Human behavioral regularity, fractional Brownian motion, and exotic phase transition

• We develop a market-based Janus game for studying the competition and cooperation between suppliers and consumers.
• Human behavioral regularity can be characterized by the fractional Brownian motion.
• An exotic transition between periodic and non-periodic phases has been revealed.
• Human experiments are conducted, yielding convincing evidences.

The mix of competition and cooperation (C&C) is ubiquitous in human society, which, however, remains poorly explored due to the lack of a fundamental method. Here, by developing a Janus game for treating C&C between two sides (suppliers and consumers), we show, for the first time, experimental and simulation evidences for human behavioral regularity. This property is proved to be characterized by fractional Brownian motion associated with an exotic transition between periodic and nonperiodic phases. Furthermore, the periodic phase echoes with business cycles, which are well-known in reality but still far from being well understood. Our results imply that the Janus game could be a fundamental method for studying C&C among humans in society, and it provides guidance for predicting human behavioral activity from the perspective of fractional Brownian motion.