Download or read book Approximate Equilibria in Large Games written by Yu Wu and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The complexity of studying Nash equilibrium in large games often scales with the size of the system: as it increases, computing the exact Nash equilibrium can soon become intractable. However, when the number of players in the system approaches infinity and no individual player has a significant impact on the system, we can approximate the system by considering each single player no longer playing against other individual players but a single aggregation of all other players. In this paper, we apply this idea to study and approximate Nash equilibria in two large scale games. In part I, we consider a model of priced resource sharing that combines both queueing behavior and strategic behavior. We study a priority service model where a single server allocates its capacity to agents in proportion to their payment to the system, and users from different classes act to minimize the sum of their cost for processing delay and payment. As the exact processing time of this system is hard to compute and cannot be characterized in closed form, we introduce the concept of aggregate equilibrium to approximate the exact Nash equilibrium, by assuming each individual player plays against a common aggregate priority that characterizes the large system. We then introduce the notion of heavy traffic equilibrium as an alternative approximation of the Nash equilibrium, derived by considering the asymptotic regime where the system load approaches capacity. We show that both aggregate equilibrium and heavy traffic equilibrium are asymptotically exact in heavy traffic. We present some numerical results for both approximate equilibria, and discuss efficiency and revenue, and in particular provide a bound for the price of anarchy of the heavy traffic equilibrium. In part II, we study the reputation system of large scale online marketplace. We develop a large market model to study reputation mechanisms in online marketplaces. We consider two types of sellers: commitment sellers, who are intrinsically honest but may be unable to accurately describe items because of limited expertise; and strategic sellers, who are driven by a profit maximization motive. We focus on stationary equilibria for this dynamic market, in particular, on separating equilibria where strategic sellers are incentivized to describe the items they have for sale truthfully, and characterize the conditions under which such equilibria exist. We then complement our theoretical results with computational analysis and provide insights on the features of markets that may incentivize truthfulness in equilibrium.
Download or read book Nash Equilibria of Games with a Continuum of Players written by Guilherme Carmona and published by . This book was released on 2006 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We characterize Nash equilibria of games with a continuum of players (Mas-Colell (1984)) in terms of approximate equilibria of large finite games. For the concept of (; ) equilibrium in which the fraction of players not optimizing is less than we show that a strategy is a Nash equilibrium in a game with a continuum of players if and only if there exists a sequence of finite games such that its restriction is an (n; n) equilibria, with n converging to zero. The same holds for equilibrium in which almost all players are optimizing provided that either players' payoff functions are equicontinuous or players' action space is finite. Furthermore, we give conditions under which the above results hold for all approximating sequences of games. In our characterizations, a sequence of finite games approaches the continuum game in the sense that the number of players converges to infinity and the distribution of characteristics and actions in the finite games converges to that of the continuum game. These results render approximate equilibria of large finite economies as an alternative way of obtaining strategic insignificance.
Download or read book Finding Equilibria in Large Sequential Games of Imperfect Information written by Andrew Gilpin and published by . This book was released on 2005 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "Computing an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomorphic abstraction transformation. For an n-player sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an abstracted smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an efficient algorithm, GameShrink, which automatically and exhuastively abstracts the game. Using GameShrink, we find an equilibrium to a poker game that is over four orders of magnitude larger than the largest poker game solved previously. To address even larger games, we introduce approximation methods that do not preserve equilibrium, but nevertheless yield (ex post) provably close-to-optimal strategies."
Download or read book Learning to play approximate nash equilibria in games with many players written by Edward Cartwright and published by . This book was released on 2004 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithmic Game Theory written by Martin Gairing and published by Springer. This book was released on 2016-09-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 9th International Symposium on Algorithmic Game Theory, SAGT 2016, held in Liverpool, UK, in September 2016.The 26 full papers presented together with 2 one-page abstracts were carefully reviewed and selected from 62 submissions. The accepted submissions cover various important aspectsof algorithmic game theory such as computational aspects of games, congestion games and networks, matching and voting, auctions and markets, and mechanism design. /div
Download or read book Equilibria and Approximate Equilibria in Infinite Potential Games written by Mark Voorneveld and published by . This book was released on 1996 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Twenty Lectures on Algorithmic Game Theory written by Tim Roughgarden and published by Cambridge University Press. This book was released on 2016-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science and economics have engaged in a lively interaction over the past fifteen years, resulting in the new field of algorithmic game theory. Many problems that are central to modern computer science, ranging from resource allocation in large networks to online advertising, involve interactions between multiple self-interested parties. Economics and game theory offer a host of useful models and definitions to reason about such problems. The flow of ideas also travels in the other direction, and concepts from computer science are increasingly important in economics. This book grew out of the author's Stanford University course on algorithmic game theory, and aims to give students and other newcomers a quick and accessible introduction to many of the most important concepts in the field. The book also includes case studies on online advertising, wireless spectrum auctions, kidney exchange, and network management.
Download or read book Exact and Approximate Equilibria for Network Formation and Cut Games written by Bugra Caskurlu and published by . This book was released on 2010 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Empirical Evaluation of Algorithms for Computing Equilibria in Games for Approximate Inference in Large Dimensional Probabilistic Graphical Models written by and published by . This book was released on 2017 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Work in graphical models for game theory typically borrows from results in probabilistic graphical models. In this work, we instead consider the opposite direction. By using recent advances in equilibrium computation, we propose game-theoretic inspired, practical methods to perform probabilistic inference. We perform synthetic experiments using several different classes of Ising models, in order to evaluate our proposed approximation algorithms along with existing methods in the probabilistic graphical model literature. We also perform experiments using Ising models learned from the popular MNIST dataset. Our experiments show that the game-theoretic inspired methods are competitive with current state-of-the-art algorithms such as tree-reweighed message passing, and even consistently outperform said algorithms in certain cases.
Download or read book Algorithmic Game Theory written by Vittorio Bilò and published by Springer. This book was released on 2017-08-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Symposium on Algorithmic Game Theory, SAGT 2017, held in L'Aquila, Italy, in September 2017. The 30 full papers presented were carefully reviewed and selected from 66 submissions. The papers cover various important aspects of algorithmic game theory such as auctions, computational aspects of games, congestion games, network and opinion formation games, mechanism design, incentives and regret minimization, and resource allocation.
Download or read book Algorithms ESA 2007 written by Lars Arge and published by Springer. This book was released on 2007-09-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th Annual European Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 in the context of the combined conference ALGO 2007. The 63 revised full papers presented together with abstracts of three invited lectures address all current subjects in algorithmics reaching from design and analysis issues of algorithms over to real-world applications and engineering of algorithms in various fields.
Download or read book A Long Run Collaboration on Long Run Games written by Drew Fudenberg and published by World Scientific. This book was released on 2009 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the joint work of Drew Fudenberg and David Levine (through 2008) on the closely connected topics of repeated games and reputation effects, along with related papers on more general issues in game theory and dynamic games. The unified presentation highlights the recurring themes of their work.
Download or read book Algorithmic Game Theory written by Ioannis Caragiannis and published by Springer Nature. This book was released on 2021-09-14 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Symposium on Algorithmic Game Theory, SAGT 2021, held in Aarhus, Denmark in September 2021. The 26 full papers presented together with 4 abstract papers were carefully reviewed and selected from 73 submissions. In addition, the volume contains abstracts from 3 invited talks and 2 tutorial talks. The papers are organized in topical sections named: auctions and mechanism design, computational aspects of games, markets and matchings, and social choice and cooperative games.
Download or read book Approximate Equilibria for Bayesian Multi criteria Games written by Lina Mallozzi and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mean Field Games written by François Delarue and published by American Mathematical Society. This book was released on 2021-12-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
Download or read book Approximating Equilibria for Infinite Horizon Dynamic Games written by Freddie García and published by . This book was released on 1997 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Equilibrium Theory written by C.D. Aliprantis and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
