Stability of Evolving Multiagent Systems

A multiagent system is a distributed system where the agents or nodes perform complex functions that cannot be written down in analytic form. Multiagent 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 multiagent 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 multiagent systems using Markov chains. In this paper, we look at multiagent 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 multiagent 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 nonevolving multiagent 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.