In a multihop wireless network, routing a packet from source to destination requires cooperation among nodes. If nodes are selfish, reputation-based mechanisms can be used to sustain cooperation without resorting to a central authority. Within a hop-by-hop reputation-based mechanism, every node listens to its relaying neighbors, and the misbehaving ones are punished by dropping a fraction of their packets, according to a Tit-for-tat strategy. Packet collisions may prevent a node from recognizing a correct transmission, distorting the evaluated reputation. Therefore, even if all the nodes are willing to cooperate, the retaliation triggered by a perceived defection may eventually lead to zero throughput. A classical solution to this problem is to add a tolerance threshold to the pure Tit-for-tat strategy, so that a limited number of defections will not be punished. In this paper, we propose a game-theoretic model to study the impact of collisions on a hop-by-hop reputation-based mechanism for regular networks with uniform random traffic. Our results show that the Nash Equilibrium of a Generous Tit-for-tat strategy is cooperative for any admissible load, if the nodes are sufficiently far-sighted, or equivalently if the value for a packet to the nodes is sufficiently high with respect to the transmission cost. We also study two more severe punishment schemes, namely One-step Trigger and Grim Trigger, that can achieve cooperation under milder conditions. 1
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