The uneven geographical distribution of economic activities is a huge challenge worldwide and also for the European Union. In Krugman's New Economic Geography economic systems have a simple spatial structure. This book shows that more sophisticated models should visualise the EU as an evolving trade network with a specific topology and different aggregation levels. At the highest level, economic geography models give a bird eye's view of spatial dynamics. At a medium level, institutions shape the economy and the structure of (financial and labour) markets. At the lowest level, individual decisions interact with the economic, social and institutional environment; the focus is on firms' decision on location and innovation. Such multilevel models exhibit complex dynamic patterns - path dependence, cumulative causation, hysteresis - on a network structure; and specific analytic tools are necessary for studying strategic interaction, heterogeneity and nonlinearities.

This monograph is devoted to the analysis and solution of singular differential games and singular $H_{\inf}$ control problems in both finite- and infinite-horizon settings. Expanding on the authors' previous work in this area, this novel text is the first to study the aforementioned singular problems using the regularization approach. After a brief introduction, solvability conditions are presented for the regular differential games and $H_{\inf}$ control problems. In the following chapter, the authors solve the singular finite-horizon linear-quadratic differential game using the regularization method. Next, they apply this method to the solution of an infinite-horizon type. The last two chapters are dedicated to the solution of singular finite-horizon and infinite-horizon linear-quadratic $H_{\inf}$ control problems. The authors use theoretical and real-world examples to illustrate the results and their applicability throughout the text, and have carefully organized the content to be as self-contained as possible, making it possible to study each chapter independently or in succession. Each chapter includes its own introduction, list of notations, a brief literature review on the topic, and a corresponding bibliography. For easier readability, detailed proofs are presented in separate subsections. Singular Linear-Quadratic Zero-Sum Differential Games and $H_{\inf}$ Control Problems will be of interest to researchers and engineers working in the areas of applied mathematics, dynamic games, control engineering, mechanical and aerospace engineering, electrical engineering, and biology. This book can also serve as a useful reference for graduate students in these area

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed.

The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options. "

Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.

Social Networks and Trust discusses two possible explanations for the emergence of trust via social networks. If network members can sanction untrustworthiness of actors, these actors may refrain from acting in an untrustworthy manner. Moreover, if actors are informed regularly about trustworthy behavior of others, trust will grow among these actors.
A unique combination of formal model building and empirical methodology is used to derive and test hypotheses about the effects of networks on trust. The models combine elements from game theory, which is mainly used in economics, and social network analysis, which is mainly used in sociology.
The hypotheses are tested (1) by analyzing contracts in information technology transactions from a survey on small and medium-sized enterprises and (2) by studying judgments of subjects in a vignette experiment related to hypothetical transactions with a used-car dealer.

The theory of dynamic games is very rich in nature and very much alive If the reader does not already agree with this statement, I hope he/she will surely do so after having consulted the contents of the current volume. The activities which fall under the heading of 'dynamic games' cannot easily be put into one scientific discipline. On the theoretical side one deals with differential games, difference games (the underlying models are described by differential, respec tively difference equations) and games based on Markov chains, with determin istic and stochastic games, zero-sum and nonzero-sum games, two-player and many-player games - all under various forms of equilibria. On the practical side, one sees applications to economics (stimulated by the recent Nobel prize for economics which went to three prominent scientists in game theory), biology, management science, and engineering. The contents of this volume are primarily based on selected presentations made at the Sixth International Symposium on Dynamic Games and Applica tions, held in St Jovite, Quebec, Canada, 13-15 July 1994. Every paper that appears in this volume has passed through a stringent reviewing process, as is the case with publications for archival technical journals. This conference, as well as its predecessor which was held in Grimentz, 1992, took place under the auspices of the International Society of Dynamic Games (ISDG), established in 1990. One of the activities of the ISDG is the publication of these Annals. The contributions in this volume have been grouped around five themes."

This book demonstrates what kind of problems, originating in a management accounting setting, may be solved with game theoretic models. Game theory has experienced growing interest and numerous applications in the field of management accounting. The main focus traditionally has been on the field of non-cooperative behaviour, but the area of cooperative game theory has developed rapidly and has received increasing attention. Intensive research, in combination with the changing culture of publishing, has produced a nearly unmanageable number of publications in the areas concerned. Therefore, one main purpose of this volume is providing an intensive analysis of the intersection of these areas. In addition, the book strengthens the relationship between the theory and the practical applications and it illustrates the two-sided relationship between game theory and management accounting: new game theoretic models offer new fields of applications and these applications raise new questions for the theory.

This is the first book to comprehensively examine the asymptotic behavior of dynamic monopolies, duopolies, and oligopolies where firms face information and implementation delays. It considers discrete and continuous timescales, continuously distributed delays, as well as single and multiple delays. It also discusses models with linear and hyperbolic price functions in three types of oligopolies: Cournot competition with quantity-adjusting firms, Bertrand competition with price-adjusting firms, and mixed oligopolies with both types of firms. In addition to the traditional Cournot-Nash equilibria, it introduces cases of partial cooperation are also introduced, leading to the analysis of cartelizing groups of firms and possible governmental actions against antitrust behavior. Further, the book investigates special processes for firms learning about the uncertain price function based on repeated market information. It addresses asymptotic properties of the associated dynamic systems, derives stability conditions, identifies stability switching curves, and presents in global analyses of cases of instability. The book includes both theoretical results and computer studies to illustrate and verify the theoretical findings.

Does game theory ? the mathematical theory of strategic interaction ? provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory ? the first monograph on the philosophy of game theory ? is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.

Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the social and political problems of their times. What we have sought to document is mathematics' central position in the culture of our day. Space has been made not only for the great mathematicians but also for literary texts, including contributions by two apparent interlopers, Robert Musil and Raymond Queneau, for whom mathematical concepts represented a valuable tool for resolving the struggle between 'soul and precision.'

The wise win before they fight, while the ignorant fight to win. So wrote Zhuge Liang, the great Chinese military strategist. He was referring to battlefield tactics, but the same can be said about any strategic situation. Even seemingly certain defeat can be turned into victory whether in battle, business, or life by those with the strategic vision to recognize how to change the game to their own advantage.

The aim of David McAdams s Game-Changer is nothing less than to empower you with this wisdom not just to win in every strategic situation (or game ) you face but to change those games and the ecosystems in which they reside to transform your life and our lives together for the better.

Game-Changer develops six basic ways to change games commitment, regulation, cartelization, retaliation, trust, and relationships enlivened by countless colorful characters and unforgettable examples from the worlds of business, medicine, finance, military history, crime, sports, and more.

The book then digs into several real-world strategic challenges, such as how to keep prices low on the Internet, how to restore the public s lost trust in for-charity telemarketers, and even how to save mankind from looming and seemingly unstoppable drug-resistant disease. In each case, McAdams uses the game-theory approach developed in the book to identify the strategic crux of the problem and then leverages that game-awareness to brainstorm ways to change the game to solve or at least mitigate the underlying problem.

So get ready for a fascinating journey. You ll emerge a deeper strategic thinker, poised to change and win all the games you play. In doing so, you can also make the world a better place. Just one Game-Changer is] enough to seed and transform an entire organization into a more productive, happier, and altogether better place, McAdams writes. Just imagine what we can do together."

Oligopoly theory is one of the most intensively studied areas of mathematical economics. On the basis of the pioneering works of Cournot (1838), many res- rchers have developed and extensively examined the different variants of oligopoly models. Initially, the existence and uniqueness of the equilibrium of the different types of oligopolies was the main concern, and later the dynamic extensions of these models became the focus. The classical result of Theocharis (1960) asserts that under discrete time scales and static expectations, the equilibrium of a sing- product oligopoly without product differentiation and with linear price and cost functions is asymptotically stable if and only if it is a duopoly. In the continuous time case, asymptotic stability is guaranteed for any number of ?rms. In these cases the resulting dynamical systems are also linear, where local and global asymptotic stability are equivalent to each other. The classical book of Okuguchi (1976) gives a comprehensive summary of the earlier results and developments. The multipr- uct extensionshave been discussed in Okuguchiand Szidarovszky(1999);however, nonlinear features were barely touched upon in these contributions. WiththedevelopmentofthecriticalcurvemethodbyGumowskiandMira(1980) (see also Mira et al. (1996))fordiscrete time systemsand the introductionof cont- uously distributed information lags by Invernizzi and Medio (1991) in continuous time systems, increasing attention has been given to the global dynamics of n- linear oligopolies. The authors of this book have devoted a great deal of research effort to this area.

An innovative feature of this book is its econocentric structure, focusing on digital designs. From the outset, econocentrism is assumed to be a core engine of capitalism, like money. The new coronavirus pandemic has changed lifestyles worldwide, which are unlikely ever to return in their original form. This great transformation will change the nature of the socio-economic system itself and will be centered on digital designs. At present, money already is beginning to undergo a major revolution in that sense. Many books dealing with digital designs and innovations have been published, but few if any of them focus on monetary and analytical methods in the way that this present volume does.The book then contains 6 parts: Evolution of money and thinking complexities in the AI era; Goods market and the future of labor market; Computational social approaches to social dilemmas, smart city, cryptocurrencies; Artificial market experiments; The randomness and high frequencies in financial data; Other trading strategy issues and the effects of AI usage. These issues may be indispensable subjects in our age. Study these subject, and have a step forward to the future society!

This book introduces research presented at the "International Conference on Artificial Intelligence: Advances and Applications-2019 (ICAIAA 2019)," a two-day conference and workshop bringing together leading academicians, researchers as well as students to share their experiences and findings on all aspects of engineering applications of artificial intelligence. The book covers research in the areas of artificial intelligence, machine learning, and deep learning applications in health care, agriculture, business and security. It also includes research in core concepts of computer networks, intelligent system design and deployment, real-time systems, WSN, sensors and sensor nodes, SDN and NFV. As such it is a valuable resource for students, academics and practitioners in industry working on AI applications.

There has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games. Exhibiting various real world problems involving major and minor agents, this book presents a systematic continuous-space approximation approach for mean-field interacting agents models and mean-field games models. After describing Markov-chain methodology and a modeling of mean-field interacting systems, the text presents various structural conditions on the chain to yield respective socio-economic models, focusing on migration models via binary interactions. The specific applications are wide-ranging - including inspection and corruption, cyber-security, counterterrorism, coalition building and network growth, minority games, and investment policies and optimal allocation - making this book relevant to a wide audience of applied mathematicians interested in operations research, computer science, national security, economics, and finance.

The chapters in this volume explore how various methods from game theory can be utilized to optimize security and risk-management strategies. Emphasizing the importance of connecting theory and practice, they detail the steps involved in selecting, adapting, and analyzing game-theoretic models in security engineering and provide case studies of successful implementations in different application domains. Practitioners who are not experts in game theory and are uncertain about incorporating it into their work will benefit from this resource, as well as researchers in applied mathematics and computer science interested in current developments and future directions. The first part of the book presents the theoretical basics, covering various different game-theoretic models related to and suitable for security engineering. The second part then shows how these models are adopted, implemented, and analyzed. Surveillance systems, interconnected networks, and power grids are among the different application areas discussed. Finally, in the third part, case studies from business and industry of successful applications of game-theoretic models are presented, and the range of applications discussed is expanded to include such areas as cloud computing, Internet of Things, and water utility networks.

Recent applications of evolutionary game theory in the merging fields of the mathematical and social sciences are brilliantly portrayed in this book, which highlights social physics and shows how the approach can help to quantitatively model complex human-environmental-social systems. First, readers are introduced to the fundamentals of evolutionary game theory. The two-player, two-strategy game, or the 2 x 2 game, is presented as an archetype to help understand the difficulty of cooperating for survival against defection in common social contexts. Subsequently, the book explains the theoretical background of the multi-player, two-strategy game, which may be more widely applicable than the 2 x 2 game for social dilemmas. The latest applications of 2 x 2 games are also discussed to explore how integrated reciprocity mechanisms can solve social dilemmas. In turn, the book describes two practical areas in which evolutionary game theory has been applied. The first concerns traffic flow analysis. In conventional interpretations, traffic flow can be understood by means of fluid dynamics, in which the flow of vehicles is evaluated as a continuum body. Such a simple idea, however, does not work well in reality, particularly if a driver's decision-making process is considered. Various dilemmas involve complex structures that depend primarily on traffic density, a revelation that should help establish a practical solution for reducing traffic congestion. Second, the book provides keen insights into how powerful evolutionary game theory can be in the context of epidemiology. Both approaches, quasi-analytical and multi-agent simulation, can clarify how an infectious disease such as seasonal influenza spreads across a complex social network, which is significantly affected by the public attitude toward vaccination. A methodology is proposed for the optimum design of a public vaccination policy incorporating subsidies to efficiently increase vaccination coverage while minimizing the social cost.

This book introduces a cross-layer design to achieve security and resilience for CPSs (Cyber-Physical Systems). The authors interconnect various technical tools and methods to capture the different properties between cyber and physical layers. Part II of this book bridges the gap between cryptography and control-theoretic tools. It develops a bespoke crypto-control framework to address security and resiliency in control and estimation problems where the outsourcing of computations is possible. Part III of this book bridges the gap between game theory and control theory and develops interdependent impact-aware security defense strategies and cyber-aware resilient control strategies. With the rapid development of smart cities, there is a growing need to integrate the physical systems, ranging from large-scale infrastructures to small embedded systems, with networked communications. The integration of the physical and cyber systems forms Cyber-Physical Systems (CPSs), enabling the use of digital information and control technologies to improve the monitoring, operation, and planning of the systems. Despite these advantages, they are vulnerable to cyber-physical attacks, which aim to damage the physical layer through the cyber network. This book also uses case studies from autonomous systems, communication-based train control systems, cyber manufacturing, and robotic systems to illustrate the proposed methodologies. These case studies aim to motivate readers to adopt a cross-layer system perspective toward security and resilience issues of large and complex systems and develop domain-specific solutions to address CPS challenges. A comprehensive suite of solutions to a broad range of technical challenges in secure and resilient control systems are described in this book (many of the findings in this book are useful to anyone working in cybersecurity). Researchers, professors, and advanced-level students working in computer science and engineering will find this book useful as a reference or secondary text. Industry professionals and military workers interested in cybersecurity will also want to purchase this book.

In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game. Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.

This book presents an epistemic framework for dealing with information-knowledge and certainty-uncertainty problems within the space of quality-quantity dualities. It bridges between theoretical concepts of entropy and entropy measurements, proposing the concept and measurement of fuzzy-stochastic entropy that is applicable to all areas of knowing under human cognitive limitations over the epistemological space. The book builds on two previous monographs by the same author concerning theories of info-statics and info-dynamics, to deal with identification and transformation problems respectively. The theoretical framework is developed by using the toolboxes such as those of the principle of opposites, systems of actual-potential polarities and negative-positive dualities, under different cost-benefit time-structures. The category theory and the fuzzy paradigm of thought, under methodological constructionism-reductionism duality, are used in the fuzzy-stochastic and cost-benefit spaces to point to directions of global application in knowing, knowledge and decision-choice actions. Thus, the book is concerned with a general theory of entropy, showing how the fuzzy paradigm of thought is developed to deal with the problems of qualitative-quantitative uncertainties over the fuzzy-stochastic space, which will be applicable to conditions of soft-hard data, fact, evidence and knowledge over the spaces of problem-solution dualities, decision-choice actions in sciences, non-sciences, engineering and planning sciences to abstract acceptable information-knowledge elements.

The contributions included in the volume are drawn from presentations at ODS2019 - International Conference on Optimization and Decision Science, which was the 49th annual meeting of the Italian Operations Research Society (AIRO) held at Genoa, Italy, on 4-7 September 2019. This book presents very recent results in the field of Optimization and Decision Science. While the book is addressed primarily to the Operations Research (OR) community, the interdisciplinary contents ensure that it will also be of very high interest for scholars and researchers from many scientific disciplines, including computer sciences, economics, mathematics, and engineering. Operations Research is known as the discipline of optimization applied to real-world problems and to complex decision-making fields. The focus is on mathematical and quantitative methods aimed at determining optimal or near-optimal solutions in acceptable computation times. This volume not only presents theoretical results but also covers real industrial applications, making it interesting for practitioners facing decision problems in logistics, manufacturing production, and services. Readers will accordingly find innovative ideas from both a methodological and an applied perspective.

This book proposes novel methods for solving different types of non-cooperative games with interval/fuzzy/intuitionistic fuzzy payoffs. It starts by discussing several existing methods and shows that some mathematically incorrect assumptions have been considered in all these methods. It then proposes solutions to adapt those methods and validate the new proposed methods, such as Gaurika method Ambika-I-IV, Mehar method and others, by using them for solving existing numerical problems. The book offers a comprehensive guide on non-cooperative games with fuzzy payoffs to both students and researchers. It provides them with the all the necessary tools to understand the methods and the theory behind them.

This book is devoted to problems of stochastic control and stopping that are time inconsistent in the sense that they do not admit a Bellman optimality principle. These problems are cast in a game-theoretic framework, with the focus on subgame-perfect Nash equilibrium strategies. The general theory is illustrated with a number of finance applications.In dynamic choice problems, time inconsistency is the rule rather than the exception. Indeed, as Robert H. Strotz pointed out in his seminal 1955 paper, relaxing the widely used ad hoc assumption of exponential discounting gives rise to time inconsistency. Other famous examples of time inconsistency include mean-variance portfolio choice and prospect theory in a dynamic context. For such models, the very concept of optimality becomes problematic, as the decision maker's preferences change over time in a temporally inconsistent way. In this book, a time-inconsistent problem is viewed as a non-cooperative game between the agent's current and future selves, with the objective of finding intrapersonal equilibria in the game-theoretic sense. A range of finance applications are provided, including problems with non-exponential discounting, mean-variance objective, time-inconsistent linear quadratic regulator, probability distortion, and market equilibrium with time-inconsistent preferences. Time-Inconsistent Control Theory with Finance Applications offers the first comprehensive treatment of time-inconsistent control and stopping problems, in both continuous and discrete time, and in the context of finance applications. Intended for researchers and graduate students in the fields of finance and economics, it includes a review of the standard time-consistent results, bibliographical notes, as well as detailed examples showcasing time inconsistency problems. For the reader unacquainted with standard arbitrage theory, an appendix provides a toolbox of material needed for the book.

This Palgrave Pivot presents tournament design mainly within the axioms of incentive compatibility and fairness. It illustrates the advantages of an axiomatic approach through various examples, including several FIFA and UEFA tournaments, and uses theoretical tools and simulation methodology in its analysis. Chapter 1 discusses scoring systems of championships with multiple competitions, ranking in Swiss-system tournaments, and tie-breaking rules in round-robin leagues. It is followed by a thorough critical analysis of the current and previous FIFA World Rankings. The broad focus is substantially narrowed in Chapter 2, which turns to the topic of incentive (in)compatibility in multiple qualifiers. It is revealed that UEFA has faced at least three times recently this problem in the qualification to the UEFA Europa League, qualification to the UEFA Champions League, and the draw of the UEFA Champions League groups. Analogously, Chapter 3 discusses incentive (in)compatibility when there is only one group-based tournament but the complex progression rules to the subsequent stage can be designed poorly. Our examples include the qualifying tournaments of recent FIFA World Cups and UEFA European Championships. Chapter 4 moves to the problem of penalty shootout rules in soccer, where the fairness and complexity of some alternative mechanisms from the literature are evaluated. Fairness remains the central issue in Chapter 5, which presents the challenges of designing a tournament with 24 teams if the number of teams per group cannot exceed four. As expected, there is no perfect solution, and both FIFA and UEFA have introduced a reform in this format recently. Chapter 6 deals with the qualification for the 2020 UEFA European Football Championship. Its tournament design is perhaps the most complicated one that has ever been implemented in the real-world and suffers from serious shortcomings.

This work presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems, in order to optimize some measure of their performance. Started in the 60's under the pressure of the "space race" between the US and the former USSR, the field now has a far wider scope, and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and management of financial markets. These emerging applications require more and more efficient numerical methods for their solution, a very difficult task due the huge number of variables. The chapters of this volume give an up-to-date presentation of several recent methods in this area including fast dynamic programming algorithms, model predictive control and max-plus techniques. This book is addressed to researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.