In reply to Shaoqi Fan.

The answer is that it doesn't matter which one you report. They are all equally valid (or invalid).

It is possible to lie with a simulation. You are using the Monte Carlo estimates to get a handle on the sampling variability, but the fact is that Monte Carlo estimators also have variance. The best advice I can give is to choose the number of MC simulations large enough so that the variance of the MC estimator is an order of magnitude smaller than the standard error of the statistic you are measuring. If that is too hard, then increase the number of MC iterations by 4, which will double the accuracy of the estimates, and see if the results change or essentially stay the same.