Winners Take All: A Reverse Consensus Model

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.