This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.

This book offers a gentle introduction to Hex, the classic board game created by Piet Hein and popularized by John Nash and Martin Gardner. The first three chapters cover rules, basic strategy, and history. The remaining eight chapters cover a variety of topics: mathematical properties (there are no draws, the first player can win, the acute corner is a losing first move), the related game of Y, winning strategies for small boards, how computers play Hex, an analysis of Random-Move Hex (where one or both players move randomly) and Dark Hex (the imperfect information version of the game, where you can't see your opponent's moves). Did we mention puzzles? There are puzzles in every chapter, with solutions. This book is intended for anyone interested in playing board games or learning some recreational mathematics. It is written for a wide audience and will be enjoyed equally by general readers and professional mathematicians. The book could be used as a textbook or companion resource for a topics course on recreational mathematics or game theory or as a source for undergraduate research questions.

This major two volume collection presents some of the most influential theoretical and empirical papers on the economic theory of auctions. Auction theory has been the basis of fundamental theoretical work in industrial economics, public economics, labour economics and finance, and has helped the understanding of price formation in markets. There has recently been an explosion of interest in its practical applications, especially in organising the sale of government assets (for example, treasury bonds, radio spectrum licenses, and firms to be privatised) and in developing new markets for electricity and transport. Because auctions are such simple and well defined environments, they provide a valuable testing ground for economic theory that has been increasingly exploited in empirical work. The book will also include important previously unpublished papers by P.R. Milgrom, R. Weber and A. Ortega-Reichert, and other hard-to-find papers by W. Vickery and others.

This addition to the ISOR series introduces complementarity models in a straightforward and approachable manner and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. In a nutshell, complementarity models generalize: a. optimization problems via their Karush-Kuhn-Tucker conditions b. on-cooperative games in which each player may be solving a separate but related optimization problem with potentially overall system constraints (e.g., market-clearing conditions) c. conomic and engineering problems that aren't specifically derived from optimization problems (e.g., spatial price equilibria) d. roblems in which both primal and dual variables (prices) appear in the original formulation (e.g., The National Energy Modeling System (NEMS) or its precursor, PIES). As such, complementarity models are a very general and flexible modeling format. A natural question is why concentrate on energy markets for this complementarity approach? s it turns out, energy or other markets that have game theoretic aspects are best modeled by complementarity problems. The reason is that the traditional perfect competition approach no longer applies due to deregulation and restructuring of these markets and thus the corresponding optimization problems may no longer hold. Also, in some instances it is important in the original model formulation to involve both primal variables (e.g., production) as well as dual variables (e.g., market prices) for public and private sector energy planning. Traditional optimization problems can not directly handle this mixing of primal and dual variables but complementarity models can and this makes them all that more effective for decision-makers.

Game Theory & Applications Volume 3

This book presents recent developments and new trends in Combinatorial Optimization. Combinatorial Optimization is an active research area that has applications in many domains such as communications, network design, VLSI, scheduling, production, computational biology. In the past years, new results and major advances have been seen in many areas including computational complexity, approximation algorithms, cutting-plane based methods and submodularity function minimization. More efficient and powerful methods have been developed for approaching real-worlds problems, and new concepts and theoritical results have been introduced.

Game Theory & Applications Volume II

An essential introduction to the analysis and verification of control system software The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Loic Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase-as evidenced by autonomous cars, drones, and satellites and landers-the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.

Game Theory & Applications

The authors stress the relative simplicity, efficiency, flexibility of use, and suitability of various approaches used to solve difficult optimization problems. The authors are experienced, interdisciplinary lecturers and researchers and in their explanations they demonstrate many shared foundational concepts among the key methodologies. This textbook is a suitable introduction for undergraduate and graduate students, researchers, and professionals in computer science, engineering, and logistics.

Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

The main purpose of the present book is to develop a general framework for population-based metaheuristics based on some basic concepts of set theory. The idea of the framework is to divide the population of individuals into subpopulations of identical sizes. Therefore, in each iteration of the search process, different subpopulations explore the search space independently but simultaneously. The framework aims to provide a suitable balance between exploration and exploitation during the search process. A few chapters containing algorithm-specific modifications of some state-of-the-art metaheuristics are also included to further enrich the book. The present book is addressed to those scientists, engineers, and students who wish to explore the potentials of newly developed metaheuristics. The proposed metaheuristics are not only applicable to structural optimization problems but can also be used for other engineering optimization applications. The book is likely to be of interest to a wide range of engineers and students who deal with engineering optimization problems.

MATRIX is Australia's international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

In a book sure to stir argument for years to come, Robert Wright challen+ges the conventional view that biological evolution and human history are aimless. Ingeniously employing game theory – the logic of ‘zero-sum’ and ‘non-zero-sum’ games – Wright isolates the impetus behind life’s basic direction: the impetus that, via biological evolution, created complex, intelligent animals, and then via cultural evolution, pushed the human species towards deeper and vaster social complexity. In this view, the coming of today’s independent global society was ‘in the cards’ – not quite inevitable, but, as Wright puts it, ‘so probable as to inspire wonder’. In a narrative of breathtaking scope and erudition, yet pungent wit, Wright takes on some of the past century’s most prominent thinkers, including Isaiah Berlin, Karl Popper, Stephen Jay Gould, and Richard Dawkins. Wright argues that a coolly specific appraisal of humanity’s three-billion-year past can give new spiritual meaning to the present and even offer political guidance for the future. This book will change the way people think about the human prospect.
 

Das im heutigen Berufsalltag so wichtige und allgegenwartige "treffsichere Umgehen" mit mathematischen Methoden und Modellen setzt voraus, dass Studierende die relevanten Werkzeuge kennen und verstehen, sie auswahlen und anwenden sowie erzielte Ergebnis (auf Plausibilitat) prufen, bewerten und je nach Bedarf auf andere Fragestellungen transferieren bzw. zum Problemloesen einsetzen koennen. Ausgehend von der Schulmathematik vermitteln die Autoren dem Leser diese berufsrelevanten Fertigkeiten didaktisch hervorragend und gut zuganglich. Dabei ist jedes Kapitel neben vielen Aufgaben mit Loesungen mit einem Eingangs- und einem Ausgangstest versehen, um eine effiziente Lernkontrolle zu ermoeglichen.

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject.

Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution.

The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations.

An essential book for anyone working on optimization and decision making under uncertainty, "Robust Optimization" also makes an ideal graduate textbook on the subject.

This is the third of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses topics that depend more on calculus than linear algebra, in order to prepare the reader for solving differential equations. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 90 examples, 200 exercises, 36 algorithms, 40 interactive JavaScript programs, 91 references to software programs and 1 case study. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.

Now in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reference for researchers.

This essential collection brings together influential classic and contemporary articles from a variety of sources to present the key topics in game theory. Rather than an exhaustive volume, this superb resource offers students and researchers an accessible treatment of game theory essentials. The text is interspersed with editorial commentary, newspaper articles and cartoons, recommendations for further reading, and a substantial amount of material on how to conduct research in this area. "

Readings in Games and Information" is an exceptional course companion, used alone or as a supplement to Rasmusen's "Games and Information" (third edition, Blackwell, 2001).

This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NP-complete problems, more. All chapters are supplemented by thought-provoking problems. A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering. "Mathematicians wishing a self-contained introduction need look no further."-American Mathematical Monthly. 1982 ed.

Many problems in statistics and econometrics offer themselves naturally to
the use of optimization heuristics. Standard methods applied to highly
complex problems often produce approximate results, of unknown quality,
based on heavy assumptions. Optimization heuristic methods provide
powerful results to many complex problems. combined with relatively
simple implementation.

• Offers a self-contained introduction to optimization heuristics in econometrics and statistics
• Features many examples of optimization heuristic methods applied to real problems
• Includes detailed coverage of the threshold accepting heuristic
• Provides suggestions for further reading

Split into three parts, the book opens with a general introduction to
optimization in statistics and econometrics, followed by detailed discussion
of a relatively new and very powerful optimization heuristic, threshold
accepting. The final part consists of many applications of the methods
described earlier, encompassing experimental design, model selection,
aggregation of tiime series, and censored quantile regression models.
Those researching and working in econometrics, statistics and operations
research are given the tools to apply optimization heuristic methods in their
work. Postgraduate students of statistics and econometrics will find the
book provides a good introduction to optimization heuristic methods.

This volume contains select papers presented during the 4th National Conference on Multidisciplinary Analysis and Optimization. It discusses new developments at the core of optimization methods and their application in multiple applications. The papers showcase fundamental problems and applications which include domains such as aerospace, automotive and industrial sectors. The variety of topics and diversity of insights presented in the general field of optimization and its use in design for different applications will be of interest to researchers in academia or industry.

This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. In the third edition, much of the material has been reorganized, new examples have been added, and a new chapter has been added describing how modelers can improve the performance of their models. The authors have also modified their recommended method for importing Pyomo. A big change in this edition is the emphasis of concrete models, which provide fewer restrictions on the specification and use of Pyomo models. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.

Das Buch fasst konkret und verstandlich die wichtigsten Gewinnstrategien fur die 50 bekanntesten Karten- Brett-, Wurfel-, Karten- und Gewinnspiele zusammen, die sofort angewandt werden koennen. Griffige Faustformeln und die wichtigsten mathematischen Berechnungen zeigen: Der Weg zum Gewinn fuhrt nicht uber Zufall und Gluck, sondern uber Logik und Strategie. Treffen Sie die richtigen Entscheidungen und verstehen Sie, warum Ihr Gegenuber bisher gewonnen hat. Aber Achtung: alle Angaben ohne Gewahr - eine Gewinngarantie liegt nicht bei. Im Blickpunkt: Klassische Brettspiele: z.B. Schach, Dame, Backgammon, Scrabble Kinder- und Familienspiele: z.B. Malefiz, Mensch argere Dich nicht, Schiffe versenken, Mastermind Gesellschaftspiele: z.B. Siedler von Catan, Monopoly, Carcassonne, Die Tore der Welt Kartenspiele: z.B. Doppelkopf, Skat, Canasta, Mau-Mau Wurfel-, Tipp-, Wett- und Gewinnspiele: z.B. Kniffel, Fussball-Tipprunden, Lotto

This book collects papers presented at the Virtual International Conference on Soft Computing, Optimization Theory and Applications (SCOTA 2021), held at the Birla Institute of Technology, Mesra, Ranchi, India, from 26-27 March 2021. Topics discussed in the book are on fuzzy logic, neural networks and optimization algorithms, as well as their hybrid combinations, and their application in areas such as intelligent control and robotics, pattern recognition, medical diagnosis, time series prediction and optimization of complex problems. The book highlights research on: (a) hybrid intelligent systems based on soft computing, new concepts and algorithms based on fuzzy logic and their applications, (b) theory and practice of meta-heuristics in different areas of application, (c) applications of fuzzy logic, (d) neural networks and hybrid intelligent systems in medical applications, (e) neural networks and optimization and evolutionary algorithms and their different applications and (f) applications of fuzzy logic, neural networks and meta-heuristics in pattern recognition problems. Some papers contain applications background like approximate solution of fractional differential equations via fixed-point algorithms and applications to equilibrium problems and image deburring problems. The book will be of great use to students, researchers and scientists in computer science, optimization and engineering, and those interested on computational intelligence and soft computing and their applications.