| Description | | - Self-contained and detailed account of mathematical methods in Minority Games
- Well-structured and rigorous mathematical approach
- Clearly explains relations between different mathematical methods
- Contains extensive numerical simulation data
| Minority games are simple mathematical models initially designed to understand the co-operative phenomena observed in markets.
Their core ingredients are large numbers of interacting decision-making agents, each aiming for personal gain in an artificial `market' by trying to anticipate (on the basis of incomplete information, and with an element of irrationality) the actions of others. Gain
is made by those who subsequently find themselves in the minority group, e.g. those who end up buying when most wish to sell or vice versa.
Aimed at researchers and students in physics, mathematics and economics this text describes the mathematical theory of Minority Games from a statistical mechanics viewpoint. It provides a detailed and explicit introduction to the advanced mathematical
analysis of these models, describes the potential and restrictions of physical methods in solving agent based market models, and outlines how different mathematical approaches are related. |
Readership: Mathematicians, physicists, economists, financial practitioners, and those interested in the dynamics of financial markets and agent-based models.
| Contents |
1.
Introduction
2.
Preparing the stage for statistical mechanics
3.
Pseudo-equilibrium replica analysis
4.
Dynamics of the batch MG with fake memory
5.
Dynamics of the on-line MG with fake memory
6.
The overall bid distribution
7.
MG versions with new types of phase transitions
8.
Dynamics of MGs with true market history
9.
Variations and generalizations
10.
Notes
Appendices
Simple mathematical conventions and tools
Integrals
Moments of random matrices
Expansion of bid sign recurrence probabilities
Combinatorics in history frequency moments
Details of numerical simulation experiments
References
Index
|
| Authors, editors,
and contributors |
A.C.C. Coolen, King's College, London
|
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