Some experimental and numerical results on Minority Game

Tadeusz Platkowski

Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, POLAND

Across many scientific disciplines there is a growing interest in modeling complex adaptive systems of heterogeneous agents. One of the simplest models for such complex adaptive systems is the Minority Game (MG), introduced by Challet and Zhang as a mathematical model of the system of inductive agents, and applied later e.g. to description of some aspects of financial markets. For various aspects of the MG the reader is refered to the Econophysic web page http://www.unifr.ch/econophysics/. The original MG is an N-person game, where N is an odd number, played by heterogeneous, inductive rational agents, who interact through an aggregate, collective variable. Each agent may choose one of two admissible actions: A or B. Only one of two actions is successful - that chosen by minority. The MG is repeated over time. In each step all agents decide whether to use A or B. Once the actions are chosen, the game is played and all agents get their payoff. All agents have access to the sequence of last M successful actions - this sequence is the only public information in the system. Each agent has at least two strategies, and the strategy with more "virtual" succeses is adopted. We designed and conducted an experiment to see what kind of coordination we can actually observe in real systems of agents which play the MG. In the experiment a group of students played the standard MG and observed the results of the game (history - public information) on monitors in a computer lab. At each unit of the game the only information displayed on the monitors consisted of a raw of M binary digits, 0 or 1, which indicated which option (0 or 1) has been chosen by the minority of the players in the previous M games. There were several rounds, each with a different value of M (varying from 3 through 11). The players knew only the basic principles of the game: those who are at a given stage of the game in minority win the stage, those in majority loose. The results of the experiment indicate that humans do coordinate when playing the MG. The level of coordination, measured by the volatility of the system, does not seem to depend substantially on the length of the memory. An interesting finding is that the random signal does not seem to lead to an efficient equilibrium. We report also results of numerical simulations of the MG in which the agents can play the game on one of two markets and can choose one of them using some optimization schemes, which depend e.g. on performances of their strategies or the wealth accumulated on the markets.