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Essentials of Econophysics Modelling$
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Frantisek Slanina

Print publication date: 2013

Print ISBN-13: 9780199299683

Published to Oxford Scholarship Online: January 2014

DOI: 10.1093/acprof:oso/9780199299683.001.0001

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Minority game

Minority game

Chapter:
(p.185) 5 Minority game
Source:
Essentials of Econophysics Modelling
Author(s):

František Slanina

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199299683.003.0006

In this chapter we present the minority game, which is one of the keystone models of econophysics. It is the mathematic implementation of the idea of inductive, rather than deductive, thinking. First, we explain how the agents adapt to each other, and how the efficiency of the system as a whole is increased by such an adaptation. Then the properties of the phase transition from efficient but non-ergodic to inefficient ergodic phase is discussed. In the following the replica formalism is introduced, and the full replica solution of the thermal batch minority game is shown. Finally, it is shown what modifications make the minority game useful as a model for stock-market fluctuations.

Keywords:   minority game, induction, frustration, efficiency, ergodicity, phase transition, replica method

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