Self-Stabilization with Selfish Agents

Self-stabilization is an excellent approach for adding fault tolerance to a distributed multi-agent system. However, two properties of self-stabilization theory, closure and convergence, may not be satisfied if agents are selfish. To guarantee closure in the presence of selfish agents, we propose fault-containment as a method to constrain legitimate configurations of the self-stabilizing system to be Nash equilibria. To guarantee convergence, we introduce probabilistic self-stabilization to set the probabilities of rules such that agents' self-interests are satisfied. We also assume selfish agents as capable of performing unauthorized actions at any time, which threatens both properties, and present a stepwise solution to handle it. As a case study, we consider the problem of distributed clustering and propose self-stabilizing algorithms for forming clusters. Simulation results show that our algorithms react correctly to rule deviations and outperform comparable schemes in terms of fairness and stabilization time.