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.

The Great War is an immense, confusing and overwhelming historical conflict - the ideal case study for teaching game theory and international relations. Using thirteen historical puzzles, from the outbreak of the war and the stability of attrition, to unrestricted submarine warfare and American entry into the war, this book provides students with a rigorous yet accessible training in game theory. Each chapter shows, through guided exercises, how game theoretical models can explain otherwise challenging strategic puzzles, shedding light on the role of individual leaders in world politics, cooperation between coalitions partners, the effectiveness of international law, the termination of conflict, and the challenges of making peace. Its analytical history of World War I also surveys cutting edge political science research on international relations and the causes of war. Written by a leading game theorist known for his expertise of the war, this textbook includes useful student features such as chapter key terms, contemporary maps, a timeline of events, a list of key characters and additional end-of-chapter game-theoretic exercises.