We live in a highly connected world with multiple self-interested agents interacting and myriad opportunities for conflict and cooperation. The goal of game theory is to understand these opportunities. This book presents a rigorous introduction to the mathematics of game theory without losing sight of the joy of the subject. This is done by focusing on theoretical highlights (e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting exciting connections of game theory to other fields such as computer science (algorithmic game theory), economics (auctions and matching markets), social choice (voting theory), biology (signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-sum games, and modern topics, such as sponsored search auctions, are covered. Along the way, beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point theorems, and probabilistic arguments. The book is appropriate for a first course in game theory at either the undergraduate or graduate level, whether in mathematics, economics, computer science, or statistics. The importance of game-theoretic thinking transcends the academic setting—for every action we take, we must consider not only its direct effects, but also how it influences the incentives of others.

This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.

Since the origins in its modern form, due to the seminal works of von Neumann and Nash, Game theory has most often been considered for its applications to economic and social sciences. However, its mathematical roots are more general, and its set of analytical tools that can be used to predict the outcome of interactive decision situations can be very relevant for many other scientific fields, especially including information and industrial engineering, where it has recently become a common curricular subject in university programs. To train the “brain muscles” to solve problems in a game theoretic way, students may find it useful to practice on concrete examples. For this reason, this book presents a collection of exercises that can be suitable for any entry-level course on Game theory. While there is no specific major for which such a practical activity can be useful, the book is conceived with an engineering spirit, and a general regard for modeling and optimization (from technological scenarios to childish gameplay). Still, some useful considerations can also be derived for other fields such as social psychology, biology, or humanities. Rather than in-depth speculative discussions, the book covers mostly practical cases, however providing a preliminary theoretical justification for the solution methods. Covered topics include static games of complete information, zero-sum games and minimax problems, lotteries, sequential games, multistage games, Bayesian games. This may also encourage the reader to approach more advanced topics, with a solid methodological background and a full-rounded appreciation of the subject.

This book offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and classical. The combination allows for a dynamic and rich tour of the subject united by a common theme of strategic reasoning. Designed as a textbook for an undergraduate mathematics class and with ample material and limited dependencies between the chapters, the book is adaptable to a variety of situations and a range of audiences. Instructors, students, and independent readers alike will appreciate the flexibility in content choices as well as the generous sets of exercises at various levels.

This book collects notes that were prepared for a university course taught in the Spring of 2018, and delivered to an audience of students enrolled in the Master course in Logic, philosophy and history of science of the University of Florence. The goal of the course was to introduce students to some basic concepts from the area of research generally known as decision theory. This is done by focussing on the concept of ‘rational choice’, which is analyzed, methodologically speaking, by the means of the theory of games. To minimize prerequisites it was decided to restrict the attention to the theory of finite games in particular. The topics treated are vary, and belongs to both the theory of games ‘in normal form’ as well as that of games ‘in extensive form’, as they are usually referred to. The classical issues in both fields, such as the theory of ‘equilibria’ and the study of properties such as determinacy, are carefully discussed to make them clear to beginners and are addressed from a novel perspective which makes use of formal methods that are typical of researches connected with the study of logic.

In recent decades game theory—the mathematics of rational decision-making by interacting individuals—has assumed a central place in our understanding of capitalist markets, the evolution of social behavior in animals, and even the ethics of altruism and fairness in human beings. With game theory’s ubiquity, however, has come a great deal of misunderstanding. Critics of the contemporary social sciences view it as part of an unwelcome trend toward the marginalization of historicist and interpretive styles of inquiry, and many accuse its proponents of presenting a thin and empirically dubious view of human choice. The World the Game Theorists Made seeks to explain the ascendency of game theory, focusing on the poorly understood period between the publication of John von Neumann and Oscar Morgenstern’s seminal Theory of Games and Economic Behavior in 1944 and the theory’s revival in economics in the 1980s. Drawing on a diverse collection of institutional archives, personal correspondence and papers, and interviews, Paul Erickson shows how game theory offered social scientists, biologists, military strategists, and others a common, flexible language that could facilitate wide-ranging thought and debate on some of the most critical issues of the day.

The 2023 2nd International Conference on Information Economy, Data Modeling and Cloud Computing (ICIDC 2023) was therefore held during June 2nd to 4th, 2023 in Nanchang, China (hybrid form). The Conference was attended by more than 100 participants and hosted four keynote speeches, more than 60 oral presentations as well as various poster presentations. The proceedings of ICIDC 2023 cover various topics, including Big Data Finance, E-Commerce and Digital Business, Modeling Method, 3D Modeling, Internet of Things, Cloud Computing Platform, etc. All the papers have been checked through rigorous review and processes to meet the requirements of publication. Data modeling allows us to obtain the dynamic change trend of various indicator data, so how to use big data information to model and study the development trend of economic operation plan is of great significance. And that is exactly the purpose of this conference, focusing on the application of big data in the economic field as well as conducting more profound research in combination with cloud computing.

Individuals, firms, governments and nations behave strategically, for good and bad. Over the last few decades, game theory has been constructed and progressively refined to become the major tool used by social scientists to understand, predict and regulate strategic interaction among agents who often have conflicting interests. In the surprisingly anodyne jargon of the theory, they ‘play games’. This book offers an introduction to the basic tools of game theory and an overview of a number of applications to real-world cases, covering the areas of economics, politics and international relations. Each chapter is accompanied by some suggestions about further reading.

The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.

"One of the best Decision Making and Game Theory books of all time." —Reid Hoffman (LinkedIn founder) and Nassim Nicholas Taleb (author of Black Swan), BookAuthority An accessible, light-hearted exploration of Game Theory—what it is, why it’s important, and how it can help us in our daily lives Game Theory is the mathematical formalization of interactive decision-making—it assumes that each player's goal is to maximize his/her benefit, whatever it may be. Players may be friends, foes, political parties, states, or any entity that behaves interactively, whether collectively or individually. One of the problems with game analysis is the fact that, as a player, it’s very hard to know what would benefit each of the other players. Some of us are not even clear about our own goals or what might actually benefit us. In Gladiators, Pirates, and Games of Trust, Haim Shapira shares humorous anecdotes and insightful examples to explain Game Theory, how it affects our daily lives, and how the different interactions between decision-makers can play out. In this book, you will: • Meet Nobel Laureate John F. Nash and familiarize yourself with Nash equilibrium • Learn the basic ideas of the art of negotiation • Visit the gladiators’ ring and apply for a coaching position • Build an airport and divide inheritance • Issue ultimatums and learn to trust • Review every aspect of the prisoner’s dilemma and learn about the importance of cooperation • Learn how statistics bolster lies • And much more