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.

Theory of Neural Information Processing Systems provides an explicit, coherent, and up-to-date account of the modern theory of neural information processing systems. It has been carefully developed for graduate students from any quantitative dsicipline, including mathematics, computer science, physics, engineering or biology, and has been thoroughly class-tested by the authors over a period of some 8 years. Exercises are presented throughout the text and notes on historical background and further reading guide the student into the literature. All mathematical details are included and appendices provide further background material, including probability theory, linear algebra and stochastic processes, making this textbook accessible to a wide audience.

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.

Theory of Neural Information Processing Systems provides an explicit, coherent, and up-to-date account of the modern theory of neural information processing systems. It has been carefully developed for graduate students from any quantitative dsicipline, including mathematics, computer science, physics, engineering or biology, and has been thoroughly class-tested by the authors over a period of some 8 years. Exercises are presented throughout the text and notes on historical background and further reading guide the student into the literature. All mathematical details are included and appendices provide further background material, including probability theory, linear algebra and stochastic processes, making this textbook accessible to a wide audience.