Resource Allocation and Pricing in Non-cooperative Interference Networks 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 general model of Multiple Access Channel (MAC) without successive interference cancellation (SIC) under Quality of Service (QoS) requirement of each user where malicious behavior exists. We model the heterogeneous behavior of users, which ranges from altruistic to selfish and then to malicious, within the analytical framework of game theory. To ensure the QoS requirements with efficient resource allocation, the noncooperative game in normal form is formulated and the Nash Equilibrium (NE) power allocation is derived in closed form. The effects of malicious behavior in network resource allocation mechanisms such as auctions and pricing schemes are studied. We consider firstly the problem of net utility maximization and then individual user QoS requirement satisfaction. We show that the well-known Vicrey-Clarke-Groves (VCG) mechanism loses its efficiency property in the presence of malicious users, which motivates the need to quantify the effect of malicious behavior. Then, the Price of Malice of the VCG mechanism and of some other network mechanisms are derived. Differentiated pricing as a method to counter adversarial behaviors is discussed. Next, we consider power allocation in wireless networks subject to QoS requirements of the users. Given the designed individual prices, the best response (BR) power converges to the unique NE power allocation rapidly, where the QoS requirement of each transmitter is satisfied. The impact of the malicious behavior on other users with QoS requirements is analyzed and the punishment prices are designed. We show that in the proposed noncooperative power allocation game, the user misbehavior is predicted, detected and prevented. As a result, all rate requirements in the capacity region of the general MAC are achieved at the NE point. Next we consider a scenario, in which a mechanism designer and legitimate users gather probabilistic information about the presence of malicious users by observing the network over a long time period and modify their actions accordingly. We analyze Bayesian mechanisms, both pricing schemes and auctions, and obtain the Bayesian Nash Equilibrium (BNE) points. The BNE points provide conditions indicating when the uncertainty about their nature (type) is better for regular users. Finally, we extend Bayesian pricing mechanisms to wireless networks subject to QoS requirements of the users.