A Coalitional Game Theoretic Outlook on Distributed Adaptive Parameter Estimation

In this paper, the parameter estimation problem based on diffusion least mean squares strategies is analyzed from a coalitional game theoretical perspective. Specifically, while selfishly minimizing only their own mean-square costs, the nodes in a network form coalitions that benefit them. Due to its nature, the problem is modeled as a non-transferable game and two scenarios are studied, one where each node’s payoff includes only a suitable estimation accuracy criterion and another one in which a graph-based communication cost is also considered. In the former scenario, we first analyze the non-emptiness of the core of the games corresponding to traditional diffusion strategies, and then, the analysis is extended to a recently proposed node-specific parameter estimation setting where the nodes have overlapped but different estimation interests. In the latter scenario, after formulating a coalitional graph game and providing sufficient conditions for its core non-emptiness, we propose a distributed graph formation algorithm, based on merge-and-split approach, which converges to a stable coalition structure.