  This paper studies the correlations of the average winnings of agents and the
volatilities of systems based on 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 results show
that the correlations between the average winnings of agents and the mean of
local volatilities are different with different combinations of agents' memory
lengths when the proportion of agents in group1 increases. The average winnings
of agents can represent the average individual performance and the volatility
of a system can represent the efficiency of the system. Therefore, these
results imply that the combinations of agents' memory lengths largely influence
the relation between the system efficiency and the average individual
performance. These results could give some guidance in designing complex
systems.
