p. This model interpolates the model of i.i.d. random payoff used in most of
the literature and the model of random potential games. First we study the
number of pure Nash equilibria in the above class of games. Then we show that,
for any positive p, asymptotically in the number of available actions, best
response dynamics reaches a pure Nash equilibrium with high probability.
