Stability of Evolving Multi-Agent Systems

TL;DR

This paper models the stability of evolving multi-agent systems using Markov chains, introduces an entropy-based measure of instability, and validates the approach through simulations, laying groundwork for digital ecosystems.

Contribution

It extends existing Markov chain models to include evolving agent populations and defines a new entropy-based stability measure for such systems.

Findings

Stability analysis aligns with previous non-evolving models.

Entropy correlates with system instability.

Simulation results support the theoretical framework.

Abstract

A Multi-Agent System is a distributed system where the agents or nodes perform complex functions that cannot be written down in analytic form. Multi-Agent Systems are highly connected, and the information they contain is mostly stored in the connections. When agents update their state, they take into account the state of the other agents, and they have access to those states via the connections. There is also external, user-generated input into the Multi-Agent System. As so much information is stored in the connections, agents are often memory-less. This memory-less property, together with the randomness of the external input, has allowed us to model Multi-Agent Systems using Markov chains. In this paper, we look at Multi-Agent Systems that evolve, i.e. the number of agents varies according to the fitness of the individual agents. We extend our Markov chain model, and define stability. This is the start of a methodology to control Multi-Agent Systems. We then build upon this to construct an entropy-based definition for the degree of instability (entropy of the limit probabilities), which we used to perform a stability analysis. We then investigated the stability of evolving agent populations through simulation, and show that the results are consistent with the original definition of stability in non-evolving Multi-Agent Systems, proposed by Chli and De Wilde. This paper forms the theoretical basis for the construction of Digital Business Ecosystems, and applications have been reported elsewhere.