The evolution of strategy scores in the Grand Canonical Minority Game

Abstract

Understanding nancial markets has always been a subject of interest for economists as well as physicists and mathematicians. In recent years there has been a lot of interest in agent-based models as a tool to understand market dynamics. Grand Canonical Minority Game (GCMG), a development of the Minority Game proposed in 1997, is an agent-based model where the agents, based on assigned strategies, choose one of two sides with the aim of choosing the minority side with the additional option to not participate (as opposed to the basic Minority Game). Such models have shown promise in regards to produce stylized facts from real markets such as heavy tailed price returns as well as volatility clustering around critical states. In this thesis we first go through the basics of the Minority Game and show its features, then we move on to describe GCMG. In this game we have identified different kind of agents, which will be described in detail. The main part of the work has been to formulate a statistical model for the game which characterize the agents mean step size, with a step being how far an agent moves in a time step. From this we have been able to calculate fractions of these different kind of agents as well as the full score distribution of all agents. Our model qualitatively reproduces results from numerical simulations within a range of the reduced amount of speculators in the market (ns 1). This represents a game with a large strategy space compared to the amount of speculators.