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.'

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.

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.

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.

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.

In a series of conversational essays, this textbook discusses the manner in which economic thought addresses a broad array of everyday issues beyond classical textbook treatments. In the spirit of popular economics books, the author uncovers economic issues and solutions from individuals, businesses, society, and the country as a whole in a decidedly non-technical and relatable manner. Should the federal government mandate use of child safety seats on commercial airlines? Can genetic information substitute for a college degree? The contents of this book touch on many of these contemporary topics in an accessible way. Addressing undergraduate and graduate students, as well as scholars in different fields of economics, this book is a must-read for everybody interested in a better understanding of economic thought.

The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

This book examines how China's decentralization process has affected and will affect the country's macroeconomic performance and the functioning of the market. With an innovative application of game theory, the author develops an analytical framework that can explain the behaviour of the central and local governments under alternative institutional environments. The study also suggests how to establish desirable rules of games in China's political and economic institutions through appropriate reforms.

This book provides a comprehensive study of asymmetric territorial conflict combining game theory, statistical empirical analysis and historiographic analysis. It proposes a model to explain the dynamics of territorial conflict between rivals with a wide disparity in capabilities between them. Using the Israeli-Palestinian conflict as a case study and testing the model on a database of almost four hundred territorial conflicts, Resnick argues that changes in 'patience' - explained by parallel evolutionary processes occurring in the respectively strong and weak societies - underlie the changing behaviour witnessed in such rivalries. Located within the general context of the interplay between material constraints and ideas, the theoretical significance of this model goes beyond the context of territorial conflict and can be seen to provide an explanation for the ideational aspects of power transitions and change in world politics.This book constitutes a significant advance in the literature on territorial conflict, which has increasingly come to be recognized as a key field of enquiry in the discipline of conflict studies and international relations scholarship in general.

As with the previous editions, this fourth edition relies on teaching by example and the Karplus Learning Cycle to convey the ideas of game theory in a way that is approachable, intuitive, and interdisciplinary. Noncooperative equilibrium concepts such as Nash equilibrium, mixed strategy equilibria, and subgame perfect equilibrium are systematically introduced in the first half of the book. Bayesian Nash equilibrium is briefly introduced. The subsequent chapters discuss cooperative solutions with and without side payments, rationalizable strategies and correlated equilibria, and applications to elections, social mechanism design, and larger-scale games. New examples include panic buying, supply-chain shifts in the pandemic, and global warming.

It is a common complaint against moral philosophers that their abstract theorising bears little relation to the practical problems of everyday life. Professor Braithwaite believes that this criticism need not be inevitable. With the help of the Theory of Games he shows how arbitration is possible between two neighbours, a jazz trumpeter and a classical pianist, whose performances are a source of mutual discord. The solution of the problem in the lecture is geometrical, and is based on the formal analogy between the logic of the situation and the geometry of a parabola. But an appendix provides the alternative algebraic treatment of a general two-person collaboration situation.

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

Game theory has been applied to a growing list of practical problems, from antitrust analysis to monetary policy; from the design of auction institutions to the structuring of incentives within firms; from patent races to dispute resolution. The purpose of Game Theory and Business Applications is to show how game theory can be used to model and analyze business decisions. The contents of this revised edition contain a wide variety of business functions - from accounting to operations, from marketing to strategy to organizational design. In addition, specific application areas include market competition, law and economics, bargaining and dispute resolution, and competitive bidding. All of these applications involve competitive decision settings, specifically situations where a number of economic agents in pursuit of their own self-interests and in accordance with the institutional "rules of the game" take actions that together affect all of their fortunes. As this volume demonstrates, game theory provides a compelling guide for analyzing business decisions and strategies.

This book focuses on the game-theoretical semantics and epistemic logic of Jaakko Hintikka. Hintikka was a prodigious and esteemed philosopher and logician, and his death in August 2015 was a huge loss to the philosophical community. This book, whose chapters have been in preparation for several years, is dedicated to the work of Jaako Hintikka, and to his memory. This edited volume consists of 23 contributions from leading logicians and philosophers, who discuss themes that span across the entire range of Hintikka's career. Semantic Representationalism, Logical Dialogues, Knowledge and Epistemic logic are among some of the topics covered in this book's chapters. The book should appeal to students, scholars and teachers who wish to explore the philosophy of Jaako Hintikka.

This book is a collection of selected papers presented at the consecutively held international conferences on "Game Theory and Networks", organized by the Department of Mathematics, Dibrugarh University, India, in collaboration with the Economics Department of Queen's University, Belfast, UK, during September 6-9, 2019 and September, 13-15 2018. The book includes chapters on network measures and network formation, application of network theory to contagion, biological data and finance and macroeconomics as expository articles. The book also contains chapters on fair allocation in the context of queuing, rationing and cooperative games with transferable utilities for engaged researchers. A few survey chapters on non-cooperative game theory, evolutionary game theory, mechanism design and social choice theory are also incorporated to cater to the needs of the beginners in the field. This book discusses the use of game theoretic tools and network models across disciplines: mathematics, statistics, economics, computer science, political science, sociology and psychology. It aims at providing a suitable learning experience to beginners on the basics of cooperative games, networks and mechanism design, as well as recent developments to research scholars having the basic knowledge of these topics.