Adaptive competition, market efficiency, and phase transitions

In many social and biological systems agents simultaneously and adaptively compete for limited resources, thereby altering their environment. We analyze a simple model that incorporates fundamental features of such systems. If the space of strategies available to the agents is small, the system is in a phase in which all information available to the agents' strategies is traded away, and agents' choices are maladaptive, resulting in a poor collective utilization of resources. For larger strategy spaces, the system is in a phase in which the agents are able to coordinate their actions to achieve a better utilization of resources. The best utilization of resources occurs at a critical point, when the dimension of the strategy space is on the order of the number of agents.