Game-theoretic probability and finance come of age Glenn Shafer and Vladimir Vovk's Probability and Finance, published in 2001, showed that perfect-information games can be used to define mathematical probability. Based on fifteen years of further research, Game-Theoretic Foundations for Probability and Finance presents a mature view of the foundational role game theory can play. Its account of probability theory opens the way to new methods of prediction and testing and makes many statistical methods more transparent and widely usable. Its contributions to finance theory include purely game-theoretic accounts of Ito's stochastic calculus, the capital asset pricing model, the equity premium, and portfolio theory. Game-Theoretic Foundations for Probability and Finance is a book of research. It is also a teaching resource. Each chapter is supplemented with carefully designed exercises and notes relating the new theory to its historical context. Praise from early readers "Ever since Kolmogorov's Grundbegriffe, the standard mathematical treatment of probability theory has been measure-theoretic. In this ground-breaking work, Shafer and Vovk give a game-theoretic foundation instead. While being just as rigorous, the game-theoretic approach allows for vast and useful generalizations of classical measure-theoretic results, while also giving rise to new, radical ideas for prediction, statistics and mathematical finance without stochastic assumptions. The authors set out their theory in great detail, resulting in what is definitely one of the most important books on the foundations of probability to have appeared in the last few decades." - Peter Grunwald, CWI and University of Leiden "Shafer and Vovk have thoroughly re-written their 2001 book on the game-theoretic foundations for probability and for finance. They have included an account of the tremendous growth that has occurred since, in the game-theoretic and pathwise approaches to stochastic analysis and in their applications to continuous-time finance. This new book will undoubtedly spur a better understanding of the foundations of these very important fields, and we should all be grateful to its authors." - Ioannis Karatzas, Columbia University

These Notes grew from my research in evolutionary biology, specifically on the theory of evolutionarily stable strategies (ESS theory), over the past ten years. Personally, evolutionary game theory has given me the opportunity to transfer my enthusiasm for abstract mathematics to more practical pursuits. I was fortunate to have entered this field in its infancy when many biologists recognized its potential but were not prepared to grant it general acceptance. This is no longer the case. ESS theory is now a rapidly expanding (in both applied and theoretical directions) force that no evolutionary biologist can afford to ignore. Perhaps, to continue the life-cycle metaphor, ESS theory is now in its late adolescence and displays much of the optimism and exuberance of this exciting age. There are dangers in writing a text about a theory at this stage of development. A comprehensive treatment would involve too many loose ends for the reader to appreciate the central message. On the other hand, the current central message may soon become obsolete as the theory matures. Although the restricted topics I have chosen for this text reflect my own research bias, I am confident they will remain the theoretical basis of ESS theory. Indeed, I feel the adult maturity of ESS theory is close at hand and I hope the text will play an important role in this achievement.

In 1984 the German Aerospace Research Establishment - Deutsche Forschungsanstalt fOr Luft-und Raumfahrt e.V. (DLR) -Initiated a series of seminars related to fundamental prob- lems In fluid mechanics, flight mechanics, guidance and control, materials and structures, non-nuclear energetics, communication technology, and remote sensing. The main purpose of the seminars Is to bring modern Ideas and techniques In these fields to the attention of DLR scientists and engineers in order to stimulate internal activities as well as International cooperation. To this end, prominent speakers are Invited to Join In a series of lectures and discussions on topics of mutual Interest. After the preceding seminars 1984 Nonlinear Dynamics In Transcritical Flows 1985 Uncertainty and Control 1986 Artificial Intelligence and Man-Machine-Systems 1987 Parallel Computing in Science and Engineering 1988 Hydrocarbon Oxidation a sixth seminar on HOptimlzation: Methods and Applications, Possibilities and LimitatlonsH Is being conducted In 1989. Optimization takes place wherever a choice among alternatives exists: in daily life, In eco- nomics, In politics, in nature and also in engineering. The availability of powerful computers makes It possible to solve complex optimization problems efficiently, and to react flexibly to changes of reqUirements. The seminar addresses the potential of a systematic, computer-aided approach to optimiza- tion problems. The presentations Include fundamental principles and practical applications to aerospace structures as well as evolution techniques and biotechnological optimization processes.

Known as the science of strategy, game theory is a branch of mathematics that has gained broad acceptance as a legitimate methodological tool, and has been widely adapted by a number of other fields. Frank C. Zagare provides an introduction to the application of game theory in the fields of security studies and diplomatic history, demonstrating the advantages of using a formal game-theoretic framework to explain complex events and strategic relationships. Comprised of three parts, the first illustrates the basic concepts of game theory, initially with abstract examples but later in the context of real world foreign policy decision-making. The author highlights the methodological problems of using game theory to construct an analytic narrative and the advantages of working around these obstacles. Part II develops three extended case studies that illustrate the theory at work: the First Moroccan Crisis of 1905-1906, the July Crisis of 1914, and the Cuban Missile Crisis of 1962. Finally, in Part III, Zagare describes a general theory of interstate conflict initiation, limitation, escalation, and resolution and rebuts criticisms of the methodology. Logically demanding, Game Theory, Diplomatic History and Security Studies conveys an intuitive understanding of the theory of games through the use of real-world examples to exemplify the 'theory in action'.

This book introduces econometric analysis of cross section, time series and panel data with the application of statistical software. It serves as a basic text for those who wish to learn and apply econometric analysis in empirical research. The level of presentation is as simple as possible to make it useful for undergraduates as well as graduate students. It contains several examples with real data and Stata programmes and interpretation of the results. While discussing the statistical tools needed to understand empirical economic research, the book attempts to provide a balance between theory and applied research. Various concepts and techniques of econometric analysis are supported by carefully developed examples with the use of statistical software package, Stata 15.1, and assumes that the reader is somewhat familiar with the Strata software. The topics covered in this book are divided into four parts. Part I discusses introductory econometric methods for data analysis that economists and other social scientists use to estimate the economic and social relationships, and to test hypotheses about them, using real-world data. There are five chapters in this part covering the data management issues, details of linear regression models, the related problems due to violation of the classical assumptions. Part II discusses some advanced topics used frequently in empirical research with cross section data. In its three chapters, this part includes some specific problems of regression analysis. Part III deals with time series econometric analysis. It covers intensively both the univariate and multivariate time series econometric models and their applications with software programming in six chapters. Part IV takes care of panel data analysis in four chapters. Different aspects of fixed effects and random effects are discussed here. Panel data analysis has been extended by taking dynamic panel data models which are most suitable for macroeconomic research. The book is invaluable for students and researchers of social sciences, business, management, operations research, engineering, and applied mathematics.

A comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems. It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.

Ken Binmore's previous game theory textbook, Fun and Games (D.C. Heath, 1991), carved out a significant niche in the advanced undergraduate market; it was intellectually serious and more up-to-date than its competitors, but also accessibly written. Its central thesis was that game theory allows us to understand many kinds of interactions between people, a point that Binmore amply demonstrated through a rich range of examples and applications. This replacement for the now out-of-date 1991 textbook retains the entertaining examples, but changes the organization to match how game theory courses are actually taught, making Playing for Real a more versatile text that almost all possible course designs will find easier to use, with less jumping about than before. In addition, the problem sections, already used as a reference by many teachers, have become even more clever and varied, without becoming too technical. Playing for Real will sell into advanced undergraduate courses in game theory, primarily those in economics, but also courses in the social sciences, and serve as a reference for economists.

This second edition of Lessons in Play reorganizes the presentation of the popular original text in combinatorial game theory to make it even more widely accessible. Starting with a focus on the essential concepts and applications, it then moves on to more technical material. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more detail and abstract results. Features Employs a widely accessible style to the explanation of combinatorial game theory Contains multiple case studies Expands further directions and applications of the field Includes a complete rewrite of CGSuite material

John von Neumann invented the digital computer, played a key role in the development of the atom bomb, constructed a branch of mathematics known as game theory, and became a defender of a movement to bomb the Russians before they could bomb us. Now comes a biography of this controversial genius and an exploration of his greatest idea--one that nearly triggered a nuclear war in 1950. Photographs.

A Beautiful Mind is Sylvia Nasar's award-winning biography about the mystery of the human mind, the triumph over incredible adversity, and the healing power of love. At the age of thirty-one, John Nash, mathematical genius, suffered a devastating breakdown and was diagnosed with schizophrenia. Yet after decades of leading a ghost-like existence, he was to re-emerge to win a Nobel Prize and world acclaim. A Beautiful Mind has inspired the Oscar-winning film directed by Ron Howard and featuring Russell Crowe in the lead role of John Nash.

Expert Guidance on the Math Needed for 3D Game ProgrammingDeveloped from the authors' popular Game Developers Conference (GDC) tutorial, Essential Mathematics for Games and Interactive Applications, Third Edition illustrates the importance of mathematics in 3D programming. It shows you how to properly animate, simulate, and render scenes and discusses the mathematics behind the processes. New to the Third EditionCompletely revised to fix errors and make the content flow better, this third edition reflects the increased use of shader graphics pipelines, such as in DirectX 11, OpenGL ES (GLES), and the OpenGL Core Profile. It also updates the material on real-time graphics with coverage of more realistic materials and lighting. The Foundation for Successful 3D ProgrammingThe book covers the low-level mathematical and geometric representations and algorithms that are the core of any game engine. It also explores all the stages of the rendering pipeline. The authors explain how to represent, transform, view, and animate geometry. They then focus on visual matters, specifically the representation, computation, and use of color. They also address randomness, intersecting geometric entities, and physical simulation. An Introduction to Creating Real and Active Virtual WorldsThis updated book provides you with a conceptual understanding of the mathematics needed to create 3D games as well as a practical understanding of how these mathematical bases actually apply to games and graphics. It not only includes the theoretical mathematical background but also incorporates many examples of how the concepts are used to affect how a game looks and plays. Web ResourceA supplementary website contains a collection of source code, supporting libraries, and interactive demonstrations that illustrate the concepts and enable you to experiment with animation and simulation applications. The site also includes slides and notes from the authors' GDC tutorials.

Few branches of mathematics have been more influential in the social sciences than game theory. In recent years, it has become an essential tool for all social scientists studying the strategic behaviour of competing individuals, firms and countries. However, the mathematical complexity of game theory is often very intimidating for students who have only a basic understanding of mathematics. Insights into Game Theory addresses this problem by providing students with an understanding of the key concepts and ideas of game theory without using formal mathematical notation. The authors use four very different topics (college admission, social justice and majority voting, coalitions and co-operative games, and a bankruptcy problem from the Talmud) to investigate four areas of game theory. The result is a fascinating introduction to the world of game theory and its increasingly important role in the social sciences.

Since there is no supranational institution which can enforce international environmental agreements (IEAs), international cooperation proves difficult in practice. Global emissions exhibit negative externalities in countries other than that of their origin and hence there is a high interdependence between countries, and strategic considerations play an important role. Game theory analyses the interaction between agents and formulates hypotheses about their behavior and the final outcomes in games. Hence, international environmental problems are particularly suited for analysis by this method. The book investigates various strategies to provide countries with an incentive to accede, agree and comply to an international environmental agreement (IEA). Finus shows that by integrating real world restrictions into a model, game theory is a powerful tool for explaining the divergence between 'first-best' policy recommendations and 'second-best' designs of actual IEAs. For instance he explains why (inefficient) uniform emission reduction quotas have played such a prominent role in past IEAs despite economists' recommendations for the use of (efficient) market-based instruments as for example emission targets and permits. Moreover, it is stated, that a single, global IEA on climate is not necessarily the best strategy and small coalitions may enjoy a higher stability and may achieve more. This book will be of great interest to scholars, researchers and lecturers in the fields of international environmental economics, game theory and international relations.

This book explains, in a straightforward way, the foundations upon which electoral techniques are based in order to shed new light on what we actually do when we vote. The intention is to highlight the fact that no matter how an electoral system has been designed, and regardless of the intentions of those who devised the system, there will be goals that are impossible to achieve but also opportunities for improving the situation in an informed way. While detailed descriptions of electoral systems are not provided, many references are made to current or past situations, both as examples and to underline particular problems and shortcomings. In addition, a new voting method that avoids the many paradoxes of voting theory is described in detail. While some knowledge of mathematics is required in order to gain the most from the book, every effort has been made to ensure that the subject matter is easily accessible for non-mathematicians, too. In short, this is a book for anyone who wants to understand the meaning of voting.

The principles of game theory apply to a wide range of topics in biology. This book presents the central concepts in evolutionary game theory and provides an authoritative and up-to-date account. The focus is on concepts that are important for biologists in their attempts to explain observations. This strong connection between concepts and applications is a recurrent theme throughout the book which incorporates recent and traditional ideas from animal psychology, neuroscience, and machine learning that provide a mechanistic basis for behaviours shown by players of a game. The approaches taken to modelling games often rest on idealized and unrealistic assumptions whose limitations and consequences are not always appreciated. The authors provide a novel reassessment of the field, highlighting how to overcome limitations and identifying future directions. Game Theory in Biology is an advanced textbook suitable for graduate level students as well as professional researchers (both empiricists and theoreticians) in the fields of behavioural ecology and evolutionary biology. It will also be of relevance to a broader interdisciplinary audience including psychologists and neuroscientists.

This book contains invited essays in memory of Leonid Hurwicz spanning a large area of economic, social and other sciences where the implementation or enforcement of institutions and rules requires the design of effective mechanisms. The foundations of these articles are set by social choice concepts; game theory; Nash, Bayesian and Walrasian equilibria; complete and incomplete information. Besides in-depth treatments of well-established parts of mechanism and implementation theory, contributions on novel directions deal, for instance, with a quantum approach to game and decision making under uncertainty; digitalization; and the design of block chain for trading. The outstanding competence and reputation of the authors reflect the appreciation of the fundamental contributions and the lasting admiration of the personality and the work of Leonid Hurwicz.

This book constitutes the refereed proceedings of the Third International Meeting on Innovation for Systems Information and Decision, INSID 2021, which was held during December 1-3, 2021. The conference was initially planned to take place in Recife, Brazil, but changed to a virtual meeting due to the COVID-19 pandemic. The 9 full papers presented in this volume were carefully reviewed and selected from a total of 76 submissions. They reflect methodological improvements and advances in multi-criteria decision-making/multi-criteria decision-aid (MCDM/MCDA) oriented toward real-world applications, which contribute to the understanding of relevant developments of current research on and future trends of innovation for systems information and decision.

This book presents an interdisciplinary approach to conflict solution focusing on a very specific type of conflict, retributive conflicts . It is unique in the treatment of these and how relative measurement is used to find equilibrium solutions. The authors present an alternative process to address the Israeli-Palestinian conflict. They do so in two ways that are different from past efforts. The first is by formally structuring the conflict and the second is the manner in which discussions were conducted and conclusions drawn. The approach will help create a solution and provide negotiators with a unique pathway to consider the thorny issues and corresponding concessions underlying the deliberations, together with their implementation. The Analytic Hierarchy Process (AHP) provides a way to conflict solution with the participation of negotiators for the parties. It is a positive approach that makes it possible to reason and express feelings and judgments with numerical intensities to derive priorities. With the assistance of panels of Israeli participants and Palestinian participants brought together in 2006 to 2017, AHP was applied for the first time in a group setting to the Palestinian-Israeli conflict. The process makes it clear that moderation in different degrees by both sides is essential to arrive at acceptable agreements on concessions proposed and agreed upon by both sides.

This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.

How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work. "The Calculus of Selfishness" looks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation.

Focusing on some of the best-known social and economic experiments, including games such as the Prisoner's Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions.

Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps, "The Calculus of Selfishness" analyzes to what extent one key facet of human nature--selfishness--can lead to cooperation.

When should you adopt an aggressive business strategy? How do we make decisions when we don't have all the information? What makes international environmental cooperation possible? Game theory is the study of how we make a decision when the outcome of our moves depends on the decisions of someone else. Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random. Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.