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 A Game with No Bayesian Approximate Equilibria written by Ziv Hellman and published by . This book was released on 2012 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Bayesian Theory of Games written by Dr Jimmy Teng and published by Chartridge Books Oxford. This book was released on 2013-10-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summary A Bayesian Theory of Games introduces a new game theoretic equilibrium concept: Bayesian equilibrium by iterative conjectures (BEIC). The new equilibrium concept achieves consistencies in results among different types of games that current games theory at times fails to. BEIC requires players to make predictions on the strategies of other players starting from first order uninformative predictive distribution functions (or conjectures) and keep updating with Bayesian statistical decision theoretic and game theoretic reasoning until a convergence of conjectures is achieved. In a BEIC, conjectures are consistent with the equilibrium or equilibriums they supported and so rationality is achieved for actions, strategies and beliefs and (statistical) decision rule. Given its ability to typically select only a unique equilibrium in games, the BEIC approach is capable of analyzing a larger set of games than current games theory, including games with noisy inaccurate observations and games with multiple sided incomplete information games. Key Features Provides a unified and consistent analysis of many categories of games. Its solution algorithm is iterative and has good computation properties. Can analyze more types of games than current existing games theory. The equilibrium concept and solution algorithm are based on Bayesian statistical decision theory. In the new equilibrium, rationality is achieved for action, strategy, belief (both prior and posterior) and decision rule. Beliefs are the results of optimization exercises of players. Uses first order uninformative conjectures and reaction functions to derive higher and higher orders of conjectures until a convergence of conjectures is achieved. Has great application value for it could solve many types of games and could model beliefs. The Author Dr Jimmy Teng currently teaches at the School of Economics of the University of Nottingham (Malaysia Campus). He is the author of many articles and two books. He received his economics PhD from the University of Toronto. He also earned a PhD in political Science and a MS in statistics from Duke University. He previously held research and teaching positions in Academia Sinica, National Taiwan University and Nanyang Technological University Readership Games theorists, decision theorists, economists, mathematicians, statisticians, operational researchers, social scientists, management researchers, public policy researchers, computer scientists Contents Preface Acknowledgments About the author Introduction Sequential games with incomplete information and noisy inaccurate observation; introduction; an inflationary game; Bayesian iterative conjectures algorithm as a Bayes decision rule; conclusions Sequential games with perfect and imperfect information; introduction; the Bayesian iterative conjecture algorithm, sub-game perfect equilibrium and perfect Bayesian equilibrium; solving sequential games of incomplete and perfect information; multiple-sided incomplete information sequential games with perfect information; conclusions Simultaneous games; introduction; complete information simultaneous games; BEIC and refinements of Nash equilibrium; simultaneous games with incomplete information; conclusions Conclusions References Index

Download or read book Equilibria Existence in Bayesian Games Climbing the Countable Borel Equivalence Relation Hierarchy written by Ziv Hellman and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution concept of a Bayesian equilibrium of a Bayesian game is inherently an interim concept. The corresponding ex ante solution concept has been termed Harsányi equilibrium; examples have appeared in the literature showing that there are Bayesian games with uncountable state spaces that have no Bayesian approximate equilibria but do admit Harsányi approximate equilibrium, thus exhibiting divergent behaviour in the ex ante and interim stages. Smoothness, a concept from descriptive set theory, has been shown in previous works to guarantee the existence of Bayesian equilibria. We show here that higher rungs in the countable Borel equivalence relation hierarchy can also shed light on equilibrium existence. In particular, hyperfiniteness, the next step above smoothness, is a sufficient condition for the existence of Harsányi approximate equilibria in purely atomic Bayesian games.

Download or read book Many Criteria Optimization and Decision Analysis written by Dimo Brockhoff and published by Springer Nature. This book was released on 2023-07-28 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art, current challenges, and future perspectives for the field of many-criteria optimization and decision analysis. The field recognizes that real-life problems often involve trying to balance a multiplicity of considerations simultaneously – such as performance, cost, risk, sustainability, and quality. The field develops theory, methods and tools that can support decision makers in finding appropriate solutions when faced with many (typically more than three) such criteria at the same time. The book consists of two parts: key research topics, and emerging topics. Part I begins with a general introduction to many-criteria optimization, perspectives from research leaders in real-world problems, and a contemporary survey of the attributes of problems of this kind. This part continues with chapters on fundamental aspects of many-criteria optimization, namely on order relations, quality measures, benchmarking, visualization, and theoretical considerations. Part II offers more specialized chapters on correlated objectives, heterogeneous objectives, Bayesian optimization, and game theory. Written by leading experts across the field of many-criteria optimization, this book will be an essential resource for researchers in the fields of evolutionary computing, operations research, multiobjective optimization, and decision science.

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 Approximation and Online Algorithms written by Evripidis Bampis and published by Springer Science & Business Media. This book was released on 2009-02-02 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 6th Workshop on Approximation and Online Algorithms (WAOA 2008) focused on the design and analysis of algorithms for online and computati- ally hard problems. Both kinds of problems have a large number of appli- tions from a variety of ?elds. WAOA 2008 took place in Karlsruhe, Germany, during September 18–19, 2008. The workshop was part of the ALGO 2008 event that also hosted ESA 2008, WABI 2008, and ATMOS 2008. The pre- ous WAOA workshops were held in Budapest (2003), Rome (2004), Palma de Mallorca (2005), Zurich (2006), and Eilat (2007). The proceedings of these p- viousWAOA workshopsappearedasLNCS volumes2909,3351,3879,4368,and 4927, respectively. Topics of interest for WAOA 2008 were: algorithmic game theory, appro- mation classes, coloring and partitioning, competitive analysis, computational ?nance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms for design and analysis of approximationand online algorithms, randomizationtechniques, real-world applications, and scheduling problems. In response to the call for - pers,wereceived56submissions.Eachsubmissionwasreviewedbyatleastthree referees, and the vast majority by at least four referees. The submissions were mainly judged on originality, technical quality, and relevance to the topics of the conference. Based on the reviews, the Program Committee selected 22 papers. We are grateful to Andrei Voronkov for providing the EasyChair conference system,whichwasusedtomanagetheelectronicsubmissions,thereviewprocess, and the electronic PC meeting. It made our task much easier. We would also like to thank all the authors who submitted papers to WAOA 2008 as well as the local organizers of ALGO 2008.

Download or read book Equilibria in Random and Bayesian Games with a Continuum of Players written by Erik Jan Balder and published by . This book was released on 1989 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Frontiers of Game Theory written by K. G. Binmore and published by MIT Press. This book was released on 1993 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: seventeen contributions reflecting the many diverse approaches in the field todayThese seventeen contributions take up the most recent research in game theory, reflecting the many diverse approaches in the field today. They are classified in five general tactical categories - prediction, explanation, investigation, description, and prescription - and wit in these along applied and theoretical divisions. The introduction clearly lays out this framework.

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 Bayesian Estimation of Discrete Games of Complete Information written by Sridhar Narayanan and published by . This book was released on 2011 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Approximation Guarantees for Game theoretic Equilibria written by Kshipra Bhawalkar and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Game-theoretic equilibria model natural outcomes of selfish behavior. The concept of the "Price of Anarchy (POA)" captures how well game-theoretic equilibria approximate the socially optimal outcome. In this dissertation, we consider the POA in three different models, as a function of different design parameters and equilibrium concepts. We first consider weighted congestion games where players compete to share resources. The cost of a resource depends on the total weight of the players using that resource and players are allowed to use only certain subsets of the resources. Routing games are a canonical example of such games. We provide a precise characterization of the POA as a function of the resource cost functions. We also explore how the POA is affected by the structure of the permitted strategies for the players. Our bounds apply to pure Nash, mixed Nash, correlated, and coarse-correlated equilibria. We next consider opinion formation games, where players in a social network choose opinions to express to minimize the cost of disagreement with their neighbors' opinions and their own intrinsic beliefs. We obtain bounds on the POA with respect to the pure Nash, mixed Nash, and correlated equilibria. We show that the POA is always at most 2 when the cost functions are convex. We provide a more detailed characterization of the the Price of Anarchy as a function of the costs of disagreement. Finally, we consider combinatorial auctions with item bidding. In this model, several goods are sold simultaneously in independent auctions to buyers who have different values for different bundles of goods. We bound the pure Nash and the Bayes-Nash POA when the individual single-item auctions are second price auctions and buyers' valuations over the bundles are subadditive. We provide the first explicit gap between the worst case pure Nash and Bayes-Nash POA. We also consider how the pure Nash POA varies as a function of the payment rule in the underlying single-item auction.

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 Characterization and Computation of Equilibria in Infinite Games written by Noah Daniel Stein and published by . This book was released on 2007 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Cont.) Nonetheless, as in finite games, computing e-Nash equilibria still appears to be difficult for infinite games. Third, we consider computing approximate correlated equilibria in polynomial games. To do so, we first prove several new characterizations of correlated equilibria in continuous games which may be of independent interest. Then we introduce three algorithms for approximating correlated equilibria of polynomial games arbitrarily accurately. These include two discretization algorithms for computing a sample correlated equilibrium: a naive linear programming approach called static discretization which operates without regard to the structure of the game, and a semidefinite programming approach called adaptive discretization which exploits the structure of the game to achieve far better performance in practice. The third algorithm consists of a nested sequence of semidefinite programs converging to a description of the entire set of correlated equilibria.