The Dynamics of Network Minority Game

The evolutionary dynamics of minority games based on three generic networks havebeen investigated :Kauffman’sNKnetworks (Kauffman nets), growing directed networks (GDNets), and growing directed networkswith a small fraction of link reversals (GDRNets).We show that the dynamics and the associated phase structure of the game depend crucially on the structure of the underlying network. The dynamics on GDNets is very stable for all values of the connection numberK, in contrast to the dynamics on Kauffman’s NK networks, which becomes chaotic when K > Kc = 2. The dynamics of GDRNets, on the other hand, is near critical. Under a simple evolutionary scheme, the network system with a “near” critical dynamics evolves to a high level of global coordination among its agents; this suggests that criticality leads to the best performance. For Kauffman nets withK > 3, the evolutionary scheme has no effect on the dynamics (it remains chaotic) and the performance of theMG resembles that of a random choice game (RCG).