A sensor coverage game with improved efficiency guarantees

Distributed sensor coverage problem deals with designing local policies which enable a collection of mobile sensors placed in a mission space to reach a stable allocation which maximizes the coverage of the mission space. Due to stringent local information restrictions, classical approaches to distributed coverage such as Lloyd's algorithm cannot guarantee the worst case performance to be greater than 1/n of the optimal where n is the number of agents. Can we improve efficiency guarantees by providing additional, but limited information about the mission space to each agent? Modeling sensor coverage problem as a strategic game, we design an agent's payoff as a combination of a local utility function, which computes the marginal contribution of the agent to the system objective, and a network utility function, which computes the potential gain in the system objective that is achievable by relocating any other agent to former's local neighborhood. We show that the worst case efficiency of the designed game is at least 50%: Finally, we prove that the game is weakly acyclic and hence local agent policies such as better/best reply dynamics are guaranteed to converge to an equilibrium.