Characterizing game dynamics in two-player strategy games using network motifs

Many complex systems, whether biological, sociological, or physical ones, can be represented using networks. In these networks, a node represents an entity, and an arc represents a relationship/constraint between two entities. In discrete dynamics, one can construct a series of networks with each network representing a time snapshot of interaction among the different components in the system. Understanding these networks is a key to understand the dynamics of real and artificial systems. Network motifs are small graphs-usually three to four nodes-representing local structures. They have been widely used in studying complex systems and in characterizing features on the system level by analyzing locally how the substructures are formed. Frequencies of different network motifs have been shown in the literature to vary from one network to another, and conclusions hypothesized that these variations are due to the evolution/dynamics of the system. In this paper, we show for the first time that in strategy games, each game (i.e., type of dynamism) has its own signature of motifs and that this signature is maintained during the evolution of the game. We reveal that deterministic strategy games have unique footprints (motifs' count) that can be used to recognize and classify the game's type and that these footprints are consistent along the evolutionary path of the game. The findings of this paper have significance for a wide range of fields in cybernetics.