The correlation functions decay exponentially, with correlation time given by the minimum eigenvalue. The last term is the average utility at the NE in presence of fluctuations. It is interesting to note that it is possible to get an average utility larger than those for NE strategy . As expected, the fluctuations grow with D i and D 0 . We have a normal behaviour with small fluctuations.
Fluctuations increase the average utility and a rational behaviour is generally more rewarding.
Then g is small and the fluctuations are proportional to n . Indeed it means that each player does not feel the effects of change in their x i directly. Large fluctuations come together with large relaxation times. Finally, the average utility is decreased. The smallest eigenvalue is small, and this means large correlation time.