2005/05/24 by K. P. Chan, P. M. Hui, Pak Ming Hui +4
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Game Theory and Applications #Opinion Dynamics and Social Influence #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.cond-mat/0505581
14 pages, 3 figures, conference paper in WEHIA 2005
openalex publication_date 2005/05/24 · arxiv created 2005/05/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Minority Game (MG) is a basic multi-agent model representing a simplified and binary form of the bar attendance model of Arthur. The model has an informationally efficient phase in which the agents lack the capability of exploiting any information in the winning action time series. We develop a theory based on the ranking patterns of the strategies and the number of agents using a particular rank of strategies as the game proceeds. The theory is applied to calculate the distribution or probability density function in the number of agents making a particular decision. From the distribution, the standard deviation in the number of agents making a particular choice (e.g., the bar attendance) can be calculated in the efficient phase as a function of the parameter m specifying the agent's memory size. Since situations with tied cumulative performance of the strategies often occur in the efficient phase and they are critical in the decision making dynamics, the present theory is developed to take into account the effects of tied strategies. The analytic results are found to be in better agreement with numerical results, when compared with the simplest forms of the crowd-anticrowd theory in which cases of tied strategies are ignored. Hence the present theory represents a generalization of the crowd-anticrowd theory of multi-agent models, by focusing on the evolution of strategy ranking patterns instead of the performance of individual strategies. Paper to be presented in the 10th Annual Workshop on Economic Heterogeneous Interacting Agents (WEHIA 2005), 13-15 June 2005, University of Essex, UK.