Coexistence with Malicious Nodes: A Game Theoretic Approach

In this paper, we use game theory to study the interactions between a malicious node and a regular node in wireless networks with unreliable channels. Since the malicious nodes do not reveal their identities to others, it is crucial for the regular nodes to detect them through monitoring and observation. We model the malicious node detection process as a Bayesian game with imperfect information and show that a mixed strategy perfect Bayesian Nash Equilibrium (also a sequential equilibrium) is attainable. While the equilibrium in the detection game ensures the identification of the malicious nodes, we argue that it might not be profitable to isolate the malicious nodes upon detection. As a matter of fact, malicious nodes and regular nodes can co-exist as long as the destruction they bring is less than the contribution they make. To show how we can utilize the malicious nodes, a post-detection game between the malicious and regular nodes is formalized. Solution to this game shows the existence of a subgame perfect Nash Equilibrium and the conditions that achieve the equilibrium. Simulation results and their discussions are also provided to illustrate the properties of the derived equilibria.