  We continue our study of evolution in minority games by examining games in
which agents with poorly performing strategies can trade in their strategies
for new ones from a different strategy space. In the context of the games
discussed in this paper, this means allowing for strategies that use
information from different numbers of time lags, m. We find, in all the games
we study, that after evolution, wealth per agent is high for agents with
strategies drawn from small strategy spaces (small m), and low for agents with
strategies drawn from large strategy spaces (large m). In the game played with
N agents, wealth per agent as a function of m is very nearly a step function.
The transition is at m=mt, where mt~mc-1. Here mc is the critical value of m at
which N agents playing the game with a fixed strategy space (fixed m) have the
best emergent coordination and the best utilization of resources. We also find
that overall system-wide utilization of resources is independent of N.
Furthermore, although overall system-wide utilization of resources after
evolution varies somewhat depending on some other aspects of the evolutionary
dynamics, in the best cases, utilization of resources is on the order of the
best results achieved in evolutionary games with fixed strategy spaces. Simple
explanations are presented for some of our main results.
