The Next Stage: Quantum Game Theory
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A History of Von Neumann and Morgenstern's Theory of Games, 12Pt Escolha Sob Incerteza Ax
Marcos Thiago Graciani Axiomatic choice under uncertainty: a history of von Neumann and Morgenstern’s Theory of Games Escolha sob incerteza axiomática: uma história do Theory of Games de von Neumann e Morgenstern São Paulo 2019 Prof. Dr. Vahan Agopyan Reitor da Universidade de São Paulo Prof. Dr. Fábio Frezatti Diretor da Faculdade de Economia, Administração e Contabilidade Prof. Dr. José Carlos de Souza Santos Chefe do Departamento de Economia Prof. Dr. Ariaster Baumgratz Chimeli Coordenador do Programa de Pós-Graduação em Economia Marcos Thiago Graciani Axiomatic choice under uncertainty: a history of von Neumann and Morgenstern’s Theory of Games Escolha sob incerteza axiomática: uma história do Theory of Games de von Neumann e Morgenstern Dissertação de Mestrado apresentada ao Departamento de Economia da Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo (FEA-USP) como requisito parcial à obtenção do título de Mestre em Ciências. Área de Concentração: Teoria Econômica. Universidade de São Paulo — USP Faculdade de Economia, Administração e Contabilidade Programa de Pós-Graduação Orientador: Pedro Garcia Duarte Versão Corrigida (A versão original está disponível na biblioteca da Faculdade de Economia, Administração e Contabilidade.) São Paulo 2019 FICHA CATALOGRÁFICA Elaborada pela Seção de Processamento Técnico do SBD/FEA com dados inseridos pelo autor. Graciani, Marcos Thiago. Axiomatic choice under uncertainty: a history of von Neumann and Morgenstern’s Theory of Games / Marcos Thiago Graciani. – São Paulo, 2019. 133p. Dissertação (Mestrado) – Universidade de São Paulo, 2019. Orientador: Pedro Garcia Duarte. 1. História da teoria dos jogos 2. Axiomática 3. Incerteza 4. Von Neumann e Morgenstern I. -
Game Theory Lecture Notes
Game Theory: Penn State Math 486 Lecture Notes Version 2.1.1 Christopher Griffin « 2010-2021 Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License With Major Contributions By: James Fan George Kesidis and Other Contributions By: Arlan Stutler Sarthak Shah Contents List of Figuresv Preface xi 1. Using These Notes xi 2. An Overview of Game Theory xi Chapter 1. Probability Theory and Games Against the House1 1. Probability1 2. Random Variables and Expected Values6 3. Conditional Probability8 4. The Monty Hall Problem 11 Chapter 2. Game Trees and Extensive Form 15 1. Graphs and Trees 15 2. Game Trees with Complete Information and No Chance 18 3. Game Trees with Incomplete Information 22 4. Games of Chance 24 5. Pay-off Functions and Equilibria 26 Chapter 3. Normal and Strategic Form Games and Matrices 37 1. Normal and Strategic Form 37 2. Strategic Form Games 38 3. Review of Basic Matrix Properties 40 4. Special Matrices and Vectors 42 5. Strategy Vectors and Matrix Games 43 Chapter 4. Saddle Points, Mixed Strategies and the Minimax Theorem 45 1. Saddle Points 45 2. Zero-Sum Games without Saddle Points 48 3. Mixed Strategies 50 4. Mixed Strategies in Matrix Games 53 5. Dominated Strategies and Nash Equilibria 54 6. The Minimax Theorem 59 7. Finding Nash Equilibria in Simple Games 64 8. A Note on Nash Equilibria in General 66 Chapter 5. An Introduction to Optimization and the Karush-Kuhn-Tucker Conditions 69 1. A General Maximization Formulation 70 2. Some Geometry for Optimization 72 3. -
Evolutionary Game Theory: ESS, Convergence Stability, and NIS
Evolutionary Ecology Research, 2009, 11: 489–515 Evolutionary game theory: ESS, convergence stability, and NIS Joseph Apaloo1, Joel S. Brown2 and Thomas L. Vincent3 1Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, 2Department of Biological Sciences, University of Illinois, Chicago, Illinois, USA and 3Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA ABSTRACT Question: How are the three main stability concepts from evolutionary game theory – evolutionarily stable strategy (ESS), convergence stability, and neighbourhood invader strategy (NIS) – related to each other? Do they form a basis for the many other definitions proposed in the literature? Mathematical methods: Ecological and evolutionary dynamics of population sizes and heritable strategies respectively, and adaptive and NIS landscapes. Results: Only six of the eight combinations of ESS, convergence stability, and NIS are possible. An ESS that is NIS must also be convergence stable; and a non-ESS, non-NIS cannot be convergence stable. A simple example shows how a single model can easily generate solutions with all six combinations of stability properties and explains in part the proliferation of jargon, terminology, and apparent complexity that has appeared in the literature. A tabulation of most of the evolutionary stability acronyms, definitions, and terminologies is provided for comparison. Key conclusions: The tabulated list of definitions related to evolutionary stability are variants or combinations of the three main stability concepts. Keywords: adaptive landscape, convergence stability, Darwinian dynamics, evolutionary game stabilities, evolutionarily stable strategy, neighbourhood invader strategy, strategy dynamics. INTRODUCTION Evolutionary game theory has and continues to make great strides. -
Introduction to Probability
Massachusetts Institute of Technology Course Notes 10 6.042J/18.062J, Fall ’02: Mathematics for Computer Science November 4 Professor Albert Meyer and Dr. Radhika Nagpal revised November 6, 2002, 572 minutes Introduction to Probability 1 Probability Probability will be the topic for the rest of the term. Probability is one of the most important sub- jects in Mathematics and Computer Science. Most upper level Computer Science courses require probability in some form, especially in analysis of algorithms and data structures, but also in infor- mation theory, cryptography, control and systems theory, network design, artificial intelligence, and game theory. Probability also plays a key role in fields such as Physics, Biology, Economics and Medicine. There is a close relationship between Counting/Combinatorics and Probability. In many cases, the probability of an event is simply the fraction of possible outcomes that make up the event. So many of the rules we developed for finding the cardinality of finite sets carry over to Proba- bility Theory. For example, we’ll apply an Inclusion-Exclusion principle for probabilities in some examples below. In principle, probability boils down to a few simple rules, but it remains a tricky subject because these rules often lead unintuitive conclusions. Using “common sense” reasoning about probabilis- tic questions is notoriously unreliable, as we’ll illustrate with many real-life examples. This reading is longer than usual . To keep things in bounds, several sections with illustrative examples that do not introduce new concepts are marked “[Optional].” You should read these sections selectively, choosing those where you’re unsure about some idea and think another ex- ample would be helpful. -
Econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Banerjee, Abhijit; Weibull, Jörgen W. Working Paper Evolution and Rationality: Some Recent Game- Theoretic Results IUI Working Paper, No. 345 Provided in Cooperation with: Research Institute of Industrial Economics (IFN), Stockholm Suggested Citation: Banerjee, Abhijit; Weibull, Jörgen W. (1992) : Evolution and Rationality: Some Recent Game-Theoretic Results, IUI Working Paper, No. 345, The Research Institute of Industrial Economics (IUI), Stockholm This Version is available at: http://hdl.handle.net/10419/95198 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu Ind ustriens Utred n i ngsi nstitut THE INDUSTRIAL INSTITUTE FOR ECONOMIC AND SOCIAL RESEARCH A list of Working Papers on the last pages No. -
Turing Learning with Nash Memory
Turing Learning with Nash Memory Machine Learning, Game Theory and Robotics Shuai Wang Master of Science Thesis University of Amsterdam Local Supervisor: Dr. Leen Torenvliet (University of Amsterdam, NL) Co-Supervisor: Dr. Frans Oliehoek (University of Liverpool, UK) External Advisor: Dr. Roderich Groß (University of Sheffield, UK) ABSTRACT Turing Learning is a method for the reverse engineering of agent behaviors. This approach was inspired by the Turing test where a machine can pass if its behaviour is indistinguishable from that of a human. Nash memory is a memory mechanism for coevolution. It guarantees monotonicity in convergence. This thesis explores the integration of such memory mechanism with Turing Learning for faster learning of agent behaviors. We employ the Enki robot simulation platform and learns the aggregation behavior of epuck robots. Our experiments indicate that using Nash memory can reduce the computation time by 35.4% and results in faster convergence for the aggregation game. In addition, we present TuringLearner, the first Turing Learning platform. Keywords: Turing Learning, Nash Memory, Game Theory, Multi-agent System. COMMITTEE MEMBER: DR.KATRIN SCHULZ (CHAIR) PROF. DR.FRANK VAN HARMELEN DR.PETER VAN EMDE BOAS DR.PETER BLOEM YFKE DULEK MSC MASTER THESIS,UNIVERSITY OF AMSTERDAM Amsterdam, August 2017 Contents 1 Introduction ....................................................7 2 Background ....................................................9 2.1 Introduction to Game Theory9 2.1.1 Players and Games................................................9 2.1.2 Strategies and Equilibria........................................... 10 2.2 Computing Nash Equilibria 11 2.2.1 Introduction to Linear Programming.................................. 11 2.2.2 Game Solving with LP............................................. 12 2.2.3 Asymmetric Games............................................... 13 2.2.4 Bimatrix Games................................................. -
Introduction to Game Theory I
Introduction to Game Theory I Presented To: 2014 Summer REU Penn State Department of Mathematics Presented By: Christopher Griffin [email protected] 1/34 Types of Game Theory GAME THEORY Classical Game Combinatorial Dynamic Game Evolutionary Other Topics in Theory Game Theory Theory Game Theory Game Theory No time, doesn't contain differential equations Notion of time, may contain differential equations Games with finite or Games with no Games with time. Modeling population Experimental / infinite strategy space, chance. dynamics under Behavioral Game but no time. Games with motion or competition Theory Generally two player a dynamic component. Games with probability strategic games Modeling the evolution Voting Theory (either induced by the played on boards. Examples: of strategies in a player or the game). Optimal play in a dog population. Examples: Moves change the fight. Chasing your Determining why Games with coalitions structure of a game brother across a room. Examples: altruism is present in or negotiations. board. The evolution of human society. behaviors in a group of Examples: Examples: animals. Determining if there's Poker, Strategic Chess, Checkers, Go, a fair voting system. Military Decision Nim. Equilibrium of human Making, Negotiations. behavior in social networks. 2/34 Games Against the House The games we often see on television fall into this category. TV Game Shows (that do not pit players against each other in knowledge tests) often require a single player (who is, in a sense, playing against The House) to make a decision that will affect only his life. Prize is Behind: 1 2 3 Choose Door: 1 2 3 1 2 3 1 2 3 Switch: Y N Y N Y N Y N Y N Y N Y N Y N Y N Win/Lose: L W W L W L W L L W W L W L W L L W The Monty Hall Problem Other games against the house: • Blackjack • The Price is Right 3/34 Assumptions of Multi-Player Games 1. -
On Limitations of Learning Algorithms in Competitive Environments
On limitations of learning algorithms in competitive environments A.Y. Klimenko and D.A. Klimenko SoMME, The University of Queensland, QLD 4072, Australia Abstract We discuss conceptual limitations of generic learning algorithms pursuing adversarial goals in competitive environments, and prove that they are subject to limitations that are analogous to the constraints on knowledge imposed by the famous theorems of G¨odel and Turing. These limitations are shown to be related to intransitivity, which is commonly present in competitive environments. Keywords: learning algorithms, competitions, incompleteness theorems 1. Introduction The idea that computers might be able to do some intellectual work has existed for a long time and, as demonstrated by recent AI developments, is not merely science fiction. AI has become successful in a range of applications, including recognising images and driving cars. Playing human games such as chess and Go has long been considered to be a major benchmark of human capabilities. Computer programs have become robust chess players and, since the late 1990s, have been able to beat even the best human chess champions; though, for a long time, computers were unable to beat expert Go players | the game of Go has proven to be especially difficult for computers. While most of the best early AI game-playing agents were specialised to play a particular game (which is less interesting from the general AI perspective), more recent game-playing agents often involve general machine learning capabilities, and sometimes evolutionary algorithms [1, 2]. Since 2005, general game playing was developed to reflect the ability of AI to play generic games with arbitrary given rules [3]. -
Modernism Revisited Edited by Aleš Erjavec & Tyrus Miller XXXV | 2/2014
Filozofski vestnik Modernism Revisited Edited by Aleš Erjavec & Tyrus Miller XXXV | 2/2014 Izdaja | Published by Filozofski inštitut ZRC SAZU Institute of Philosophy at SRC SASA Ljubljana 2014 CIP - Kataložni zapis o publikaciji Narodna in univerzitetna knjižnica, Ljubljana 141.7(082) 7.036(082) MODERNISM revisited / edited by Aleš Erjavec & Tyrus Miller. - Ljubljana : Filozofski inštitut ZRC SAZU = Institute of Philosophy at SRC SASA, 2014. - (Filozofski vestnik, ISSN 0353-4510 ; 2014, 2) ISBN 978-961-254-743-1 1. Erjavec, Aleš, 1951- 276483072 Contents Filozofski vestnik Modernism Revisited Volume XXXV | Number 2 | 2014 9 Aleš Erjavec & Tyrus Miller Editorial 13 Sascha Bru The Genealogy-Complex. History Beyond the Avant-Garde Myth of Originality 29 Eva Forgács Modernism's Lost Future 47 Jožef Muhovič Modernism as the Mobilization and Critical Period of Secular Metaphysics. The Case of Fine/Plastic Art 67 Krzysztof Ziarek The Avant-Garde and the End of Art 83 Tyrus Miller The Historical Project of “Modernism”: Manfredo Tafuri’s Metahistory of the Avant-Garde 103 Miško Šuvaković Theories of Modernism. Politics of Time and Space 121 Ian McLean Modernism Without Borders 141 Peng Feng Modernism in China: Too Early and Too Late 157 Aleš Erjavec Beat the Whites with the Red Wedge 175 Patrick Flores Speculations on the “International” Via the Philippine 193 Kimmo Sarje The Rational Modernism of Sigurd Fosterus. A Nordic Interpretation 219 Ernest Ženko Ingmar Bergman’s Persona as a Modernist Example of Media Determinism 239 Rainer Winter The Politics of Aesthetics in the Work of Michelangelo Antonioni: An Analysis Following Jacques Rancière 255 Ernst van Alphen On the Possibility and Impossibility of Modernist Cinema: Péter Forgács’ Own Death 271 Terry Smith Rethinking Modernism and Modernity 321 Notes on Contributors 325 Abstracts Kazalo Filozofski vestnik Ponovno obiskani modernizem Letnik XXXV | Številka 2 | 2014 9 Aleš Erjavec & Tyrus Miller Uvodnik 13 Sascha Bru Genealoški kompleks. -
Navigating the Landscape of Multiplayer Games ✉ Shayegan Omidshafiei 1,4 , Karl Tuyls1,4, Wojciech M
ARTICLE https://doi.org/10.1038/s41467-020-19244-4 OPEN Navigating the landscape of multiplayer games ✉ Shayegan Omidshafiei 1,4 , Karl Tuyls1,4, Wojciech M. Czarnecki2, Francisco C. Santos3, Mark Rowland2, Jerome Connor2, Daniel Hennes 1, Paul Muller1, Julien Pérolat1, Bart De Vylder1, Audrunas Gruslys2 & Rémi Munos1 Multiplayer games have long been used as testbeds in artificial intelligence research, aptly referred to as the Drosophila of artificial intelligence. Traditionally, researchers have focused on using well-known games to build strong agents. This progress, however, can be better 1234567890():,; informed by characterizing games and their topological landscape. Tackling this latter question can facilitate understanding of agents and help determine what game an agent should target next as part of its training. Here, we show how network measures applied to response graphs of large-scale games enable the creation of a landscape of games, quanti- fying relationships between games of varying sizes and characteristics. We illustrate our findings in domains ranging from canonical games to complex empirical games capturing the performance of trained agents pitted against one another. Our results culminate in a demonstration leveraging this information to generate new and interesting games, including mixtures of empirical games synthesized from real world games. 1 DeepMind, Paris, France. 2 DeepMind, London, UK. 3 INESC-ID and Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal. 4These authors ✉ contributed equally: Shayegan Omidshafiei, Karl Tuyls. email: somidshafi[email protected] NATURE COMMUNICATIONS | (2020) 11:5603 | https://doi.org/10.1038/s41467-020-19244-4 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-19244-4 ames have played a prominent role as platforms for the games. -
Evolutionary Game Theory: a Renaissance
games Review Evolutionary Game Theory: A Renaissance Jonathan Newton ID Institute of Economic Research, Kyoto University, Kyoto 606-8501, Japan; [email protected] Received: 23 April 2018; Accepted: 15 May 2018; Published: 24 May 2018 Abstract: Economic agents are not always rational or farsighted and can make decisions according to simple behavioral rules that vary according to situation and can be studied using the tools of evolutionary game theory. Furthermore, such behavioral rules are themselves subject to evolutionary forces. Paying particular attention to the work of young researchers, this essay surveys the progress made over the last decade towards understanding these phenomena, and discusses open research topics of importance to economics and the broader social sciences. Keywords: evolution; game theory; dynamics; agency; assortativity; culture; distributed systems JEL Classification: C73 Table of contents 1 Introduction p. 2 Shadow of Nash Equilibrium Renaissance Structure of the Survey · · 2 Agency—Who Makes Decisions? p. 3 Methodology Implications Evolution of Collective Agency Links between Individual & · · · Collective Agency 3 Assortativity—With Whom Does Interaction Occur? p. 10 Assortativity & Preferences Evolution of Assortativity Generalized Matching Conditional · · · Dissociation Network Formation · 4 Evolution of Behavior p. 17 Traits Conventions—Culture in Society Culture in Individuals Culture in Individuals · · · & Society 5 Economic Applications p. 29 Macroeconomics, Market Selection & Finance Industrial Organization · 6 The Evolutionary Nash Program p. 30 Recontracting & Nash Demand Games TU Matching NTU Matching Bargaining Solutions & · · · Coordination Games 7 Behavioral Dynamics p. 36 Reinforcement Learning Imitation Best Experienced Payoff Dynamics Best & Better Response · · · Continuous Strategy Sets Completely Uncoupled · · 8 General Methodology p. 44 Perturbed Dynamics Further Stability Results Further Convergence Results Distributed · · · control Software and Simulations · 9 Empirics p. -
Game Theory and Evolutionary Biology 1
Chapter 28 GAME THEORY AND EVOLUTIONARY BIOLOGY PETER HAMMERSTEIN Max-Planck-Institut für Verhaltensphysiologie REINHARD SELTEN University of Bonn Contents 1. Introduction 931 2. Conceptual background 932 2.1. Evolutionary stability 932 2.2. The Darwinian view of natural selection 933 2.3. Payoffs 934 2.4. Game theory and population genetics 935 2.5. Players 936 2.6. Symmetry 936 3. Symmetric two-person games 937 3.1. Definitions and notation 937 3.2. The Hawk-Dove garne 937 3.3. Evolutionary stability 938 3.4. Properties ofevolutionarily stable strategies 940 4. Playing the field 942 5. Dynamic foundations 948 5.1. Replicator dynamics 948 5.2. Disequilibrium results 951 5.3. A look at population genetics 952 6. Asymmetric conflicts 962 * We are grateful to Olof Leimar, Sido Mylius, Rolf Weinzierl, Franjo Weissing, and an anonymous referee who all helped us with their critical comments. We also thank the Institute for Advanced Study Berlin for supporting the final revision of this paper. Handbook of Garne Theory, Volume 2, Edited by R.J. Aumann and S. Hart © Elsevier Science B.V., 1994. All rights reserved 930 P. Hammerstein and R. Selten 7. Extensive two-person games 965 7.1. Extensive garnes 965 7.2. Symmetric extensive garnes 966 7.3. Evolutionary stability 968 7.4. Image confrontation and detachment 969 7.5. Decomposition 970 8. Biological applications 971 8.1. Basic qnestions about animal contest behavior 972 8.2. Asymmetric animal contests 974 8.3. War of attrition, assessment, and signalling 978 8.4. The evolution of cooperation 980 8.5.