An Evolutionary Game model for threat revocation in ephemeral networks

We consider a wireless network of M nodes connected together in a decentralized way (for example as an ad hoc network), and according to pre-specified rules. There are other malicious node(s) which can be either inserted or infected which are trying to disturb the operation of the network. The nodes are cooperating to defend the network (and eventually themselves) by isolating the misbehaved node(s). We approach this problem using Evolutionary Game Theory (EGT), and characterize the robust equilibrium point(s) for this game. The game is formulated such that all the nodes take part in the decision process to avoid problems caused by unsuccessful revocation or over reacted revocation decisions. Each node in the network (interchangeably called benign node to distinguish it from the malicious node or the intruder) has three decisions to make: (a) abstain or do nothing; (b) self-sacrifice by disconnecting the intruder and itself; and (c) voting to isolate the intruding node. Each decision has its advantages and disadvantages and the Replicator Dynamics (RD) is used to show the dynamics of the nodes' decisions. By simulating the RD equation, two different cases emerge as Evolutionary Stable Strategies (ESS) where one of them is the desired ESS, and the other is not. Phase portrait diagrams are used to characterize the fraction of the M nodes needed to choose each one of these ESS's, the rate of convergence, and the effect of increasing the cooperation rewards.