Dynamic Peer-to-Peer Competition

TL;DR

This paper models market competition among agents using a Lotka-Volterra framework, revealing how agent size dynamics can lead to chaotic or stable behaviors depending on parameters and initial conditions.

Contribution

It introduces a novel nonlinear dynamic model for market competition based on prey-predator equations, analyzing stability and complex behaviors in multiagent systems.

Findings

Different dynamic regimes from chaos to stability depending on parameters.

Analytical fixed points and their stability for small systems.

Self-organized competition emerging from size similarity dynamics.

Abstract

The dynamic behavior of a multiagent system in which the agent size $s_{i}$ is variable it is studied along a Lotka-Volterra approach. The agent size has hereby for meaning the fraction of a given market that an agent is able to capture (market share). A Lotka-Volterra system of equations for prey-predator problems is considered, the competition factor being related to the difference in size between the agents in a one-on-one competition. This mechanism introduces a natural self-organized dynamic competition among agents. In the competition factor, a parameter $\sigma$ is introduced for scaling the intensity of agent size similarity, which varies in each iteration cycle. The fixed points of this system are analytically found and their stability analyzed for small systems (with $n=5$ agents). We have found that different scenarios are possible, from chaotic to non-chaotic motion with cluster formation as function of the $\sigma$ parameter and depending on the initial conditions imposed to the system. The present contribution aim is to show how a realistic though minimalist nonlinear dynamics model can be used to describe market competition (companies, brokers, decision makers) among other opinion maker communities.