Some ways to see two in one

Abstract

We present work towards claryfing whether and how the idea of agents as "subsystems" of an underlying (artificial) universe can be captured formally. For this we propose formal notions of a universe, a decomposition into subsystems and a criterion to prefer some choices of such decompositions over others. Universes are modelled by finite Markov chains, a decomposition is an information conserving set of subprocesses induced by partitions of the state space and our criterion prefers decompositions that improve predictability by minimizing stochastic interaction. Using very simple examples we find three different classes of Markov chains, with respect to their "decomposability". Our approach also highlights the fact that the stochastic interaction of multivariate finite Markov chains crucially depends on the chosen multivariate structure of the state space.