Using decentralized reputation systems is a promising approach to ensuring cooperation and fairness in Mobile Ad-Hoc Networks. However they are vulnerable to liars and robustness has not been analyzed in detail. With our work, we provide a first step to the analysis of a reputation system based on a deviation test. Nodes accept second hand information only if this does not differ too much from their reputation values. Whereas our earlier paper [13] dealt with a simplified one-dimensional model, we now consider the original two-dimensional system. We show that the system exhibits a phase transition: In the subcritical regime, it is robust and lying has no effect. In the supercritical regime, lying does have an impact. We compute the critical values via a mean-field approach and use simulations to verify our results. Thus, we obtain conditions for the deviation test to make the reputation system robust and provide guidelines for a good choice of parameters.
