Analyzing the dynamics of stigmergetic interactions through pheromone games

The concept of stigmergy provides a simple framework for interaction and coordination in multi-agent systems. However, determining the global system behavior that will arise from local stigmergetic interactions is a complex problem. In this paper we propose to use Game Theory to analyze stigmergetic interactions. We show that a system where agents coordinate by sharing local pheromone information can be approximated by a limiting pheromone game in which different pheromone vectors represent player strategies. This game view allows us to use established methods and solution concepts from game theory to describe the properties of stigmergy based systems. Our goal is to provide a new framework to aid in the understanding and design of pheromone interactions. We demonstrate how we can use this system to determine the long term system behavior of a simple pheromone model, by analyzing the convergence properties of the pheromone update rule in the approximating game. We also apply this model to cases where multiple colonies of agents concurrently optimize different objectives. In this case a limiting colony game can be linked to colony level interactions to characterize the global system behavior.