The evolution of strategy scores in the Grand Canonical Minority Game
2016
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 rst go through the basics of the Minority Game and show its
features, then we move on to describe GCMG. In this game we have identied
dierent 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 dierent 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.
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