The Mathematical Theory Of Minority Games: Statistical Mechanics Of Interacting Agents

Hardcover | January 15, 2005

byA.C.C. Coolen

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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 whosubsequently 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 thepotential and restrictions of physical methods in solving agent based market models, and outlines how different mathematical approaches are related.

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From the Publisher

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 ...

A.C.C. Coolen is at King's College, London.

other books by A.C.C. Coolen

Format:HardcoverDimensions:344 pages, 9.45 × 6.61 × 0.93 inPublished:January 15, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198520808

ISBN - 13:9780198520801

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Extra Content

Table of Contents

1. Introduction2. Preparing the stage for statistical mechanics3. Pseudo-equilibrium replica analysis4. Dynamics of the batch MG with fake memory5. Dynamics of the on-line MG with fake memory6. The overall bid distribution7. MG versions with new types of phase transitions8. Dynamics of MGs with true market history9. Variations and generalizations10. NotesAppendicesSimple mathematical conventions and toolsIntegralsMoments of random matricesExpansion of bid sign recurrence probabilitiesCombinatorics in history frequency momentsDetails of numerical simulation experimentsReferencesIndex