We study a mixed population of adaptive agents with small and large memorie
s, competing in a minority game. If the agents are sufficiently adaptive, w
e find that the average winnings per agent can exceed that obtainable in th
e corresponding pure populations. In contrast to the pure population, the a
verage success rate of the large-memory agents can be greater than 50%. The
present results are not reproduced if the agents are fed a random history,
thereby demonstrating the importance of memory in this system.