  A supermarket game is considered with $N$ FCFS queues with unit exponential
service rate and global Poisson arrival rate $N \lambda$. Upon arrival each
customer chooses a number of queues to be sampled uniformly at random and joins
the least loaded sampled queue. Customers are assumed to have cost for both
waiting and sampling, and they want to minimize their own expected total cost.
  We study the supermarket game in a mean field model that corresponds to the
limit as $N$ converges to infinity in the sense that (i) for a fixed symmetric
customer strategy, the joint equilibrium distribution of any fixed number of
queues converges as $N \to \infty$ to a product distribution determined by the
mean field model and (ii) a Nash equilibrium for the mean field model is an
$\epsilon$-Nash equilibrium for the finite $N$ model with $N$ sufficiently
large. It is shown that there always exists a Nash equilibrium for $\lambda <1$
and the Nash equilibrium is unique with homogeneous waiting cost for $\lambda^2
\le 1/2$. Furthermore, we find that the action of sampling more queues by some
customers has a positive externality on the other customers in the mean field
model, but can have a negative externality for finite $N$.
