Design and Mathematical Analysis of Agent-Based Systems

Abstract

Agent-based systems that are composed of simple locally interacting agents but which demonstrate complex group behavior offer several advantages over traditional multi-agent systems. A well-designed complex agent-based systems is an efficient, robust, adaptive and stable system. It has very low communication and computational requirements, meaning that there are virtually no constraints on the system size. The simplicity of agent interactions also makes it amenable to quantitative mathematical analysis. In addition to offering predictive power, mathematical analysis enables the system designer to optimize system performance.To date, there have been relatively few implementations of complex agent-based systems, mainly because of the difficulty of determining what simple agent strategies will lead to desirable collective behavior in a large system. We claim that there exists a set of primitive agent strategies, similar to the basis behaviors in behavior-based robotics, from which complex group behavior can be designed. Moreover, these simple primitive strategies naturally lend themselves to mathematical description, making a quantitative study of agent-based systems possible. We present a case study of coalition formation to show that two simple behaviors, dispersion and aggregation, can lead to coalition formation in a multi-agent system under some conditions. We use this system to illustrate the process by which a mathematical description of the agent-based system is created and analyzed, and discuss the insights the analysis provides for designing coalition forming agents.