Models and Games

Author: Jouko Väänänen

Publisher: Cambridge University Press

ISBN: 1139496336

Category: Mathematics

Page: N.A

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This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.

Algebraic Computability and Enumeration Models

Recursion Theory and Descriptive Complexity

Author: Cyrus F. Nourani

Publisher: CRC Press

ISBN: 1771882484

Category: Mathematics

Page: 310

View: 2135

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This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.

Generalized Descriptive Set Theory and Classification Theory

Author: Sy-David Friedman,Tapani Hyttinen, Vadim Kulikov

Publisher: American Mathematical Soc.

ISBN: 0821894757

Category: Mathematics

Page: 80

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Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Probabilistic Theory of Mean Field Games with Applications I

Mean Field FBSDEs, Control, and Games

Author: René Carmona,François Delarue

Publisher: Springer

ISBN: 3319589202

Category: Mathematics

Page: 714

View: 2449

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This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Probabilistic Theory of Mean Field Games with Applications II

Mean Field Games with Common Noise and Master Equations

Author: René Carmona,François Delarue

Publisher: Springer

ISBN: 3319564366

Category: Mathematics

Page: 700

View: 8192

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This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.

Geometric Analysis

Author: Peter Li

Publisher: Cambridge University Press

ISBN: 1107020646

Category: Mathematics

Page: 406

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Basic techniques for researchers interested in the field of geometric analysis.

Network Economics and the Allocation of Savings

A Model of Peering in the Voice-over-IP Telecommunications Market

Author: Philipp Servatius

Publisher: Springer Science & Business Media

ISBN: 9783642210969

Category: Business & Economics

Page: 297

View: 9305

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This book provides a game theoretic model of interaction among VoIP telecommunications providers regarding their willingness to enter peering agreements with one another. The author shows that the incentive to peer is generally based on savings from otherwise payable long distance fees. At the same time, termination fees can have a countering and dominant effect, resulting in an environment in which VoIP firms decide against peering. Various scenarios of peering and rules for allocation of the savings are considered. The first part covers the relevant aspects of game theory and network theory, trying to give an overview of the concepts required in the subsequent application. The second part of the book introduces first a model of how the savings from peering can be calculated and then turns to the actual formation of peering relationships between VoIP firms. The conditions under which firms are willing to peer are then described, considering the possible influence of a regulatory body.

Generative Social Science: Studies in Agent-Based Computational Modeling

Studies in Agent-Based Computational Modeling

Author: Joshua M. Epstein

Publisher: Princeton University Press

ISBN: 1400842875

Category: Business & Economics

Page: 384

View: 4961

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Agent-based computational modeling is changing the face of social science. In Generative Social Science, Joshua Epstein argues that this powerful, novel technique permits the social sciences to meet a fundamentally new standard of explanation, in which one "grows" the phenomenon of interest in an artificial society of interacting agents: heterogeneous, boundedly rational actors, represented as mathematical or software objects. After elaborating this notion of generative explanation in a pair of overarching foundational chapters, Epstein illustrates it with examples chosen from such far-flung fields as archaeology, civil conflict, the evolution of norms, epidemiology, retirement economics, spatial games, and organizational adaptation. In elegant chapter preludes, he explains how these widely diverse modeling studies support his sweeping case for generative explanation. This book represents a powerful consolidation of Epstein's interdisciplinary research activities in the decade since the publication of his and Robert Axtell's landmark volume, Growing Artificial Societies. Beautifully illustrated, Generative Social Science includes a CD that contains animated movies of core model runs, and programs allowing users to easily change assumptions and explore models, making it an invaluable text for courses in modeling at all levels.

The World in the Model

How Economists Work and Think

Author: Mary S. Morgan

Publisher: Cambridge University Press

ISBN: 0521176190

Category: Business & Economics

Page: 421

View: 3619

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Describes the radical shift in the study of economic science; where arguing with words was replaced by reasoning with mathematical models.

Formal Models of Domestic Politics

Author: Scott Gehlbach

Publisher: Cambridge University Press

ISBN: 0521767156

Category: Mathematics

Page: 228

View: 4919

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A unified and accessible treatment of important formal models of domestic politics appropriate for students in political science and economics.

Analytical Network and System Administration

Managing Human-Computer Systems

Author: Mark Burgess

Publisher: Wiley

ISBN: N.A

Category: Technology & Engineering

Page: 382

View: 7602

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Network and system administration usually refers to the skill of keeping computers and networks running properly. But in truth, the skill needed is that of managing complexity. This book describes the science behind these complex systems, independent of the actual operating systems they work on. It provides a theoretical approach to systems administration that: saves time in performing common system administration tasks. allows safe utilization of untrained and trained help in maintaining mission-critical systems. allows efficient and safe centralized network administration. Managing Human-Computer Networks: Will show how to make informed analyses and decisions about systems, how to diagnose faults and weaknesses Gives advice/guidance as to how to determine optimal policies for system management Includes exercises that illustrate the key points of the book The book provides a unique approach to an old problem and will become a classic for researchers and graduate students in Networking and Computer Science, as well as practicing system managers and system administrators.

Conference Record of FPCA '95

SIGPLAN-SIGARCH-WG2.8 Conference on Functional Programming Languages and Computer Architecture : Papers Presented at the Conference, La Jolla, California, 25-28 June 1995

Author: N.A

Publisher: Assn for Computing Machinery

ISBN: N.A

Category: Computer architecture

Page: 333

View: 1354

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Debt Games

Strategic Interaction in International Debt Rescheduling

Author: Vinod K. Aggarwal,Aggarwal Vinod K.

Publisher: Cambridge University Press

ISBN: 9780521555524

Category: Business & Economics

Page: 613

View: 9992

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This book explains the significant variation that has emerged over time and across cases in international debt rescheduling during the past one hundred and seventy years. Based on a novel situational theory of bargaining, Professor Aggarwal's study provides a method to deduce actors' payoffs in different bargaining situations to develop "debt games," which are then used to predict negotiating outcomes. This integrated political-economic approach to analyze bargaining episodes goes beyond simple economic models or purely descriptive studies. In doing so, it contributes to international political and economic theory, game theory, and historical research on debt negotiations.

Modeling and Simulation

Author: Hartmut Bossel

Publisher: Springer-Verlag

ISBN: 3663108228

Category: Technology & Engineering

Page: 484

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This book is the the English Language Version of the very successful German textbook, "Modellbildung und Simulation". It provides a self-contained and complete guide to the methods and mathematical background of modeling and simulation software of dynamic systems. Furthermore, an appropriate simulation software and a collection of dynamic system models (on the accompanying disk) are highlights of the book/software-Package.Dies ist die englischsprachige Ausgabe des sehr erfolgreichen Lehrbuches "Modellbildung und Simulation". Geboten wird eine vollständige Einführung in die Methoden der Simulation dynamischer Systeme, wobei auch der notwendige mathematische Hintergrund vermittelt wird. Außerdem ist eine Simulationssoftware Bestandteil des Werkes; auf der beiliegenden Diskette befinden sich ferner 50 Beispielsysteme ("Systemzoo"), die zur spielerischen Einübung der verwendeten Verfahren hilfreich sind.

Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

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Introduction to Mathematical Portfolio Theory

Author: Mark S. Joshi,Jane M. Paterson

Publisher: Cambridge University Press

ISBN: 1107042313

Category: Business & Economics

Page: 314

View: 5017

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This concise yet comprehensive guide focuses on the mathematics of portfolio theory without losing sight of the finance.

Mathematics of Collective Action

Author: James Samuel Coleman

Publisher: Transaction Publishers

ISBN: 9780202367316

Category: SOCIAL SCIENCE

Page: 191

View: 5804

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"Philosophers, social scientists, and laymen have used two perspectives in analyzing social action. One sees man's action as the result of causal forces, and the other sees action as purposive and goal directed. Mathematical treatment of social action has shown this same dichotomy. Some models of behavior describe a causal process, in which there is no place for intention or purpose. Most stochastic models of behavior, whether individual or group, are like this. Another body of work, however, employs purpose, anticipation of some future state, and action designed to maximize the proximity to some goal. Classical microeconomic theory, statistical decision theory, and game theory exemplify this direction.This book examines these two directions of work, and makes original contributions to the second. An introductory chapter outlines these two bodies of work, and casts them in a common frame, to display their similarities and differences. Chapter 2 reviews at length recent work in stochastic processes that makes up the first body of work, which sees social action as the resultant of causal forces. The remaining chapters develop a mathematical framework for the study of systems of social action using a purposive theoretical base. These chapters are designed particularly to contribute to the study of collective decisions, a form of social action that has proved particularly challenging to theoretical analysis. First published in 1973, this became a significant work both in problem solving and in the future career of the author. It is of continuing importance to researchers and students interested in statistical analysis."--Provided by publisher.