Distributed payoff allocation in coalitional games via time varying paracontractions

TL;DR

This paper introduces a distributed algorithm for payoff allocation in coalitional games, utilizing time-varying paracontractions and operator theory to ensure convergence to consensus within a desired set.

Contribution

It provides a novel operator-theoretic framework for analyzing distributed payoff allocation algorithms in dynamic communication networks.

Findings

The proposed algorithm converges to a consensus within the desired set.

Operator-theoretic characterization ensures robustness in time-varying networks.

The approach extends existing methods by incorporating paracontractions for convergence analysis.

Abstract

We present a partial operator-theoretic characterization of approachability principle and based on this characterization, we interpret a particular distributed payoff allocation algorithm to be a sequence of time-varying paracontractions. Further, we also propose a distributed algorithm, under the context of coalitional game, on time-varying communication networks. The state in the proposed algorithm converges to a consensus within, the predefined, desired set. For convergence analysis, we rely on the operator-theoretic property of paracontraction.