We consider a version of large population games whose agents compete for resources using strategies with adaptable preferences. The games can be used to model economic markets, ecosystems, or distributed control. Diversity of initial preferences of strategies is introduced by randomly assigning biases to the strategies of different agents. We find that diversity among the agents reduces their maladaptive behavior. We find interesting scaling relations with diversity for the variance and other parameters such as the convergence time, the fraction of fickle agents, and the variance of wealth, illustrating their dynamical origin. When diversity increases, the scaling dynamics is modified by kinetic sampling and waiting effects. Analyses yield excellent agreement with simulations.

We present detailed numerical results for a modified form of the so-called Minority Game, which provides a simplified model of a competitive market. Each agent has a limited set of strategies, and competes to be in a minority. An evolutionary rule for strategy modification is included to mimic simple learning. The results can be understood by considering crowd formation within the population.

We consider a version of large population games whose players compete for resources using strategies with adaptable preferences. The system efficiency is measured by the variance of the decisions. In the regime where the system can be plagued by the maladaptive behavior of the players, we find that diversity among the players improves the system efficiency, though it slows the convergence to the steady state. Diversity causes a mild spread of resources at the transient state, but reduces the uneven distribution of resources in the steady state.

We consider multiagent systems whose agents compete for resources using strategies with adaptable preferences. Diversity of initial preferences of strategies is introduced by randomly assigning virtual points to the strategies of each agent. When diversity increases, the successive appearance of scaling, kinetic sampling and waiting mechanisms shows that agent cooperation becomes increasingly important. Analyses yield excellent agreement with simulations over nine decades of data. Many natural and artificial systems involve interacting agents, each making independent decisions to compete for limited resources, but globally exhibit coordinated behavior through their mutual adaptation [1,2]. Examples include the competition of predators in ecology, buyers or sellers in economic markets, and routers in computer networks. While a standard approach is to analyze the steady state behavior of the system described by the Nash equilibria [3], it is interesting to consider the dynamics of how the steady state is approached. Dynamical effects are especially relevant in a changing environment, such as that in economics or distributed control.Adaptation is a collective dynamical process. When it is achieved by small iterative steps taken by many agents, Hamiltonian functions can be used to analyze the steadystate behavior [4]. However, when it proceeds in large steps, a dynamical approach is more applicable than a gametheoretic approach. For example, when the complexity of the agents in a multiagent system is low, a maladaptive behavior takes place, in which there are bursts of the population's decisions due to their premature rush to certain states they perceive to be advantageous [5,6]. The resultant large fluctuations indicate that the agents fail to cooperate with each other.Maladaptation originates from the uniformly zero preference of strategies in the initial condition. The dependence of initial conditions was noted in a statistical mechanical approach [4]. System efficiency can be improved by random initial conditions in systems driven by internal information [7], or external information [8], accompanied by hysteresis [9]. The same is valid in models with batch update [10] and their noisy extension [11].In this Rapid Communication, we numerically and analytically study the dynamical mechanisms by which agents cooperate with each other to reach steady states. This is done by tuning the diversity of the agents in their initial preferences of strategies, so that the population of agents adapting to the environment at each step becomes increasingly sparse with diversity. When maladaptation gradually vanishes, we look for evidence that cooperative mechanisms among agents become favored or even indispensable. Concretely, we consider a prototype of multiagent systems, in which a population of N agents compete in an environment of limited resources, N being odd [2]. Each agent makes a decision + or − at each time step, and the minority group wins. The decisions of each agent are prescribed by strategies, which are Boolean fu...