  We study a competition dynamics, based on the minority game, endowed with
various substrate network structures. We observe the effects of the network
topologies by investigating the volatility of the system and the structure of
follower networks. The topology of substrate structures significantly
influences the system efficiency represented by the volatility and such
substrate networks are shown to amplify the herding effect and cause
inefficiency in most cases. The follower networks emerging from the leadership
structure show a power-law incoming degree distribution. This study shows the
emergence of scale-free structures of leadership in the minority game and the
effects of the interaction among players on the networked version of the game.
