Bi-CrowdCache: a Decentralized Game-Theoretic Model for Edge Content Sharing over Time-varying Communication Networks

Mobile edge computing (MEC) is a promising solution for enhancing user experience, minimizing content delivery expenses, and reducing backhaul traffic. This paper presents a game-theoretic framework to address the edge resource crowdsourcing problem, where mobile edge devices (MEDs) provide idle storage for content caching in exchange for rewards from a content provider (CP). We model the interaction between the CP and MEDs as a Stackelberg game, with the CP as the leader setting the reward structure and the MEDs as followers competing in a non-cooperative game for these rewards. We propose a novel privacy-preserving method to derive the Stackelberg equilibrium of the game. Notably, our algorithm is designed to operate effectively in time-varying communication networks, addressing the high mobility inherent in MEC environments. This contrasts with state-of-the-art algorithms, which assume a static communication network among MEDs–an impractical condition that does not account for the mobility of MEDs during algorithm execution. Specifically, our approach employs consensus-based algorithms to compute the Nash equilibrium (NE) for MEDs, with MEDs exchanging NE profile estimates with neighbors via row-stochastic mixing matrices and performing gradient steps to optimize their utility in a fully decentralized manner. Based on the computed NE strategies, we propose a zeroth-order reward search algorithm for the CP to determine the optimal strategy for profit maximization. Our comprehensive analysis details the properties of the equilibrium and establishes the geometric convergence of the proposed algorithms to the NE. We also derive explicit bounds for the stepsizes based on the game's properties and the graphs' connectivity structure. Extensive numerical results validate the efficacy of our proposed approach.