Behaviour Analysis of Mixed Game-Theoretic Learning Algorithms

Distributed optimisation becomes ever more important to boost the operational efficiency of autonomous systems and a number of decision algorithms have been proposed in recent years. A common assumption is usually made that individual agents use the same type of learning algorithm. There are however applications, such as reconfigurable robotics and coordination within robot teams, where this assumption is not always valid. In this paper we propose a methodology that allows the study of agents' joint behaviour when they use different game-theoretic learning algorithms. Our methodology is based on probabilistic model checking, and we use a new a behaviour-similarity-relation to build compact state spaces. Our theory and computational procedures for formal verification provide a framework to study the properties of various algorithms. The proposed methodology is demonstrated on four learning algorithms that are used to provide decisions in distributed optimisation tasks formulated as multi-player games.