Asymptotic Consensus Without Self-Confidence

TL;DR

This paper demonstrates that asymptotic consensus can be achieved without agents having self-confidence by using aperiodic cores, enabling convergence even with message delays and memory loss.

Contribution

It introduces the concept of aperiodic cores as a replacement for self-confidence, broadening the conditions under which consensus is guaranteed.

Findings

Aperiodic cores ensure asymptotic consensus without self-confidence.

Results apply to systems with message delays and memory loss.

Self-confidence can be replaced by stable aperiodic subgraphs.

Abstract

This paper studies asymptotic consensus in systems in which agents do not necessarily have self-confidence, i.e., may disregard their own value during execution of the update rule. We show that the prevalent hypothesis of self-confidence in many convergence results can be replaced by the existence of aperiodic cores. These are stable aperiodic subgraphs, which allow to virtually store information about an agent's value distributedly in the network. Our results are applicable to systems with message delays and memory loss.