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Neural Approximations for Optimal Control and Decision provides a comprehensive methodology for the approximate solution of functional optimization problems using neural networks and other nonlinear approximators where the use of traditional optimal control tools is prohibited by complicating factors like non-Gaussian noise, strong nonlinearities, large dimension of state and control vectors, etc. Features of the text include: * a general functional optimization framework; * thorough illustration of recent theoretical insights into the approximate solutions of complex functional optimization problems; * comparison of classical and neural-network based methods of approximate solution; * bounds to the errors of approximate solutions; * solution algorithms for optimal control and decision in deterministic or stochastic environments with perfect or imperfect state measurements over a finite or infinite time horizon and with one decision maker or several; * applications of current interest: routing in communications networks, traffic control, water resource management, etc.; and * numerous, numerically detailed examples. The authors' diverse backgrounds in systems and control theory, approximation theory, machine learning, and operations research lend the book a range of expertise and subject matter appealing to academics and graduate students in any of those disciplines together with computer science and other areas of engineering.
Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Its central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. 1982 edition.
Addressed to 2nd- and 3rd-year students, this work by a
world-famous teacher skillfully spans the pure and applied
branches, so that applied aspects gain in rigor while pure
mathematics loses none of its dignity. Equally essential as a text,
a reference, or simply as a brilliant mathematical exercise. 1971
The results presented here (including the assessment of a new tool - inhibitory trees) offer valuable tools for researchers in the areas of data mining, knowledge discovery, and machine learning, especially those whose work involves decision tables with many-valued decisions. The authors consider various examples of problems and corresponding decision tables with many-valued decisions, discuss the difference between decision and inhibitory trees and rules, and develop tools for their analysis and design. Applications include the study of totally optimal (optimal in relation to a number of criteria simultaneously) decision and inhibitory trees and rules; the comparison of greedy heuristics for tree and rule construction as single-criterion and bi-criteria optimization algorithms; and the development of a restricted multi-pruning approach used in classification and knowledge representation.
'A comprehensive, concise, and practical guide that will enable anyone, in any situation, to develop their strategic thinking' Tiffani Bova, Chief Growth Evangelist, Salesforce, WSJ bestselling author, Growth IQ Being strategic is a critical skill. It enables you to solve problems on a day-to-day basis while also keeping an eye on the long term, anticipating and mitigating opportunities and threats along the way. How to be Strategic is your accessible but comprehensive guide to strategic thinking in any situation. Fred Pelard distills 20 years' experience training executives at all levels from leading companies around the world into a range of smartly-illustrated, workable methodologies that will enable you to understand each approach and find your own path to the right solution every time. 'A wonderful and inspirational look into wide-ranging frameworks and theories to spark new thinking and strategy' Tom Goodwin, author of Digital Darwinism and Head of Futures and Insight at Publicis Groupe 'Practical and comprehensive' Roeland Assenberg, Director, Strategy and Banking, Monitor Deloitte Netherlands
Game theory means rigorous strategic thinking. It s the art of anticipating your opponent s next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies from pop culture, TV, movies, sports, politics, and history the authors show how nearly every business and personal interaction has a game-theory component to it. Mastering game theory will make you more successful in business and life, and this lively book is the key to that mastery."
This comprehensive textbook introduces readers to the principal ideas and applications of game theory, in a style that combines rigor with accessibility. Steven Tadelis begins with a concise description of rational decision making, and goes on to discuss strategic and extensive form games with complete information, Bayesian games, and extensive form games with imperfect information. He covers a host of topics, including multistage and repeated games, bargaining theory, auctions, rent-seeking games, mechanism design, signaling games, reputation building, and information transmission games. Unlike other books on game theory, this one begins with the idea of rationality and explores its implications for multiperson decision problems through concepts like dominated strategies and rationalizability. Only then does it present the subject of Nash equilibrium and its derivatives.
"Game Theory" is the ideal textbook for advanced undergraduate and beginning graduate students. Throughout, concepts and methods are explained using real-world examples backed by precise analytic material. The book features many important applications to economics and political science, as well as numerous exercises that focus on how to formalize informal situations and then analyze them. Introduces the core ideas and applications of game theory Covers static and dynamic games, with complete and incomplete information Features a variety of examples, applications, and exercises Topics include repeated games, bargaining, auctions, signaling, reputation, and information transmission Ideal for advanced undergraduate and beginning graduate students Complete solutions available to teachers and selected solutions available to students
Following the successful PCS Auction conducted by the US Federal Communications Commission in 1994, auctions have replaced traditional ways of allocating valuable radio spectrum, a key resource for any mobile telecommunications operator. Spectrum auctions have raised billions of dollars worldwide and have become a role model for market-based approaches in the public and private sectors. The design of spectrum auctions is a central application of game theory and auction theory due to its importance in industry and the theoretical challenges it presents. Several auction formats have been developed with different properties addressing fundamental questions about efficiently selling multiple objects to a group of buyers. This comprehensive handbook features classic papers and new contributions by international experts on all aspects of spectrum auction design, including pros and cons of different auctions and lessons learned from theory, experiments, and the field, providing a valuable resource for regulators, telecommunications professionals, consultants, and researchers.
Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.
The Selfish Gene is a classic exposition of evolutionary thought. In it Professor Dawkins articulates a gene's eye view of evolution - a view giving centre stage to these persistent units of information, and in which organisms can be seen as vehicles for the replication of genes. The book provoked widespread and heated debate, which in part led Dawkins to write The Extended Phenotype, in which he gave a deeper clarification of the central concept of the gene as the unit of selection, as well as contributing his own development of this insight. For the first time, The Extended Selfish Gene brings these two books together, by including two key chapters from The Extended Phenotype. These chapters provide Dawkins's detailed and powerful response to two issues raised by critics of The Selfish Gene: the accusations of genetic determinism (the idea that our behaviour is entirely determined by our genes), and of "adaptationism " (that all traits are indiscriminately perceived to be adaptations resulting from natural selection). While written in particular for the biology community, Dawkins's clarity of expression allows these chapters to be accessible to all who are seriously engaged with the gene's eye view and its implications. The imaginative, powerful, and stylistically brilliant Selfish Gene not only brought the insights of Neo-Darwinism to a wide audience, but galvanized the biology community, generating much debate and stimulating whole new areas of research. Forty years later, its insights remain as significant as on the day it was published. Along with the two extra chapters, The Extended Selfish Gene includes a new epilogue to The Selfish Gene from the author which highlights the relevance of the gene's eye view to evolutionary biology today.
Games are everywhere: Drivers manoeuvring in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. A firm negotiating next year's wage is playing a bargaining game. The opposing candidates in an election are playing a political game. The supermarket's price for corn flakes is decided by playing an economic game. Game theory is about how to play such games in a rational way. Even when the players have not thought everything out in advance, game theory often works for the same reason that mindless animals sometimes end up behaving very cleverly: evolutionary forces eliminate irrational play because it is unfit. Game theory has seen spectacular successes in evolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science. This Very Short Introduction introduces the fascinating world of game theory, showing how it can be understood without mathematical equations, and revealing that everything from how to play poker optimally to the sex ratio among bees can be understood by anyone willing to think seriously about the problem. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rely almost entirely on a single analysis framework, that of worst-case analysis, wherein an algorithm is assessed by its worst performance on any input of a given size. The purpose of this book is to popularize several alternatives to worst-case analysis and their most notable algorithmic applications, from clustering to linear programming to neural network training. Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.
The Great War is an immense, confusing and overwhelming historical conflict - the ideal case study for teaching game theory and international relations. Using thirteen historical puzzles, from the outbreak of the war and the stability of attrition, to unrestricted submarine warfare and American entry into the war, this book provides students with a rigorous yet accessible training in game theory. Each chapter shows, through guided exercises, how game theoretical models can explain otherwise challenging strategic puzzles, shedding light on the role of individual leaders in world politics, cooperation between coalitions partners, the effectiveness of international law, the termination of conflict, and the challenges of making peace. Its analytical history of World War I also surveys cutting edge political science research on international relations and the causes of war. Written by a leading game theorist known for his expertise of the war, this textbook includes useful student features such as chapter key terms, contemporary maps, a timeline of events, a list of key characters and additional end-of-chapter game-theoretic exercises.
Game theory has revolutionised our understanding of industrial organisation and the traditional theory of the firm. Despite these advances, industrial economists have tended to rely on a restricted set of tools from game theory, focusing on static and repeated games to analyse firm structure and behaviour. Luca Lambertini, a leading expert on the application of differential game theory to economics, argues that many dynamic phenomena in industrial organisation (such as monopoly, oligopoly, advertising, R&D races) can be better understood and analysed through the use of differential games. After illustrating the basic elements of the theory, Lambertini guides the reader through the main models, spanning from optimal control problems describing the behaviour of a monopolist through to oligopoly games in which firms' strategies include prices, quantities and investments. This approach will be of great value to students and researchers in economics and those interested in advanced applications of game theory.
The second edition of this 5-volume handbook is intended to be a basic yet comprehensive reference work in combinatorial optimization that will benefit newcomers and researchers for years to come. This multi-volume work deals with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The editors have brought together almost every aspect of this enormous field of combinatorial optimization, an area of research at the intersection of applied mathematics, computer science, and operations research and which overlaps with many other areas such as computation complexity, computational biology, VLSI design, communications networks, and management science. An international team of 30-40 experts in the field form the editorial board. The Handbook of Combinatorial Optimization, second edition is addressed to all scientists who use combinatorial optimization methods to model and solve problems. Experts in the field as well as non-specialists will find the material stimulating and useful.
ELEMENTARY LINEAR ALGEBRA, 8E, INTERNATIONAL METRIC EDITION's clear, careful, and concise presentation of material helps you fully understand how mathematics works. The author balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system. To engage you in the material, a new design highlights the relevance of the mathematics and makes the book easier to read. Data and applications reflect current statistics and examples, demonstrating the link between theory and practice. The companion website LarsonLinearAlgebra.com offers free access to multiple study tools and resources. CalcChat.com offers free step-by-step solutions to the odd-numbered exercises in the text.
Andreu Mas-Colell revolutionized our understanding of competitive markets, price formation, and the behavior of market participants. General Equilibrium and Game Theory offers readers a compendium of his most important scholarly contributions, gathering in a single volume the groundbreaking papers that have solidified his standing as one of the preeminent economic theorists of our time. Built upon the foundations of neoclassical economics, Mas-Colell's work is distinguished by a mathematical and analytical elegance that brings theory closer to real-world situations. He overturns the standard assumption of general equilibrium theory-that markets are perfectly competitive and their participants are perfectly rational-and concludes that neither the law of supply and demand nor the existence of equilibrium prices depends on the rationality of agents. Similarly, Mas-Colell (working with Sergiu Hart) challenges classical game theory's reliance on rational behavior, demonstrating that adaptation and learning shape the dynamics of repeated games. Addressing central questions of finance, trade, industrial organization, and welfare economics, Mas-Colell shows the surprising power and versatility of differentiability and linear-space mathematical techniques, and he emphasizes the fruitfulness of cooperative game-theory approaches, such as Shapley value theory and the Bargaining Set, for understanding competition and distribution. General Equilibrium and Game Theory is a signal contribution to economic theory and an invaluable resource for anyone wishing to study the craft of a master of economic modeling.
This book offers a unique and insightful econometric evaluation of the policies used to fight transnational terrorism between 1990 and 2014. It uses the tools of modern economics, game theory and structural econometrics to analyze the roles of foreign aid, educational capital, and military intervention. Jean-Paul Azam and Veronique Thelen analyze panel data over 25 years across 124 countries. They prove that foreign aid plays a key role in inducing recipient governments to protect the donors' political and economic interests within their sphere of influence. Demonstrating that countries endowed with better educational capital export fewer terrorist attacks, they also illustrate that, in contrast, military intervention is counter-productive in abating terrorism. Recognizing the strides taken by the Obama administration to increase the role of foreign aid and reduce the use of military interventions, this book shows the significant impact this has had in reducing the number of transnational terrorist attacks per source country, and suggests further developments in this vein. Practical and timely, this book will be of particular interest to students and scholars of economics and political science, as well as those working on the wider issue of terrorism. Presenting a series of new findings, the book will also appeal to international policy makers and government officials.
Contests are prevalent in many areas, including sports, rent seeking, patent races, innovation inducement, labor markets, scientific projects, crowdsourcing and other online services, and allocation of computer system resources. This book provides unified, comprehensive coverage of contest theory as developed in economics, computer science, and statistics, with a focus on online services applications, allowing professionals, researchers and students to learn about the underlying theoretical principles and to test them in practice. The book sets contest design in a game-theoretic framework that can be used to model a wide-range of problems and efficiency measures such as total and individual output and social welfare, and offers insight into how the structure of prizes relates to desired contest design objectives. Methods for rating the skills and ranking of players are presented, as are proportional allocation and similar allocation mechanisms, simultaneous contests, sharing utility of productive activities, sequential contests, and tournaments.
Key environmental issues, such as biodiversity and climate change, have in recent years become more pressing than ever. Where the critical papers in the early 1990s explained the difficulties of cooperation in tackling transboundary environmental problems, later works have analyzed the various alternatives, and increased our understanding of various institutional designs and negotiation protocols' impact on the success of cooperation. This collection brings together the most important articles on the game theoretic analysis of international environmental cooperation to both confront the cooperative and non-cooperative approaches to this, and demonstrate the diversity of methods used to analyze international environmental agreements.
Building on the success of the first edition, Game Theory and Public Policy, Second Edition provides a critical, selective review of key concepts in game theory with a view to their applications in public policy. The author further suggests modifications for some of the models (chiefly in cooperative game theory) to improve their applicability to economics and public policy. Roger McCain makes use of the analytical tools of game theory for the pragmatic purpose of identifying problems and exploring potential solutions, providing a toolkit for the analysis of public policy allowing for a clearer understanding of the public policy enterprise itself. His critical review of major topics from both cooperative and non-cooperative game theory includes less-known ideas and constructive proposals for new approaches. This revised edition features a new second half that focuses on biform games, combining cooperative and non-cooperative decisions in a simple and natural way to provide a working model of externalities that can be applied to issues such as monopoly policy and labor market policies. Drawing on comparatively well understood models in cooperative game theory and the author's own research on mathematical models of biform games, this unique approach and treatment of game theory, updated and expanded to stay on the cutting edge, will be a useful resource for students and scholars of economics and public policy, as well as for policymakers themselves.
Optimization is used to determine the most appropriate value of variables under given conditions. The primary focus of using optimisation techniques is to measure the maximum or minimum value of a function depending on the circumstances. This book discusses problem formulation and problem solving with the help of algorithms such as secant method, quasi-Newton method, linear programming and dynamic programming. It also explains important chemical processes such as fluid flow systems, heat exchangers, chemical reactors and distillation systems using solved examples. The book begins by explaining the fundamental concepts followed by an elucidation of various modern techniques including trust-region methods, Levenberg-Marquardt algorithms, stochastic optimization, simulated annealing and statistical optimization. It studies the multi-objective optimization technique and its applications in chemical engineering and also discusses the theory and applications of various optimization software tools including LINGO, MATLAB, MINITAB and GAMS.
Targeted at graduate students, researchers and practitioners in the field of science and engineering, this book gives a self-contained introduction to a measure-theoretic framework in laying out the definitions and basic concepts of random variables and stochastic diffusion processes. It then continues to weave into a framework of several practical tools and applications involving stochastic dynamical systems. These include tools for the numerical integration of such dynamical systems, nonlinear stochastic filtering and generalized Bayesian update theories for solving inverse problems and a new stochastic search technique for treating a broad class of non-convex optimization problems. MATLAB (R) codes for all the applications are uploaded on the companion website.
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