  this paper addresses the issue of the relation between the system efficiency
and the individual performance with different combinations of agent memory
lengths in mix-game model which is an extension of minority game (MG). In
mix-game, there are two groups of agents; group1 plays the majority game, but
the group2 plays the minority game. The average winnings of agents can
represent the average individual performance and the volatility of a system can
represent the efficiency of the system. It is found the correlations between
the average winnings of agents and the medians of local volatilities are
different when agent memory lengths change with different combinations of
m1=m2, m1<m2=6 and m2<m1=6. This paper also gives some suggestions for
designing complex competing systems.
