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Author : Paul Weirich
Publisher : MDPI
Page : 189 pages
File Size : 48,9 Mb
Release : 2018-04-27
Category : Epistemics
ISBN : 9783038424222
This book is a printed edition of the Special Issue "Epistemic Game Theory and Modal Logic" that was published in Games
Author : M. Bacharach,Louis André Gerard-Varet,Philippe Mongin,H.S. Shin
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461311393
The convergence of game theory and epistemic logic has been in progress for two decades and this book explores this further by gathering specialists from different professional communities, i.e., economics, mathematics, philosophy, and computer science. This volume considers the issues of knowledge, belief and strategic interaction, with each contribution evaluating the foundational issues. In particular, emphasis is placed on epistemic logic and the representative topics of backward induction arguments and syntax/semantics and the logical omniscience problem. Part I of this collection deals with iterated knowledge in the multi-agent context, and more particularly with common knowledge. The first two papers in Part II of the collection address the so-called logical omniscience problem, a problem which has attracted much attention in the recent epistemic logic literature, and is pertinent to some of the issues discussed by decision theorists under the heading 'bounded rationality'. The remaining two chapters of section II provide two quite different angles on the strength of S5 (or the partitional model of information)- and so two different reasons for eschewing the strong form of logical omniscience implicit in S5. Part III gives attention to application to game theory and decision theory.
Author : Herbert Gintis,Paul Weirich
Publisher : Unknown
Page : 128 pages
File Size : 50,9 Mb
Release : 2017
Category : Business
ISBN : 3038424234
Game theory addresses situations with multiple agents in which the outcome of an agent's act depends on the acts of the other agents. The agents may be mindless organisms. Epistemic game theory addresses games in which the agents have minds. An agent reasons about the acts of other agents and-if the other agents observe the agent's act-reasons about the other agents' responses to the act. The agents use logic to draw conclusions about the prospects of the acts that they can perform. This Special Issue of Games deals with epistemic game theory and the contributions that logic makes to an agent's practical reasoning about the strategy to adopt in a game. Although behavioral studies are relevant, the emphasis is on rational reasoning. Models of such reasoning may deal with cognitively ideal agents as well as humans. Possible topics include the players' common knowledge of their game and their rationality; reasoning that supports the players' in playing their part in a Nash equilibrium of the game; backwards induction, its results, and the conditions that support it; forward induction; learning in sequential games or in repetitions of games; Hintikka models and Kripke models of agents' information; applications of modal logic's methods to epistemic logic; interactive epistemology; Bayesian game theory and Bayesian equilibrium; and games with imperfect, incomplete, or asymmetric information
Author : Boudewijn de Bruin
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 52,8 Mb
Release : 2010-08-18
Category : Science
ISBN : 9781402099069
Does game theory - the mathematical theory of strategic interaction - provide genuine explanations of human behaviour? Can game theory be used in economic consultancy or other normative contexts? Explaining Games: The Epistemic Programme in Game Theory - the first monograph on the philosophy of game theory - is a bold attempt to combine insights from epistemic logic and the philosophy of science to investigate the applicability of game theory in such fields as economics, philosophy and strategic consultancy. De Bruin proves new mathematical theorems about the beliefs, desires and rationality principles of individual human beings, and he explores in detail the logical form of game theory as it is used in explanatory and normative contexts. He argues that game theory reduces to rational choice theory if used as an explanatory device, and that game theory is nonsensical if used as a normative device. A provocative account of the history of game theory reveals that this is not bad news for all of game theory, though. Two central research programmes in game theory tried to find the ultimate characterisation of strategic interaction between rational agents. Yet, while the Nash Equilibrium Refinement Programme has done badly thanks to such research habits as overmathematisation, model-tinkering and introversion, the Epistemic Programme, De Bruin argues, has been rather successful in achieving this aim.
Author : Andrés Perea
Publisher : Cambridge University Press
Page : 581 pages
File Size : 45,5 Mb
Release : 2012-06-07
Category : Business & Economics
ISBN : 9781107008915
The first textbook to explain the principles of epistemic game theory.
Author : Johan Van Benthem
Publisher : MIT Press
Page : 567 pages
File Size : 42,8 Mb
Release : 2014-01-24
Category : Computers
ISBN : 9780262019903
A comprehensive examination of the interfaces of logic, computer science, and game theory, drawing on twenty years of research on logic and games. This book draws on ideas from philosophical logic, computational logic, multi-agent systems, and game theory to offer a comprehensive account of logic and games viewed in two complementary ways. It examines the logic of games: the development of sophisticated modern dynamic logics that model information flow, communication, and interactive structures in games. It also examines logic as games: the idea that logical activities of reasoning and many related tasks can be viewed in the form of games. In doing so, the book takes up the “intelligent interaction” of agents engaging in competitive or cooperative activities and examines the patterns of strategic behavior that arise. It develops modern logical systems that can analyze information-driven changes in players' knowledge and beliefs, and introduces the “Theory of Play” that emerges from the combination of logic and game theory. This results in a new view of logic itself as an interactive rational activity based on reasoning, perception, and communication that has particular relevance for games. Logic in Games, based on a course taught by the author at Stanford University, the University of Amsterdam, and elsewhere, can be used in advanced seminars and as a resource for researchers.
Author : Adam Brandenburger
Publisher : World Scientific
Page : 300 pages
File Size : 49,6 Mb
Release : 2014-03-12
Category : Mathematics
ISBN : 9789814513456
This volume contains eight papers written by Adam Brandenburger and his co-authors over a period of 25 years. These papers are part of a program to reconstruct game theory in order to make how players reason about a game a central feature of the theory. The program — now called epistemic game theory — extends the classical definition of a game model to include not only the game matrix or game tree, but also a description of how the players reason about one another (including their reasoning about other players' reasoning). With this richer mathematical framework, it becomes possible to determine the implications of how players reason for how a game is played. Epistemic game theory includes traditional equilibrium-based theory as a special case, but allows for a wide range of non-equilibrium behavior. Contents:An Impossibility Theorem on Beliefs in Games (Adam Brandenburger and H Jerome Keisler)Hierarchies of Beliefs and Common Knowledge (Adam Brandenburger and Eddie Dekel)Rationalizability and Correlated Equilibria (Adam Brandenburger and Eddie Dekel)Intrinsic Correlation in Games (Adam Brandenburger and Amanda Friedenberg)Epistemic Conditions for Nash Equilibrium (Robert Aumann and Adam Brandenburger)Lexicographic Probabilities and Choice Under Uncertainty (Lawrence Blume, Adam Brandenburger, and Eddie Dekel)Admissibility in Games (Adam Brandenburger, Amanda Friedenberg and H Jerome Keisler)Self-Admissible Sets (Adam Brandenburger and Amanda Friedenberg) Readership: Graduate students and researchers in the fields of game theory, theoretical computer science, mathematical logic and social neuroscience. Keywords:Game Theory;Epistemic Game Theory;Foundations;Applied Mathematics;Social Neuroscience;Rationalizability;Nash Equilibrium;Probability;UncertaintyKey Features:Focuses on epistemic game theory — an emerging approach to game theoryLikely strong interest in these tools from other disciplines, includingtheoretical computer science, mathematical logic, and social neuroscienceProminent co-author team: Robert Aumann (Hebrew University, Nobel Laureate 2005); Lawrence Blume (Cornell University); Eddie Dekel (Northwestern University and Tel Aviv University); Amanda Freedeneurg (Arizona State University); H Jerome Keisler (University of Wisconsin Madison)Reviews: "Adam Brandenburger's work on the knowledge requirements implicit in game theory has become classic. These are of profound importance in understanding the relevance of game theory and, indeed, economic theory in general to the real economy. It is very good to have them collected, with an introduction that brings out the underlying themes." Kenneth J Arrow Stanford University, USA "Over the past decade epistemic game theory has emerged as one of the principled alternatives to more traditional approaches to economic interactions and Adam Brandenburger has played a central role in that emergence. For anyone interested in epistemic game theory, or game theory in general, this book is a must have. But even more important is the opportunity this volume, and epistemic game theory in general, presents to empirical scientists. As Brandenburger notes in his Introduction, until now epistemic game theory has been a theoretical discipline. This volume should make it clear, however, that it could be — and likely soon will be — an empirical undertaking. Anyone interested in behavioral, psychological, or neurobiological studies of how we make decisions during strategic play will find in this volume a profoundly fascinating set of empirically testable hypotheses just waiting to be examined." Paul Glimcher New York University, USA "Three hundred years ago, Francis Waldegrave found the first minimax solution of a matrix game. But in his correspondence with mathematicians Pierre Rémond de Montmort and Nicolaus Bernoulli, Waldegrave counseled that epistemic considerations involving knowledge, beliefs, uncertainty, and incomplete information also mattered. The principal practitioners of game theory, with the notable exceptions of John Harsanyi and Robert Aumann, have ignored this advice. In recent years, these two theorists have been joined by Adam Brandenburger, whose work on epistemic game theory has been collected in this splendid volume. Eight classic papers by Brandenburger with a number of co-authors present an authoritative view of the field while an insightful introduction provides a roadmap to research both present and future." Harold W Kuhn Princeton University, USA "This book features a collection of foundational papers by Adam Brandenburger in epistemic game theory. Though still evolving, this approach marks a tectonic shift in game theory by offering a new, epistemic dimension which might be compared to the introduction of synchronized sound to motion pictures in the early 20th century: it might not immediately provide a complete picture, but it has the potential of changing the field forever." Sergei N Artemov The Graduate Center of the City University of New York, USA "Adam Brandenburger has played a leading role in developing the program of epistemic game theory, the goal of which is to provide a deeper and clearer foundation for game theory as a whole. This volume collects a remarkable body of work by Brandenburger and his collaborators, in which penetrating conceptual analysis and the development of a rich mathematical theory go hand in hand. The work offers much of great interest to computer scientists, who will see many connections with their study of recursive and corecursive structures, of processes and their logics, and of multi-agent systems; and to mathematicians and logicians interested in making precise models of the reflexive structures inherent in systems containing rational agents who can reason about the system of which they form a part. I hope that this timely collection will help to stimulate cross-disciplinary work on these fundamental topics." Samson Abramsky Oxford University, UK "Games are playgrounds where players meet and interact, guided by streams of information and opinion. Adam Brandenburger's work has been instrumental in creating a new rich epistemic framework doing justice to both games and their players. This timely book will help a broader audience learn and appreciate the resulting theory." Johan van Benthem University of Amsterdam, The Netherlands and Stanford University, USA "Economics, so grounded in the notion of equilibrium, has required substantial foundational work on reasoning about reasoning — epistemics — in interacting situations (games). Yet, if plain reasoning is difficult enough, just imagine epistemics. Adam Brandenburger, as is evident from the elegant and clear chapters of this book, is a master of the trade. His highly regarded research, always subtle and deep, is of the kind that establishes milestones while at the same time opening up vistas to new, and unexpected, frontiers. This book is specialized, certainly, but it is a must." Andreu Mas-Colell Universitat Pompeu Fabra, Spain “The papers in this book had a huge impact on the field, created an inter– and multi–discipliner research within the intersection of economics, philosophy, mathematics and computer science, and also inspired countless amount of PhD dissertations. Brandenburger's work contains very precise and beautiful mathematics, an earthly reading of epistemics and a puzzling innovation.” Zentralblatt MATH
Author : Cristina Bicchieri,Richard C. Jeffrey,Brian Skyrms
Publisher : Oxford University Press, USA
Page : 208 pages
File Size : 54,9 Mb
Release : 1999
Category : Game theory
ISBN : 9780195117158
Edited by three leading figures in the field, this exciting volume presents cutting-edge work in decision theory by a distinguished international roster of contributors. These mostly unpublished papers address a host of crucial areas in the contemporary philosophical study of rationality and knowledge. Topics include causal versus evidential decision theory, game theory, backwards induction, bounded rationality, counterfactual reasoning in games and in general, analyses of the famous common knowledge assumptions in game theory, and evaluations of the normal versus extensive form formulations of complex decision problems.
Author : Johan van Benthem,Amitabha Gupta,Eric Pacuit
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 55,6 Mb
Release : 2011-03-30
Category : Philosophy
ISBN : 9789400707146
Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement.
Author : Wiebe van der Hoek
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 51,5 Mb
Release : 2005-12-06
Category : Philosophy
ISBN : 9781402040948
Contemporary epistemological and cognitive studies, as well as recent trends in computer science and game theory have revealed an increasingly important and intimate relationship between Information, Interaction, and Agency. Agents perform actions based on the available information and in the presence of other interacting agents. From this perspective Information, Interaction, and Agency neatly ties together classical themes like rationality, decision-making and belief revision with games, strategies and learning in a multi-agent setting. Unified by the central notions Information, Interaction, and Agency, the essays in this volume provide refreshing methodological perspectives on belief revision, dynamic epistemic logic, von Neumann games, and evolutionary game theory; all of which in turn are central approaches to understanding our own rationality and that of other agents.
Author : Krzysztof R. Apt,Robert Van Rooij
Publisher : Amsterdam University Press
Page : 331 pages
File Size : 54,5 Mb
Release : 2008
Category : Games & Activities
ISBN : 9789089640574
This volume is a collection of papers presented at the 2007 colloquium on new perspectives on games and interaction at the Royal Dutch Academy of Sciences in Amsterdam.
Author : Johan van Benthem,Sujata Ghosh,Rineke Verbrugge
Publisher : Springer
Page : 333 pages
File Size : 45,8 Mb
Release : 2016-01-08
Category : Mathematics
ISBN : 9783662485408
Strategic behavior is the key to social interaction, from the ever-evolving world of living beings to the modern theatre of designed computational agents. Strategies can make or break participants’ aspirations, whether they are selling a house, playing the stock market, or working toward a treaty that limits global warming. This book aims at understanding the phenomenon of strategic behavior in its proper width and depth. A number of experts have combined forces in order to create a comparative view of the different frameworks for strategic reasoning in social interactions that have been developed in game theory, computer science, logic, linguistics, philosophy, and cognitive and social sciences. The chapters are organized in three topic-based sections, namely reasoning about games; formal frameworks for strategies; and strategies in social situations. The book concludes with a discussion on the future of logical studies of strategies.
Author : M. O. L. Bacharach
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 1997
Category : Electronic
ISBN : OCLC:535297835
Author : Andrés Perea
Publisher : Cambridge University Press
Page : 581 pages
File Size : 50,8 Mb
Release : 2012-06-07
Category : Business & Economics
ISBN : 9781139510547
In everyday life we must often reach decisions while knowing that the outcome will not only depend on our own choice, but also on the choices of others. These situations are the focus of epistemic game theory. Unlike classical game theory, it explores how people may reason about their opponents before they make their final choice in a game. Packed with examples and practical problems based on stories from everyday life, this is the first textbook to explain the principles of epistemic game theory. Each chapter is dedicated to one particular, natural way of reasoning. The book then shows how each of these ways of reasoning will affect the final choices that can rationally be made and how these choices can be found by iterative procedures. Moreover, it does so in a way that uses elementary mathematics and does not presuppose any previous knowledge of game theory.
Author : Johan van Benthem
Publisher : Cambridge University Press
Page : 387 pages
File Size : 53,6 Mb
Release : 2011-09-29
Category : Mathematics
ISBN : 9781139500463
This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.