Volume 8 Issue 8+9 2020
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
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. -
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. -
Chapter 16 Oligopoly and Game Theory Oligopoly Oligopoly
Chapter 16 “Game theory is the study of how people Oligopoly behave in strategic situations. By ‘strategic’ we mean a situation in which each person, when deciding what actions to take, must and consider how others might respond to that action.” Game Theory Oligopoly Oligopoly • “Oligopoly is a market structure in which only a few • “Figuring out the environment” when there are sellers offer similar or identical products.” rival firms in your market, means guessing (or • As we saw last time, oligopoly differs from the two ‘ideal’ inferring) what the rivals are doing and then cases, perfect competition and monopoly. choosing a “best response” • In the ‘ideal’ cases, the firm just has to figure out the environment (prices for the perfectly competitive firm, • This means that firms in oligopoly markets are demand curve for the monopolist) and select output to playing a ‘game’ against each other. maximize profits • To understand how they might act, we need to • An oligopolist, on the other hand, also has to figure out the understand how players play games. environment before computing the best output. • This is the role of Game Theory. Some Concepts We Will Use Strategies • Strategies • Strategies are the choices that a player is allowed • Payoffs to make. • Sequential Games •Examples: • Simultaneous Games – In game trees (sequential games), the players choose paths or branches from roots or nodes. • Best Responses – In matrix games players choose rows or columns • Equilibrium – In market games, players choose prices, or quantities, • Dominated strategies or R and D levels. • Dominant Strategies. – In Blackjack, players choose whether to stay or draw. -
Nash Equilibrium
Lecture 3: Nash equilibrium Nash equilibrium: The mathematician John Nash introduced the concept of an equi- librium for a game, and equilibrium is often called a Nash equilibrium. They provide a way to identify reasonable outcomes when an easy argument based on domination (like in the prisoner's dilemma, see lecture 2) is not available. We formulate the concept of an equilibrium for a two player game with respective 0 payoff matrices PR and PC . We write PR(s; s ) for the payoff for player R when R plays 0 s and C plays s, this is simply the (s; s ) entry the matrix PR. Definition 1. A pair of strategies (^sR; s^C ) is an Nash equilbrium for a two player game if no player can improve his payoff by changing his strategy from his equilibrium strategy to another strategy provided his opponent keeps his equilibrium strategy. In terms of the payoffs matrices this means that PR(sR; s^C ) ≤ P (^sR; s^C ) for all sR ; and PC (^sR; sC ) ≤ P (^sR; s^C ) for all sc : The idea at work in the definition of Nash equilibrium deserves a name: Definition 2. A strategy s^R is a best-response to a strategy sc if PR(sR; sC ) ≤ P (^sR; sC ) for all sR ; i.e. s^R is such that max PR(sR; sC ) = P (^sR; sC ) sR We can now reformulate the idea of a Nash equilibrium as The pair (^sR; s^C ) is a Nash equilibrium if and only ifs ^R is a best-response tos ^C and s^C is a best-response tos ^R. -
What Is Local Optimality in Nonconvex-Nonconcave Minimax Optimization?
What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization? Chi Jin Praneeth Netrapalli University of California, Berkeley Microsoft Research, India [email protected] [email protected] Michael I. Jordan University of California, Berkeley [email protected] August 18, 2020 Abstract Minimax optimization has found extensive application in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises—“what is a proper definition of local optima?” Most previous work answers this question using classical notions of equilibria from simultaneous games, where the min-player and the max-player act simultaneously. In contrast, most applications in machine learning, including GANs and adversarial training, correspond to sequential games, where the order of which player acts first is crucial (since minimax is in general not equal to maximin due to the nonconvex-nonconcave nature of the problems). The main contribution of this paper is to propose a proper mathematical definition of local optimality for this sequential setting—local minimax—as well as to present its properties and existence results. Finally, we establish a strong connection to a basic local search algorithm—gradient descent ascent (GDA)—under mild conditions, all stable limit points of GDA are exactly local minimax points up to some degenerate points. 1 Introduction arXiv:1902.00618v3 [cs.LG] 15 Aug 2020 Minimax optimization refers to problems of two agents—one agent tries to minimize the payoff function f : X × Y ! R while the other agent tries to maximize it. -
Game Theory: Basic Concepts and Terminology
Leigh Tesfatsion 29 December 2019 Game Theory: Basic Concepts and Terminology A GAME consists of: • a collection of decision-makers, called players; • the possible information states of each player at each decision time; • the collection of feasible moves (decisions, actions, plays,...) that each player can choose to make in each of his possible information states; • a procedure for determining how the move choices of all the players collectively determine the possible outcomes of the game; • preferences of the individual players over these possible out- comes, typically measured by a utility or payoff function. 1 EMPLOYER CD C (40,40) (10,60) WORKER D (60,10) (20,20) Illustrative Modeling of a Work-Site Interaction as a \Prisoner's Dilemma Game" D = Defect (Shirk) C = Cooperate (Work Hard), (P1,P2) = (Worker Payoff, Employer Payoff) 2 A PURE STRATEGY for a player in a particular game is a complete contingency plan, i.e., a plan describing what move that player should take in each of his possible information states. A MIXED STRATEGY for a player i in a particular game is a probability distribution defined over the collection Si of player i's feasible pure strategy choices. That is, a mixed strategy assigns a nonnegative probability Prob(s) to each pure strategy s in Si, with X Prob(s) = 1 : (1) s2Si EXPOSITIONAL NOTE: For simplicity, the remainder of these brief notes will develop defi- nitions in terms of pure strategies; the unqualified use of \strategy" will always refer to pure strategy. Extension to mixed strategies is conceptually straightforward. 3 ONE-STAGE SIMULTANEOUS-MOVE N-PLAYER GAME: • The game is played just once among N players. -
Regulation and the Marginalist Revolution
Florida Law Review Volume 71 Issue 2 Article 4 Regulation and the Marginalist Revolution Herbert Hovenkamp Follow this and additional works at: https://scholarship.law.ufl.edu/flr Part of the Antitrust and Trade Regulation Commons Recommended Citation Herbert Hovenkamp, Regulation and the Marginalist Revolution, 71 Fla. L. Rev. 455 (). Available at: https://scholarship.law.ufl.edu/flr/vol71/iss2/4 This Article is brought to you for free and open access by UF Law Scholarship Repository. It has been accepted for inclusion in Florida Law Review by an authorized editor of UF Law Scholarship Repository. For more information, please contact [email protected]. Hovenkamp: Regulation and the Marginalist Revolution REGULATION AND THE MARGINALIST REVOLUTION Herbert Hovenkamp* Abstract The marginalist revolution in economics became the foundation for the modern regulatory State with its “mixed” economy. For the classical political economists, value was a function of past averages. Marginalism substituted forward looking theories based on expectations about firm and market performance. Marginalism swept through university economics, and by 1920 or so virtually every academic economist was a marginalist. This Article considers the historical influence of marginalism on regulatory policy in the United States. My view is at odds with those who argue that marginalism saved capitalism by rationalizing it as a more defensible buttress against incipient socialism. While marginalism did permit economists and policy makers to strike a middle ground between laissez faire and socialism, the “middle ground” tilted very strongly toward public control. Ironically, regulation plus private ownership was able to go much further in the United States than socialism ever could because it preserved the rhetoric of capital as privately owned, even as it deprived firms of many of the most important indicia of ownership. -
Nash Equilibrium and Mechanism Design ✩ ∗ Eric Maskin A,B, a Institute for Advanced Study, United States B Princeton University, United States Article Info Abstract
Games and Economic Behavior 71 (2011) 9–11 Contents lists available at ScienceDirect Games and Economic Behavior www.elsevier.com/locate/geb Commentary: Nash equilibrium and mechanism design ✩ ∗ Eric Maskin a,b, a Institute for Advanced Study, United States b Princeton University, United States article info abstract Article history: I argue that the principal theoretical and practical drawbacks of Nash equilibrium as a Received 23 December 2008 solution concept are far less troublesome in problems of mechanism design than in most Available online 18 January 2009 other applications of game theory. © 2009 Elsevier Inc. All rights reserved. JEL classification: C70 Keywords: Nash equilibrium Mechanism design Solution concept A Nash equilibrium (called an “equilibrium point” by John Nash himself; see Nash, 1950) of a game occurs when players choose strategies from which unilateral deviations do not pay. The concept of Nash equilibrium is far and away Nash’s most important legacy to economics and the other behavioral sciences. This is because it remains the central solution concept—i.e., prediction of behavior—in applications of game theory to these fields. As I shall review below, Nash equilibrium has some important shortcomings, both theoretical and practical. I will argue, however, that these drawbacks are far less troublesome in problems of mechanism design than in most other applications of game theory. 1. Solution concepts Game-theoretic solution concepts divide into those that are noncooperative—where the basic unit of analysis is the in- dividual player—and those that are cooperative, where the focus is on coalitions of players. John von Neumann and Oskar Morgenstern themselves viewed the cooperative part of game theory as more important, and their seminal treatise, von Neumann and Morgenstern (1944), devoted fully three quarters of its space to cooperative matters. -
Publics and Markets. What's Wrong with Neoliberalism?
12 Publics and Markets. What’s Wrong with Neoliberalism? Clive Barnett THEORIZING NEOLIBERALISM AS A egoists, despite much evidence that they POLITICAL PROJECT don’t. Critics of neoliberalism tend to assume that increasingly people do act like this, but Neoliberalism has become a key object of they think that they ought not to. For critics, analysis in human geography in the last this is what’s wrong with neoliberalism. And decade. Although the words ‘neoliberal’ and it is precisely this evaluation that suggests ‘neoliberalism’ have been around for a long that there is something wrong with how while, it is only since the end of the 1990s neoliberalism is theorized in critical human that they have taken on the aura of grand geography. theoretical terms. Neoliberalism emerges as In critical human geography, neoliberal- an object of conceptual and empirical reflec- ism refers in the first instance to a family tion in the process of restoring to view a of ideas associated with the revival of sense of political agency to processes previ- economic liberalism in the mid-twentieth ously dubbed globalization (Hay, 2002). century. This is taken to include the school of This chapter examines the way in which Austrian economics associated with Ludwig neoliberalism is conceptualized in human von Mises, Friedrich von Hayek and Joseph geography. It argues that, in theorizing Schumpeter, characterized by a strong com- neoliberalism as ‘a political project’, critical mitment to methodological individualism, an human geographers have ended up repro- antipathy towards centralized state planning, ducing the same problem that they ascribe commitment to principles of private property, to the ideas they take to be driving forces and a distinctive anti-rationalist epistemo- behind contemporary transformations: they logy; and the so-called Chicago School of reduce the social to a residual effect of more economists, also associated with Hayek but fundamental political-economic rationalities. -
Microeconomics 2. Game Theory
Microeconomics - 2.1 Strategic form games Description idsds Nash Rationalisability Correlated eq Microeconomics 2. Game Theory Alex Gershkov http://www.econ2.uni-bonn.de/gershkov/gershkov.htm 21. November 2007 1 / 41 Microeconomics - 2.1 Strategic form games Description idsds Nash Rationalisability Correlated eq Strategic form games 1.a Describing a game in strategic form 1.b Iterated deletion of strictly dominated strategies 1.c Nash equilibrium and examples 1.d Mixed strategies 1.e Existence of Nash equilibria 1.f Rationilazability 1.g Correlated equilibrium 2 / 41 Microeconomics - 2.1 Strategic form games Description idsds Nash Rationalisability Correlated eq 1.a Describing a game in strategic form Example: Entry game 1. 2 ice cream vendors decide whether or not to open an ice cream stand in a particular street 2. the decision is taken without observing the other vendor’s action 3. if only one stand is opened, this vendor earns $ 3 (the other vendor earns zero) 4. if both stands open, they share profits and earn $ 1.5 each 3 / 41 Microeconomics - 2.1 Strategic form games Description idsds Nash Rationalisability Correlated eq 1.a Describing a game in strategic form Let’s use a matrix to organise this information entry no entry entry 1.5,1.5 3,0 no entry 0,3 0,0 we use the following conventions 1. rows contain vendor 1’s decisions, columns contain vendor 2’s decisions 2. each outcome of the game is located in one cell of the matrix 3. outcomes (payoffs, profits) are given in expected utility in the form (u1, u2). -
The Encyclopedia of Public Choice Volume I the Editors
The Encyclopedia of Public Choice Volume I The Editors CHARLES K. ROWLEY, Duncan Black Professor of Economics, George Mason University and General Director, The Locke Institute; and Dr. Dr. h.c.mult. FRIEDRICH SCHNEIDER, Department of Economics, The University of Linz Advisory Board JAMES M. BUCHANAN, Buchanan House, George Mason University BERNARD GROFMAN, Department of Political Science, University of California, Irvine ARYE L. HILLMAN, Department of Economics, Bar-Ilan University MARTIN PALDAM, Department of Economics, Aarhus University WILLIAM F. SHUGHART II, Department of Economics, University of Mississippi ROBERT D. TOLLISON, Department of Economics, Clemson University DENNIS C. MUELLER, Department of Economics, University of Vienna MICHAEL C. MUNGER, Department of Political Science, Duke University PETER C. ORDESHOOK, Humanities and Social Sciences, Cal Tech GORDON TULLOCK, School of Law, George Mason University HANNELORE WECK-HANNEMANN, Institut Fur Finanzwissenschaft, Universitat Innsbruck The Encyclopedia of Public Choice Editors CHARLES K. ROWLEY The Locke Institute, and George Mason University and FRIEDRICH SCHNEIDER Johannes Kepler University of Linz, Institute of Economic Policy KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 0-306-47828-5 Print ISBN: 0-7923-8607-8 ©2004 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com We dedicate ‘The Encyclopedia of Public Choice’ to the memory of Duncan Black 23 May 1908 to 14 January 1991 The Founding Father of Public Choice TABLE OF CONTENTS Preface . -
Regulation and the Marginalist Revolution
University of Pennsylvania Carey Law School Penn Law: Legal Scholarship Repository Faculty Scholarship at Penn Law 5-29-2018 Regulation and the Marginalist Revolution Herbert J. Hovenkamp University of Pennsylvania Carey Law School Follow this and additional works at: https://scholarship.law.upenn.edu/faculty_scholarship Part of the Antitrust and Trade Regulation Commons, Courts Commons, Economic History Commons, Growth and Development Commons, Industrial Organization Commons, Inequality and Stratification Commons, Intellectual Property Law Commons, Law and Economics Commons, Public History Commons, and the Technology and Innovation Commons Repository Citation Hovenkamp, Herbert J., "Regulation and the Marginalist Revolution" (2018). Faculty Scholarship at Penn Law. 1984. https://scholarship.law.upenn.edu/faculty_scholarship/1984 This Article is brought to you for free and open access by Penn Law: Legal Scholarship Repository. It has been accepted for inclusion in Faculty Scholarship at Penn Law by an authorized administrator of Penn Law: Legal Scholarship Repository. For more information, please contact [email protected]. Hovenkamp Marginalism and Regulation June 2018, Page 1 REGULATION AND THE MARGINALIST REVOLUTION Herbert Hovenkamp* PRELIMINARY DRAFT: PLEASE CONSULT AUTHOR BEFORE CITING Abstract The marginalist revolution in economics became the foundation for the modern regulatory State with its “mixed” economy. Marginalism, whose development defines the boundary between classical political economy and neoclassical economics, completely overturned economists’ theory of value. It developed in the late nineteenth century in England, the Continent and the United States. For the classical political economists, value was a function of past averages. One good example is the wage-fund theory, which saw the optimal rate of wages as a function of the firm’s ability to save from previous profits.