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A wireless ad hoc network does not have an infrastructure, and thus, needs the cooperation of nodes in forwarding other nodes' packets. Reputation system is an effective approach to give nodes incentives to cooperate in packet forwarding. However, existing reputation systems either lack rigorous analysis, or have analysis in unrealistic models. In this paper, we propose FITS, the first reputation system that has rigorous analysis and guaranteed incentive compatibility in a practical model. FITS has two schemes: the first scheme is very simple, but needs a Perceived Probability Assumption (PPA); the second scheme uses more sophisticated techniques to remove the need for PPA. We show that both of these two FITS schemes have a subgame perfect Nash equilibrium in which the packet forwarding probability of every node is one. Experimental results verify that FITS provides strong incentives for nodes to cooperate.