In a multi-agent system such as the minority game, a large population of agents complete for limited resources using their own strategies adaptively. The efficiency of system can be revealed from the variance of decisions. By introducing diversity among agents, the system efficiency can be improved. We find that the dynamics depends on the payoff function used by the agents to evaluate their strategies. For step payoff functions used in the basic minority game, the variance shows the scaling behavior over a wide range of diversity. For linear payoff functions, a phase transition appears on varying the diversity in the limit of very low complexity. While for the quadratic payoff functions, small and large variances coexist at the same diversity, with the basins of attraction varying with...[ Read more ]

In a multi-agent system such as the minority game, a large population of agents complete for limited resources using their own strategies adaptively. The efficiency of system can be revealed from the variance of decisions. By introducing diversity among agents, the system efficiency can be improved. We find that the dynamics depends on the payoff function used by the agents to evaluate their strategies. For step payoff functions used in the basic minority game, the variance shows the scaling behavior over a wide range of diversity. For linear payoff functions, a phase transition appears on varying the diversity in the limit of very low complexity. While for the quadratic payoff functions, small and large variances coexist at the same diversity, with the basins of attraction varying with the diversity and the variance depends on the initial position.