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What is a game? Classically, a game is perceived as something played by human beings. Its mathematical analysis is human-centered, explores the structures of particular games, economic or social environments and tries to model supposedly "rational" human behavior in search of appropriate "winning strategies". This point of view places game theory into a very special scientific corner where mathematics, economics and psychology overlap and mingle. This book takes a novel approach to the subject. Its focus is on mathematical models that apply to game theory in particular but exhibit a universal character and thus extend the scope of game theory considerably. This textbook addresses anyone interested in a general game-theoretic view of the world. The reader should have mathematical knowledge at the level of a first course in real analysis and linear algebra. However, possibly more specialized aspects are further elaborated and pointers to relevant supplementary literature are given. Moreover, many examples invite the reader to participate "actively" when going through the material. The scope of the book can be covered in one course on Mathematical Game Theory at advanced undergraduate or graduate level.

Game theory. --- Théorie des jeux

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This book is an introduction to the mathematics of non-cooperative game theory. Each concept is explained in detail, starting from a main example, with a slowpaced proof of each theorem. The book has been designed and tested for self-study, and as an undergraduate course text with core chapters and optional chapters for different audiences. It has been developed over 15 years for a one-semester course on game theory at the London School of Economics and the distance learning program of the University of London, attended each year by about 200 third-year students in mathematics, economics, management, and other degrees. After studying this book, a student who started from first-year mathematics (the basics of linear algebra, analysis, and probability) will have a solid understanding of the most important concepts and theorems of non-cooperative game theory.

Game theory --- Game theory. --- Théorie des jeux. --- Théorie des jeux.

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This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff's Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth-death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.

Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- kansrekening

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Control theory --- Game theory. --- Mathematical models. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics

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"Résister signifie s'obstiner à prophétiser la vie éternelle de la pensée non comme simulation automatique mais comme répétition infinie de son commencement." Considérée comme de l'information, la connaissance est aujourd'hui produite de manière automatique, devenant le principal bien de consommation au sein d'une économie se régissant d'après l'innovation permanente. Cet ouvrage va parcourir les étapes les plus significatives du débat qui a conduit à l'élaboration de la procédure d'apprentissage probabiliste permettant aujourd'hui d'automatiser et d'accélérer l'évolution du savoir dans le cadre compétitif de la théorie des jeux. Contre le régime de vérité lié à l'efficacité pragmatique des stratégies adoptées, il propose de reconsidérer le rôle de la connaissance esthétique et de la réflexion philosophique comme visant la vérité du singulier, ce qui échappe à toute généralisation statistique.

Théorie de la connaissance. --- Réflexion (philosophie) --- Information, Théorie de l'. --- Knowledge economy --- Game theory --- Induction (Logic)