On the Effectiveness of Punishments in a Repeated Epidemic Dissemination Game

This work uses Game Theory to study the effectiveness of punishments as an incentive for rational nodes to follow an epidemic dissemination protocol. We consider asymmetric interactions and an arbitrary graph. The dissemination process is modeled as an infinite repetition of a stage game, where nodes disseminate a sequence of messages and monitor the actions of their neighbors. At the end of each stage, a monitoring mechanism informs each player of the actions of other nodes. A punishment strategy initially prescribes cooperation between every pair of nodes and triggers defection after any detected misbehavior. The effectiveness of a punishing strategy is measured as the range of values for the benefit-to-cost ratio that sustain cooperation. By initially assuming public monitoring, we show that while direct reciprocity has a low effectiveness for many real scenarios, full indirect reciprocity, where all neighbors of any node i punish i after any deviation, is nearly optimal under certain assumptions. We then extend these results by considering private monitoring, where dissemination of monitoring information is restricted by the topology and may have delays. We first derive a necessary condition for a topology to allow punishments to be effective as an incentive. Then, we show that, unless full indirect reciprocity is used and punishments are coordinated, the effectiveness of any punishing strategy decreases monotonically with an increase in the reliability of the dissemination process. We conclude the paper with a derivation of a lower bound for the effectiveness of coordinated punishments that use full indirect reciprocity, quantifying the impact of delays. From here, we reach the conclusion that punishments should have a duration at least as high as the maximum delay of the monitoring process in order to be effective.