Bayesian Mechanisms and Detection Methods for Wireless Network with Malicious Users

Abstract

Strategic users in a wireless network cannot be assumed to follow the network algorithms blindly. Moreover, some of these users aim to use their knowledge about network algorithms to maliciously gain more resources and also to create interference to other users. We consider a scenario, in which the network and legitimate users gather probabilistic information about the presence of malicious users by observing the network over a long time period. The network (mechanism designer) and legitimate users modify their actions according to this Bayesian information. We consider Bayesian mechanisms, both pricing schemes and auctions, and obtain the Bayesian Nash Equilibrium (BNE) points. The BNE points provide conditions under which, the uncertainty about user's nature (type) is better for regular (legitimate) users. To derive these conditions, we compare the Bayesian case to the complete information case. We obtain the optimal prices and allocations, which counter the malicious users. We also provide detection methods based on machine learning algorithms for the detection of malicious users, by observing the prices and rate allocations. In addition, we provide detection using regression learning by observing the anomalies in the utility functions of malicious users from prices, which is implemented along with the pricing mechanism itself. For the designer and the regular users, in a complementary fashion, the results of the detections provide a better estimate of the statistics of malicious users to implement the pricing mechanisms. We have also proposed a truthful Bayesian mechanism in the presence of malicious users. The numerical studies for malicious user detection are carried out with the model proposed in the paper as well as using real Botnet dataset.