Winner of the 2017 De Groot Prize awarded by the International Society for Bayesian Analysis (ISBA) A relatively new area of research, adversarial risk analysis (ARA) informs decision making when there are intelligent opponents and uncertain outcomes. Adversarial Risk Analysis develops methods for allocating defensive or offensive resources against intelligent adversaries. Many examples throughout illustrate the application of the ARA approach to a variety of games and strategic situations. Focuses on the recent subfield of decision analysis, ARA Compares ideas from decision theory and game theory Uses multi-agent influence diagrams (MAIDs) throughout to help readers visualize complex information structures Applies the ARA approach to simultaneous games, auctions, sequential games, and defend-attack games Contains an extended case study based on a real application in railway security, which provides a blueprint for how to perform ARA in similar security situations Includes exercises at the end of most chapters, with selected solutions at the back of the book The book shows decision makers how to build Bayesian models for the strategic calculation of their opponents, enabling decision makers to maximize their expected utility or minimize their expected loss. This new approach to risk analysis asserts that analysts should use Bayesian thinking to describe their beliefs about an opponent's goals, resources, optimism, and type of strategic calculation, such as minimax and level-k thinking. Within that framework, analysts then solve the problem from the perspective of the opponent while placing subjective probability distributions on all unknown quantities. This produces a distribution over the actions of the opponent and enables analysts to maximize their expected utilities.

Terrorism, piracy and Low Intensity Maritime Operations are certainly not games, and neither are the responses to thwart them! The two sides are nonetheless locked in an endless mind game with each trying to out-think the other. Game Theory is a branch of applied mathematics that has been used extensively in fields ranging from economics and political science to psychology and biology. The 'game' involves two or more players making decisions so as to maximise their returns. In attempting to do so, they must anticipate the response of their adversaries, sometimes even in the absence of precise information. It is essentially about 'outguessing' the adversary, by putting yourself in the opponents' position. Since a logical adversary would presumably do the same - the interplay between the players and the choices they must make often mirror real-life situations. The book aims to introduce the concept of Game Theory to the uninitiated reader, with the focus on its application to combating terrorism, piracy and for Low Intensity Maritime Operations. Whilst the subject itself involves a fair amount of mathematics, the attempt here has been to emphasise the underlying logic and strategies rather than the full mathematical details.

This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, reflexion in chess, art works, etc. The present book is intended for experts in decision making and control of systems of an interdisciplinary nature, as well as for undergraduates and postgraduates.

Dynamic games arise between players (individuals, firms, countries, animals, etc.) when the strategic interactions among them recur over time and decisions made during one period affect both current and future payoffs. Dynamic games provide conceptually rich paradigms and tools to deal with these situations.This volume provides a uniform approach to game theory and illustrates it with present-day applications to economics and management, including environmental, with the emphasis on dynamic games.At the end of each chapter a case study called game engineering (GE) is provided, to help readers understand how problems of high social priority, such as environmental negotiations, exploitation of common resources, can be modeled as games and how solutions can be engineered.

The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it
In the tradition of "Fermatas Enigma" and "Prime Obsession," George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri PoincarA(c) developed the PoincarA(c) Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldnat prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.
Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.

A major step in differential games is determining an explicit form of the strategies of players who follow a certain optimality principle. To do this, the associated modification of Bellman dynamic programming problems has to be solved; for some differential games this could be Lyapunov functions whose "aresenal" has been supplied by stability theory. This approach, which combines dynamic programming and the Lyapunov function method, leads to coefficient critera, or ratios of the game math model parameters with which optimal strategies of the players not only exist but their analytical form can be specified. In this book coefficient criteria are derived for numerous new and relevant problems in the theory of linear - quadratic multi-player differential games in cases when:
* the player formulate their strategies independently (non co-operative games) and use non-Nash equilibria
* the game model recognises noise, perturbation and other uncertainties of which only their ranges are known (differential games under uncertainty)

The Unpredictability of Gameplay explores the many forms of unpredictability in games and proposes a comprehensive theoretical framework for understanding and categorizing non-deterministic game mechanics. Rather than viewing all game mechanics with unpredictable outcomes as a single concept, Mark R. Johnson develops a three-part typology for such mechanics, distinguishing between randomness, chance, and luck in gameplay, assessing games that range from grand strategy and MMORPGs to slot machines and card games. He also explores forms of unanticipated unpredictability, where elements of games fail to function as intended and create new forms of gameplay in the process. Covering a range of game concepts using these frameworks, The Unpredictability of Gameplay then explores three illustrative case studies: 1) procedural generation, 2) replay value and grinding, and 3) player-made practices designed to reduce the level of luck in non-deterministic games. Throughout, Johnson demonstrates the importance of looking more deeply at unpredictability in games and game design and the various ways in which unpredictability manifests while offering an invaluable tool for game scholars and game designers seeking to integrate unpredictability into their work.

A mathematical tool for scientists and researchers who work with computer and communication networks, Game Theory in Communication Networks: Cooperative Resolution of Interactive Networking Scenarios addresses the question of how to promote cooperative behavior in interactive situations between heterogeneous entities in communication networking scenarios. It explores network design and management from a theoretical perspective, using game theory and graph theory to analyze strategic situations and demonstrate profitable behaviors of the cooperative entities.

The book promotes the use of Game Theory to address important resource management and security issues found in next generation communications networks, particularly heterogeneous networks, for cases where cooperative interactive networking scenarios can be formulated. It provides solutions for representative mechanisms that need improvement by presenting a theoretical step-by-step approach. The text begins with a presentation of theory that can be used to promote cooperation for the entities in a particular interactive situation. Next, it examines two-player interaction as well as interactions between multiple players. The final chapter presents and examines a performance evaluation framework based on MATLAB(r).

Each chapter begins by introducing basic theory for dealing with a particular interactive situation and illustrating how particular aspects of game theory can be used to formulate and solve interactive situations that appear in communication networks regularly. The second part of each chapter presents example scenarios that demonstrate the applicability and power of the theory illustrating a number of cooperative interactions and discussing how they could be addressed within the theoretical framework presented in the first part of the chapter.

The book also includes simulation code that can be downloaded so you can use some or all of the proposed models to improve your own network designs. Specific topics covered include network selection, user-network interaction, network synthesis, and context-aware security provisioning.

This book is taken from the lectures given at the ENSAE in March 1998 and at the Scuola Normale Superiore in May 1998. At the beginning of the 70's, the set of mathematical methods of finance were reduced to actuarial calculus. The modern approach uses the stochastic calculus theory and evidences the duality between problems of arbitrage and valorisation and a set of martingale probabilities.