Evolutionary game theoretic analysis of distributed denial of service attacks in a wireless network

We consider a wireless network of M users connected to an access point in the presence of N jammers whose purpose is to deny or degrade the performance of the users by injecting interference. Using the achieved signal to inference plus noise ratio (SINR) as the performance metric, we study the dynamics of such a distributed denial of service attack (DDoA) by using Evolutionary Game Theory (EGT). Specifically, we consider a cooperative network model, where the M users (and N jammers) can collectively enhance their achieved SINR (degrade the user SINR). We model the strategic transmission decisions of the users (and the jammers) using simple random access techniques where the users (and jammers) decide to transmit or not with a transmission probability, taking into account their energy costs. Using the replicator dynamics (RD), we characterize the evolutionary stable strategies (ESS's) of the game and observe that the resulting transmission probabilities turn out to be either 0 or 1. Further, given a network (channel) setting, we show using a phase portrait of the replicator dynamics how the ESS strategies evolve for different cooperation levels of the users and jammers populations. We also provide insights into resulting ESS strategies as a function of the number of users and jammers, and their channel qualities.