Information-Sharing over Adaptive Networks with Self-interested Agents

TL;DR

This paper studies multi-agent networks with costly information sharing, proposing a reputation-based protocol to incentivize cooperation, which improves overall network performance and stability in mean-square-error estimation tasks.

Contribution

Introduces a reputation protocol that encourages cooperation among self-interested agents, enhancing social benefits in adaptive networks with communication costs.

Findings

Reputation protocol effectively incentivizes cooperation.

Proposed method outperforms always-sharing strategies at high costs.

Network stability is achieved with small step-sizes.

Abstract

We examine the behavior of multi-agent networks where information-sharing is subject to a positive communications cost over the edges linking the agents. We consider a general mean-square-error formulation where all agents are interested in estimating the same target vector. We first show that, in the absence of any incentives to cooperate, the optimal strategy for the agents is to behave in a selfish manner with each agent seeking the optimal solution independently of the other agents. Pareto inefficiency arises as a result of the fact that agents are not using historical data to predict the behavior of their neighbors and to know whether they will reciprocate and participate in sharing information. Motivated by this observation, we develop a reputation protocol to summarize the opponent's past actions into a reputation score, which can then be used to form a belief about the opponent's subsequent actions. The reputation protocol entices agents to cooperate and turns their optimal strategy into an action-choosing strategy that enhances the overall social benefit of the network. In particular, we show that when the communications cost becomes large, the expected social benefit of the proposed protocol outperforms the social benefit that is obtained by cooperative agents that always share data. We perform a detailed mean-square-error analysis of the evolution of the network over three domains: far field, near-field, and middle-field, and show that the network behavior is stable for sufficiently small step-sizes. The various theoretical results are illustrated by numerical simulations.