Multi-hop ad hoc networks are susceptible to selfish misbehavior such as traffic remapping attacks (TRAs). Selfish nodes launching such attacks receive unjustifiably high quality of service (QoS) by assigning higher priority to source packets and lower priority to transit packets. TRAs are easy to execute, impossible to prevent, difficult to detect, and detrimental to the QoS of non-selfish nodes. In this paper we adopt a game-theoretic approach to analyze TRAs in multi-hop ad hoc networks. We present a formal model of plausible opportunistic TRAs and the corresponding one-shot and multistage non-cooperative games. Using a heuristic rank-based payoff function, we propose a boundedly rational multistage attack strategy called REST (Random Exploration until Satisfaction Threshold) that both selfish and non-selfish nodes are free to use, and that allows non-selfish nodes to respond in kind to TRAs. We use simulations to analyze the properties of REST: convergence (whether all nodes eventually become satisfied), rationality (whether all nodes have better QoS), and defensibility (whether non-selfish nodes can improve their QoS). We show that REST converges towards equilibria at which nodes are restrained from executing harmful TRAs, whereas harmless TRAs are permitted. Therefore, REST can be considered an effective countermeasure to TRAs in multi-hop networks.