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 nontransferable 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 nonemptiness 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 nonemptiness, we propose a distributed graph formation algorithm, based on merge-and-split approach, which converges to a stable coalition structure.