Agents Play Mix-game

Abstract

In recent years, economics and finance see the shift of paradigm from representative agent models to heterogeneous agent models [1, 2]. More and more economists and physicists made efforts in research on heterogeneous agent models for financial markets. Minority game (MG) proposed by D. Challet, and Y. C. Zhang [3] is an example among such efforts. Challet and Zhang’s MG model, together with the original bar model of Arthur, attracts a lot of following studies [4–6]. Given MG’s richness and yet underlying simplicity, MG has also received much attention as a financial market model [4]. MG comprises an odd number of agents choosing repeatedly between the options of buying (1) and selling (0) a quantity of a risky asset. The agents continually try to make the minority decision, i.e. buy assets when the majority of other agents are selling, and sell when the majority of other agents are buying. Neil F. Johnson [4, 5] and coworkers extended MG by allowing a variable number of active traders at each timestep— they called their modified game as the Grand Canonical Minority Game (GCMG). GCMG, and to a lesser extent the basic MG itself, can reproduce the stylized facts of financial markets, such as volatility clustering and fat-tail distributions.