Reputation plays a key role among the mechanisms supporting cooperation in our society. This is a well-known observation and, in fact, several studies have shown that reputation may substantially increase cooperation among subjects playing Prisoner's Dilemma games in the laboratory. Unfortunately, recent experiments indicate that when reputation can be faked cooperation can still be maintained at the expense of honest subjects who are deceived by the dishonest ones. As experimental work is limited due to financial and other reasons, we present here an agent-based simulation model inspired by, and calibrated against, the results obtained in the experiment. We thus simulate much larger population sizes over longer times, and test other model parameters to see whether the observed behavior generalizes in those yet untried conditions. The results show that the collective behavior is qualitatively similar in larger systems and stable over longer times horizons. We conclude that the findings of the experimental work are meaningful, taking into account that the model is strictly tailored to our particular experimental setting and therefore it is a possible explanation of our observations whose applicability to other contexts requires further research. We argue that simulations like the ones presented here may also be useful to cheaply and quickly suggest settings and options to enhance and facilitate further experiments, which, in turn, may provide new tests of the models themselves.