Nash equilibrium is the central solution concept in Game Theory. Since Nash's original paper in 1951, it has found countless applications in modeling strategic behavior of traders in markets, (human) drivers and (electronic) routers in congested networks, nations in nuclear disarmament negotiations, and more. A decade ago, the relevance of this solution concept was called into question by computer scientists, who proved (under appropriate complexity assumptions) that computing a Nash equilibrium is an intractable problem. And if centralized, specially designed algorithms cannot find Nash equilibria, why should we expect distributed, selfish agents to converge to one? The remaining hope was that at least approximate Nash equilibria can be efficiently computed.Understanding whether there is an efficient algorithm for approximate Nash equilibrium has been the central open problem in this field for the past decade. In this book, we provide strong evidence that even finding an approximate Nash equilibrium is intractable. We prove several intractability theorems for different settings (two-player games and many-player games) and models (computational complexity, query complexity, and communication complexity). In particular, our main result is that under a plausible and natural complexity assumption ("Exponential Time Hypothesis for PPAD"), there is no polynomial-time algorithm for finding an approximate Nash equilibrium in two-player games. The problem of approximate Nash equilibrium in a two-player game poses a unique technical challenge: it is a member of the class PPAD, which captures the complexity of several fundamental total problems, i.e., problems that always have a solution; and it also admits a quasipolynomial time algorithm. Either property alone is believed to place this problem far below NP-hard problems in the complexity hierarchy; having both simultaneously places it just above P, at what can be called the frontier of intractability. Indeed, the tools we develop in this book to advance on this frontier are useful for proving hardness of approximation of several other important problems whose complexity lies between P and NP: Brouwer's fixed point, market equilibrium, CourseMatch (A-CEEI), densest k-subgraph, community detection, VC dimension and Littlestone dimension, and signaling in zero-sum games.

Alternate Reality Games (ARGs) challenge what players understand as "real." Alternate Reality Games and the Cusp of Digital Gameplay is the first collection to explore and define the possibilities of ARGs. Though prominent examples have existed for more than two decades, only recently have ARGs come to the prominence as a unique and highly visible digital game genre. Adopting many of the same strategies as online video games, ARGs blur the distinction between real and fictional. With ARGs continuing to be an important and blurred space between digital and physical gameplay, this volume offers clear analysis of game design, implementation, and ramifications for game studies. Divided into three distinct sections, the contributions include first hand accounts by leading ARG creators, scholarly analysis of the meaning behind ARGs, and explorations of how ARGs are extending digital tools for analysis. By balancing the voices of designers, players, and researchers, this collection highlights how the Alternate Reality Game genre is transforming the ways we play and interact today.

The advent of the internet largely changed the landscape of marketing to adopt a wide variety of communication techniques and creative selling on virtual platforms. Gaming provides a highly pervasive and influential mode of offering new media communication to consumers that can be further improved by digital innovation. Application of Gaming in New Media Marketing is a collection of vital research on the methods and applications of gaming in marketing, including its growth, recent trends, practices, issues, and main challenges. Highlighting a range of topics including digital advertising, media planning, and social media marketing, this book is ideally designed for marketers, software developers, managers, business researchers, academicians, and graduate-level students seeking current research on new and innovative methods to reach and connect with audiences through games in a highly interactive, measurable, and focused way.

This book explores what it means to be rational in a variety of contexts, from personal decisions to those affecting large groups of people. It introduces ideas from economics, philosophy, and other areas, showing how the theory applies to particular situations such as gambling and the allocation of resources.

The mathematical challenges coming from the social and behavioral sciences differ significantly from typical applied mathematical concerns. ""Change,"" for instance, is ubiquitous, but without knowing the fundamental driving force, standard differential and iterative methods are not appropriate. Although differing forms of aggregation are widely used, a general mathematical assessment of potential pitfalls is missing. These realities provide opportunities to create new mathematical approaches. These themes are described in an introductory, expository, and accessible manner by exploring new ways to handle dynamics and evolutionary game theory, to identify subtleties of decision and voting methods, to recognize unexpected modeling concerns, and to introduce new approaches with which to examine game theory. Applications range from avoiding undesired consequences when designing policy to identifying unanticipated voting (where the ""wrong"" person could win), nonparametric statistical, and economic ""supply and demand"" properties.

The description for this book, Contributions to the Theory of Games (AM-40), Volume IV, will be forthcoming.

Rooted in a pedagogically successful problem-solving approach to linear algebra, the present work fills a gap in the literature that is sharply divided between elementary texts and books that are too advanced to appeal to a wide audience. It clearly develops the theoretical foundations of vector spaces, linear equations, matrix algebra, eigenvectors, and orthogonality, while simultaneously emphasizing applications and connections to fields such as biology, economics, computer graphics, electrical engineering, cryptography, and political science. Ideal as an introduction to linear algebra, the extensive exercises and well-chosen applications also make this text suitable for advanced courses at the junior or senior undergraduate level. Furthermore, it can serve as a colorful supplementary problem book, reference, or self-study manual for professional scientists and mathematicians. Complete with bibliography and index, "Essential Linear Algebra with Applications" is a natural bridge between pure and applied mathematics and the natural and social sciences, appropriate for any student or researcher who needs a strong footing in the theory, problem-solving, and model-building that are the subject's hallmark.

The use of game theory (GT) in water resources by different disciplinary professions including, but not limited to, engineers, international relations experts, economists, and geographers, is vast and impressive. The objective of Game Theory and Water Resources is to collect this vast literature, catalogue it, and provide present and future practitioners of game theory in water resources with a source of information that can be useful for their research. The authors assume that readers of this monograph have the basic skills in game theory, and have kept explanations of game theory concepts to a minimum. Game Theory and Water Resources introduces the topics and moves onto reporting the historical trends observed in the accumulation of GT publications on water between 1942 and 2013. Section 3 describes the developments in Cooperative GT-methodologies to water issues, whose applications ruled the GT applications during the period 1950-1990. Section 4 reviews the development of Non-Cooperative GT (NCGT) methodologies to various water issues. Section 5 provides a comprehensive review of GT surveys that have been published in the literature. Section 6 reviews Game Theory applications by sub-sector -- the authors identify 11 sub-sectors and review the applications of GT approaches to each of them. The monograph ends with a conclusion and identification of remaining problems to be addressed in the future.

This is a guide, in theory and in practice, to how current technological changes have impacted our interaction with texts and with each other. Henry Sussman rereads pivotal moments in literary, philosophical and cultural modernity as anticipating the cybernetic discourse that has increasingly defined theory since the computer revolution. Cognitive science, psychoanalysis and systems theory are paralleled to current trends in literary and philosophical theory. Chapters alternate between theory and readings of literary texts, resulting in a broad but rigorously grounded framework for the relation between literature and computer science. This book is a refreshing perspective on the analog-orientated tradition of theory in the humanities - and offers the first literary-textual genealogy of the digital.

Complex-Valued Modeling in Economics and Finance outlines the theory, methodology, and techniques behind modeling economic processes using complex variables theory. The theory of complex variables functions is widely used in many scientific fields, since work with complex variables can appropriately describe different complex real-life processes. Many economic indicators and factors reflecting the properties of the same object can be represented in the form of complex variables. By describing the relationship between various indicators using the functions of these variables, new economic and financial models can be created which are often more accurate than the models of real variables. This book pays critical attention to complex variables production in stock market modeling, modeling illegal economy, time series forecasting, complex auto-aggressive models, and economic dynamics modeling. Very little has been published on this topic and its applications within the fields of economics and finance, and this volume appeals to graduate-level students studying economics, academic researchers in economics and finance, and economists.