A New Framework for Analysis of Coevolutionary Systems - Directed Graph Representation and Random Walks

Studying coevolutionary systems in the context of simplified models (i.e. games with pairwise interactions between coevolving solutions modelled as self plays) re-mains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problem that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modelled as a specific type of Markov chains – random walks on digraphs. Using this framework, we show that coevolu-tionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (t...