Winners Take All: A Reverse Consensus Model

TL;DR

This paper presents a nonlinear multi-agent model illustrating winners-take-all dynamics in resource allocation, which, when reversed in time, resembles a consensus model, with thorough analysis of its properties.

Contribution

It introduces a novel reverse consensus model derived from a winners-take-all framework, linking resource competition with consensus dynamics through rigorous analysis.

Findings

Demonstrates winners-take-all behavior in a zero-sum game

Shows the model converges to equilibrium states of winners and losers

Reveals the reverse-time dynamics resemble a consensus model

Abstract

This paper introduces a nonlinear multi-agent dynamic model that characterizes the resource-seizing mechanism for a fixed amount of resources. The model demonstrates a winners-take-all behavior within a zero-sum game framework. It represents one of the simplest dynamics where equilibria correspond to states of winners and losers, with every trajectory converging to such an equilibrium. Notably, when the model operates in reverse time, it resembles a multi-agent consensus model, referred to as a reverse consensus model. The key characteristics of this model are explored through rigorous analysis.