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. Also, x i fluctuate in phase, thus yielding a large fluctuation of their sum. Finally, the fluctuations may decrease the average utility in this case. Conclusions - Competitive Nash equilibria are usually affected by very large fluctuations, which increase with the number of players.