Minority game with interaction via various networks

We generalize Anghel et al.'s minority game with a substrate network structure among players [Phys. B.ev. Lett. 92, 058701 (2004)]. Changing the type of substrate networks, we investigate the volatility of the system, the structure of follower networks, and the spatial pattern of players' choice. The topology of substrate networks, especially the disorderedness of the small-world substrate network, significantly influences the form of the volatility function. For Erdos-Renyi random networks and scale-free networks as substrate, the follower networks show a power-law degree distribution. In addition, the minority game on two-dimensional regular lattices shows a power-law distribution for the size of the clusters in which all players make the same choice. These findings show the emergence of scale-free structures of cooperation in the minority game and the effects of the underlying substrate structures on the networked version of the game.