The Experiment in the History of Economics
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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. -
Uniqueness and Symmetry in Bargaining Theories of Justice
Philos Stud DOI 10.1007/s11098-013-0121-y Uniqueness and symmetry in bargaining theories of justice John Thrasher Ó Springer Science+Business Media Dordrecht 2013 Abstract For contractarians, justice is the result of a rational bargain. The goal is to show that the rules of justice are consistent with rationality. The two most important bargaining theories of justice are David Gauthier’s and those that use the Nash’s bargaining solution. I argue that both of these approaches are fatally undermined by their reliance on a symmetry condition. Symmetry is a substantive constraint, not an implication of rationality. I argue that using symmetry to generate uniqueness undermines the goal of bargaining theories of justice. Keywords David Gauthier Á John Nash Á John Harsanyi Á Thomas Schelling Á Bargaining Á Symmetry Throughout the last century and into this one, many philosophers modeled justice as a bargaining problem between rational agents. Even those who did not explicitly use a bargaining problem as their model, most notably Rawls, incorporated many of the concepts and techniques from bargaining theories into their understanding of what a theory of justice should look like. This allowed them to use the powerful tools of game theory to justify their various theories of distributive justice. The debates between partisans of different theories of distributive justice has tended to be over the respective benefits of each particular bargaining solution and whether or not the solution to the bargaining problem matches our pre-theoretical intuitions about justice. There is, however, a more serious problem that has effectively been ignored since economists originally J. -
Game Theory- Prisoners Dilemma Vs Battle of the Sexes EXCERPTS
Lesson 14. Game Theory 1 Lesson 14 Game Theory c 2010, 2011 ⃝ Roberto Serrano and Allan M. Feldman All rights reserved Version C 1. Introduction In the last lesson we discussed duopoly markets in which two firms compete to sell a product. In such markets, the firms behave strategically; each firm must think about what the other firm is doing in order to decide what it should do itself. The theory of duopoly was originally developed in the 19th century, but it led to the theory of games in the 20th century. The first major book in game theory, published in 1944, was Theory of Games and Economic Behavior,byJohnvon Neumann (1903-1957) and Oskar Morgenstern (1902-1977). We will return to the contributions of Von Neumann and Morgenstern in Lesson 19, on uncertainty and expected utility. Agroupofpeople(orteams,firms,armies,countries)areinagame if their decision problems are interdependent, in the sense that the actions that all of them take influence the outcomes for everyone. Game theory is the study of games; it can also be called interactive decision theory. Many real-life interactions can be viewed as games. Obviously football, soccer, and baseball games are games.Butsoaretheinteractionsofduopolists,thepoliticalcampaignsbetweenparties before an election, and the interactions of armed forces and countries. Even some interactions between animal or plant species in nature can be modeled as games. In fact, game theory has been used in many different fields in recent decades, including economics, political science, psychology, sociology, computer science, and biology. This brief lesson is not meant to replace a formal course in game theory; it is only an in- troduction. -
Introduction to Computational Social Choice
1 Introduction to Computational Social Choice Felix Brandta, Vincent Conitzerb, Ulle Endrissc, J´er^omeLangd, and Ariel D. Procacciae 1.1 Computational Social Choice at a Glance Social choice theory is the field of scientific inquiry that studies the aggregation of individual preferences towards a collective choice. For example, social choice theorists|who hail from a range of different disciplines, including mathematics, economics, and political science|are interested in the design and theoretical evalu- ation of voting rules. Questions of social choice have stimulated intellectual thought for centuries. Over time the topic has fascinated many a great mind, from the Mar- quis de Condorcet and Pierre-Simon de Laplace, through Charles Dodgson (better known as Lewis Carroll, the author of Alice in Wonderland), to Nobel Laureates such as Kenneth Arrow, Amartya Sen, and Lloyd Shapley. Computational social choice (COMSOC), by comparison, is a very young field that formed only in the early 2000s. There were, however, a few precursors. For instance, David Gale and Lloyd Shapley's algorithm for finding stable matchings between two groups of people with preferences over each other, dating back to 1962, truly had a computational flavor. And in the late 1980s, a series of papers by John Bartholdi, Craig Tovey, and Michael Trick showed that, on the one hand, computational complexity, as studied in theoretical computer science, can serve as a barrier against strategic manipulation in elections, but on the other hand, it can also prevent the efficient use of some voting rules altogether. Around the same time, a research group around Bernard Monjardet and Olivier Hudry also started to study the computational complexity of preference aggregation procedures. -
M31193119 - BBRUNIRUNI TTEXT.Inddext.Indd 2200 227/02/20137/02/2013 08:1708:17 Altruistic Reciprocity 21
2. Altruistic reciprocity Herbert Gintis OTHER- REGARDING PREFERENCES AND STRONG RECIPROCITY By a self- regarding actor we mean an individual who maximizes his own payoff in social interactions. A self- regarding actor thus cares about the behavior of and payoffs to the other individuals only insofar as these impact his own payoff. The term ‘self- regarding’ is more accurate than ‘self- interested’ because an other-regarding individual is still acting to maximize utility and so can be described as self- interested. For instance, if I get great pleasure from your consumption, my gift to you may be self- interested, even though it is surely other- regarding. We can avoid confusion (and much pseudo- philosophical dis- cussion) by employing the self-regarding/other- regarding terminology. One major result of behavioral game theory is that when modeling market processes with well- specified contracts, such as double auctions (supply and demand) and oligopoly, game- theoretic predictions assuming self- regarding actors are accurate under a wide variety of social settings (see Kachelmaier and Shehata, 1992; Davis and Holt, 1993). The fact that self- regarding behavior explains market dynamics lends credence to the practice in neoclassical economics of assuming that individuals are self- regarding. However, it by no means justifies ‘Homo economicus’ because many economic transac- tions do not involve anonymous exchange. This includes employer- employee, creditor- debtor, and firm- client relationships. Nor does this result apply to the welfare implications of economic outcomes (e.g., people may care about the overall degree of economic inequality and/or their positions in the income and wealth distribution), to modeling the behavior of taxpayers (e.g., they may be more or less honest than a self- regarding indi- vidual, and they may prefer to transfer resources toward or away from other individu- als even at an expense to themselves) or to important aspects of economic policy (e.g., dealing with corruption, fraud, and other breaches of fiduciary responsibility). -
Strong Reciprocity and Human Sociality∗
Strong Reciprocity and Human Sociality∗ Herbert Gintis Department of Economics University of Massachusetts, Amherst Phone: 413-586-7756 Fax: 413-586-6014 Email: [email protected] Web: http://www-unix.oit.umass.edu/˜gintis Running Head: Strong Reciprocity and Human Sociality March 11, 2000 Abstract Human groups maintain a high level of sociality despite a low level of relatedness among group members. The behavioral basis of this sociality remains in doubt. This paper reviews the evidence for an empirically identifi- able form of prosocial behavior in humans, which we call ‘strong reciprocity,’ that may in part explain human sociality. A strong reciprocator is predisposed to cooperate with others and punish non-cooperators, even when this behavior cannot be justified in terms of extended kinship or reciprocal altruism. We present a simple model, stylized but plausible, of the evolutionary emergence of strong reciprocity. 1 Introduction Human groups maintain a high level of sociality despite a low level of relatedness among group members. Three types of explanation have been offered for this phe- nomenon: reciprocal altruism (Trivers 1971, Axelrod and Hamilton 1981), cultural group selection (Cavalli-Sforza and Feldman 1981, Boyd and Richerson 1985) and genetically-based altruism (Lumsden and Wilson 1981, Simon 1993, Wilson and Dugatkin 1997). These approaches are of course not incompatible. Reciprocal ∗ I would like to thank Lee Alan Dugatkin, Ernst Fehr, David Sloan Wilson, and the referees of this Journal for helpful comments, Samuel Bowles and Robert Boyd for many extended discussions of these issues, and the MacArthur Foundation for financial support. This paper is dedicated to the memory of W. -
Stable Matching: Theory, Evidence, and Practical Design
THE PRIZE IN ECONOMIC SCIENCES 2012 INFORMATION FOR THE PUBLIC Stable matching: Theory, evidence, and practical design This year’s Prize to Lloyd Shapley and Alvin Roth extends from abstract theory developed in the 1960s, over empirical work in the 1980s, to ongoing efforts to fnd practical solutions to real-world prob- lems. Examples include the assignment of new doctors to hospitals, students to schools, and human organs for transplant to recipients. Lloyd Shapley made the early theoretical contributions, which were unexpectedly adopted two decades later when Alvin Roth investigated the market for U.S. doctors. His fndings generated further analytical developments, as well as practical design of market institutions. Traditional economic analysis studies markets where prices adjust so that supply equals demand. Both theory and practice show that markets function well in many cases. But in some situations, the standard market mechanism encounters problems, and there are cases where prices cannot be used at all to allocate resources. For example, many schools and universities are prevented from charging tuition fees and, in the case of human organs for transplants, monetary payments are ruled out on ethical grounds. Yet, in these – and many other – cases, an allocation has to be made. How do such processes actually work, and when is the outcome efcient? Matching theory The Gale-Shapley algorithm Analysis of allocation mechanisms relies on a rather abstract idea. If rational people – who know their best interests and behave accordingly – simply engage in unrestricted mutual trade, then the outcome should be efcient. If it is not, some individuals would devise new trades that made them better of. -
Prisoners of Reason Game Theory and Neoliberal Political Economy
C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iii [1–28] 11.8.2015 9:57PM Prisoners of Reason Game Theory and Neoliberal Political Economy S. M. AMADAE Massachusetts Institute of Technology C:/ITOOLS/WMS/CUP-NEW/6549131/WORKINGFOLDER/AMADAE/9781107064034PRE.3D iv [1–28] 11.8.2015 9:57PM 32 Avenue of the Americas, New York, ny 10013-2473, usa Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning, and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107671195 © S. M. Amadae 2015 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2015 Printed in the United States of America A catalog record for this publication is available from the British Library. Library of Congress Cataloging in Publication Data Amadae, S. M., author. Prisoners of reason : game theory and neoliberal political economy / S.M. Amadae. pages cm Includes bibliographical references and index. isbn 978-1-107-06403-4 (hbk. : alk. paper) – isbn 978-1-107-67119-5 (pbk. : alk. paper) 1. Game theory – Political aspects. 2. International relations. 3. Neoliberalism. 4. Social choice – Political aspects. 5. Political science – Philosophy. I. Title. hb144.a43 2015 320.01′5193 – dc23 2015020954 isbn 978-1-107-06403-4 Hardback isbn 978-1-107-67119-5 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate. -
ON the EARLY HISTORY of EXPERIMENTAL ECONOMICS Alvin E
ON THE EARLY HISTORY OF EXPERIMENTAL ECONOMICS Alvin E. Roth I. INTRODUCTION In the course of coediting the Handbook of Experimental Economics it became clear to me that contemporary experimental economists tend to carry around with them different and very partial accounts of the history of this still emerging field. This project began as an attempt to merge these "folk histories" of the origins of what I am confident will eventually be seen as an important chapter in the history and sociology of economics. I won't try to pin down the first economic experiment, although I am partial to Bernoulli (1738) on the St. Petersburg paradox. The Bernoullis (Daniel and Nicholas) were not content to rely solely on their own intuitions, and resorted to the practice of asking other famous scholars for their opinions on that difficult choice problem. Allowing for their rather informal report, this is not so different from the practice of using hypothetical choice problems to generate hypotheses about individual choice behavior, which has been used to good effect in much more modern research on individual choice. But I think that searching for scientific "firsts" is often less illuminating than it is sometimes thought to be. In connection with the history of an entirely different subject, I once had occasion to draw the following analogy (Roth and Sotomayor 1990, p. 170): Columbus is viewed as the discoverer of America, even though every school child knows that the Americas were inhabited when he arrived, and that he was not even the first to have made a round trip, having been preceded by Vikings and perhaps by others. -
Who Are the Behavioral Economists and What Do They Say?
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Heukelom, Floris Working Paper Who are the Behavioral Economists and what do they say? Tinbergen Institute Discussion Paper, No. 07-020/1 Provided in Cooperation with: Tinbergen Institute, Amsterdam and Rotterdam Suggested Citation: Heukelom, Floris (2007) : Who are the Behavioral Economists and what do they say?, Tinbergen Institute Discussion Paper, No. 07-020/1, Tinbergen Institute, Amsterdam and Rotterdam This Version is available at: http://hdl.handle.net/10419/86489 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 TI 2007-020/1 Tinbergen Institute Discussion Paper Who are the Behavioral Economists and what do they say? Floris Heukelom University of Amsterdam, and Tinbergen Institute. -
Introduction to Game Theory
Economic game theory: a learner centred introduction Author: Dr Peter Kührt Introduction to game theory Game theory is now an integral part of business and politics, showing how decisively it has shaped modern notions of strategy. Consultants use it for projects; managers swot up on it to make smarter decisions. The crucial aim of mathematical game theory is to characterise and establish rational deci- sions for conflict and cooperation situations. The problem with it is that none of the actors know the plans of the other “players” or how they will make the appropriate decisions. This makes it unclear for each player to know how their own specific decisions will impact on the plan of action (strategy). However, you can think about the situation from the perspective of the other players to build an expectation of what they are going to do. Game theory therefore makes it possible to illustrate social conflict situations, which are called “games” in game theory, and solve them mathematically on the basis of probabilities. It is assumed that all participants behave “rationally”. Then you can assign a value and a probability to each decision option, which ultimately allows a computational solution in terms of “benefit or profit optimisation”. However, people are not always strictly rational because seemingly “irrational” results also play a big role for them, e.g. gain in prestige, loss of face, traditions, preference for certain colours, etc. However, these “irrational" goals can also be measured with useful values so that “restricted rational behaviour” can result in computational results, even with these kinds of models.