We study a variation of the minority game. There are N agents. Each has to
choose between one of two alternatives everyday, and there is reward to each
member of the smaller group. The agents cannot communicate with each other, but
try to guess the choice others will make, based only the past history of number
of people choosing the two alternatives. We describe a simple probabilistic
strategy using which the agents acting independently, can still maximize the
average number of people benefitting every day. The strategy leads to a very
efficient utilization of resources, and the average deviation from the maximum
possible can be made of order $(N^{\epsilon})$, for any $\epsilon >0$. We also
show that a single agent does not expect to gain by not following the strategy.