Effects of diversity on multiagent systems: Minority games

Abstract

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.

Cascades of Dynamical Transitions in an Adaptive Population

“…As shown in Fig. 1, the dependence of the variance σ 2 /N on the complexity α for linear payoffs is very similar to that for step payoffs [14,15]. For α above a universal critical value α c (≈ 0.3), the variance drops when α is reduced.…”

“…Following steps similar to those in [15], we find that for m not too large, and for convergence within time steps much less than √ R,…”

“…For m = 1, the attractor is described by the sequence µ * (t) = 0, 1, 1, 0, and takes the L-shape as shown in Fig. 3 [15]. Note that the displacements in the two directions may not have the same amplitude.…”

“…In this paper, we compare the behavior of MGs using step and linear payoffs. Previously, we found that the population variance scales as a power law of the diversity for a step payoff [14,15]. Diversity refers to the variance of the initial biases of the strategy payoffs of the agents.…”

Evolutionary dynamics in financial markets with heterogeneities in strategies and risk tolerance

“…For a homogeneous population, the same beliefs and strategies may lead to the same buyingselling actions, which may further lead to the occurrence of herding effect and crowding effect [3,4]. For a heterogeneous population, the different beliefs and strategies may lead to the different buying-selling actions, which may further lead to the slow changes of the prices [5,6,7,8,9,10,11]. Understanding the effects of homogeneous and heterogeneous population on the evolution of stock market is quite important for the risk management and the construction of an efficient market [12,13,14,15,16,17,18].…”