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Viable Nash Equilibria: Formation and Defection (Feb 2020)
VIABLE NASH EQUILIBRIA: FORMATION AND DEFECTION (FEB 2020) EHUD KALAI In memory of John Nash Abstract. To be credible, economic analysis should restrict itself to the use of only those Nash equilibria that are viable. To assess the viability of an equilibrium , I study simple dual indices: a formation index, F (), that speci…es the number of loyalists needed to form ; and a defection index, D(), that speci…es the number of defectors that can sustain. Surprisingly, these simple indices (1) predict the performance of Nash equilibria in social systems and lab experiments, and (2) uncover new prop- erties of Nash equilibria and stability issues that have so far eluded game theory re…nements. JEL Classi…cation Codes: C0, C7, D5, D9. 1. Overview Current economic analysis often relies on the notion of a Nash equilibrium. Yet there are mixed opinions about the viability of this notion. On the one hand, many equilibria, referred to as viable in this paper, play critical roles in functioning social systems and perform well in lab and …eld experiments. Date: March 9, 2018, this version Feb 24, 2020. Key words and phrases. Normal form games, Nash equilibrium, Stability, Fault tolerance, Behavioral Economics. The author thanks the following people for helpful conversations: Nemanja Antic, Sunil Chopra, Vince Crawford, K…r Eliaz, Drew Fudenberg, Ronen Gradwohl, Yingni Guo, Adam Kalai, Fern Kalai, Martin Lariviere, Eric Maskin, Rosemarie Nagel, Andy Postlewaite, Larry Samuelson, David Schmeidler, James Schummer, Eran Shmaya, Joel Sobel, and Peyton Young; and seminar participants at the universities of the Basque Country, Oxford, Tel Aviv, Yale, Stanford, Berkeley, Stony Brook, Bar Ilan, the Technion, and the Hebrew University. -
Updating Beliefs When Evidence Is Open to Interpretation: Implications for Bias and Polarization∗
Updating Beliefs when Evidence is Open to Interpretation: Implications for Bias and Polarization∗ Roland G. Fryer, Jr., Philipp Harms, and Matthew O. Jacksony This Version: October 2017 Forthcoming in Journal of the European Economic Association Abstract We introduce a model in which agents observe signals about the state of the world, some of which are open to interpretation. Our decision makers first interpret each signal and then form a posterior on the sequence of interpreted signals. This `double updating' leads to confirmation bias and can lead agents who observe the same information to polarize. We explore the model's predictions in an on-line experiment in which individuals interpret research summaries about climate change and the death penalty. Consistent with the model, there is a significant relationship between an individual's prior and their interpretation of the summaries; and - even more striking - over half of the subjects exhibit polarizing behavior. JEL classification numbers: D10, D80, J15, J71, I30 Keywords: beliefs, polarization, learning, updating, Bayesian updating, biases, dis- crimination, decision making ∗We are grateful to Sandro Ambuehl, Ken Arrow, Tanaya Devi, Juan Dubra, Jon Eguia, Ben Golub, Richard Holden, Lawrence Katz, Peter Klibanoff, Scott Kominers, Franziska Michor, Giovanni Parmigiani, Matthew Rabin, Andrei Shleifer, and Joshua Schwartzein for helpful comments and suggestions. Adriano Fernandes provided exceptional research assistance. yFryer is at the Department of Economics, Harvard University, and the NBER, ([email protected]); Jackson is at the Department of Economics, Stanford University, the Santa Fe Institute, and CIFAR (jack- [email protected]); and Harms is at the Department of Mathematical Stochastics, University of Freiburg, ([email protected]). -
DP Cover1512 Kalai.Cdr
Discussion Paper #1512 June 16, 2010 A A Cooperative Value for Bayesian Games Key words: cooperative game theory, non- cooperative game theory, bargaining, min-max value JEL classification: C70, C71, C72, C78 Adam Kalai Microsoft Research Ehud Kalai Northwestern University www.kellogg.northwestern.edu/research/math everone Hall Evanston, IL 60208-2014 US CMS-EMS oad 580 L The Center for Mathematical Studies in Economics & Management Sciences Northwestern University 2001 Sheridan R A COOPERATIVE VALUE FOR BAYESIAN GAMES ADAM TAUMAN KALAI∗ AND EHUD KALAIy;x Abstract. Selfish, strategic players may benefit from cooperation, provided they reach agreement. It is therefore important to construct mechanisms that facilitate such cooperation, especially in the case of asymmetric private information. The two major issues are: (1) singling out a fair and efficient outcome among the many individually rational possibilities in a strategic game, and (2) establishing a play protocol under which strategic players may achieve this outcome. The paper presents a general solution for two-person Bayesian games with monetary payoffs, under a strong revealed-payoff assumption. The proposed solution builds upon earlier concepts in game theory. It coincides with the von Neumann minmax value on the class of zero sum games and with the major solution concepts to the Nash Bargaining Problem. Moreover, the solution is based on a simple decomposition of every game into cooperative and competitive components, which is easy to compute. 1. Introduction Selfish players in strategic games benefit from cooperation, provided they come to mutually beneficial agreements. In the case of asymmetric private information, the benefits may be even greater, but avoiding strategic manipulations is more subtle. -
(Eds.) Foundations in Microeconomic Theory Hugo F
Matthew O. Jackson • Andrew McLennan (Eds.) Foundations in Microeconomic Theory Hugo F. Sonnenschein Matthew O. Jackson • Andrew McLennan (Eds.) Foundations in Microeconomic Theory A Volume in Honor of Hugo F. Sonnenschein ^ Springer Professor Matthew O. Jackson Professor Andrew McLennan Stanford University School of Economics Department of Economics University of Queensland Stanford, CA 94305-6072 Rm. 520, Colin Clark Building USA The University of Queensland [email protected] NSW 4072 Australia [email protected] ISBN: 978-3-540-74056-8 e-ISBN: 978-3"540-74057-5 Library of Congress Control Number: 2007941253 © 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMX Design GmbH, Heidelberg Printed on acid-free paper 987654321 spnnger.com Contents Introduction 1 A Brief Biographical Sketch of Hugo F. Sonnenschein 5 1 Kevin C. Sontheimer on Hugo F. -
The Case of the Market for Non-Prime Mortgage-Based Securities Br
Made centro de pesquisa em macroeconomia das desigualdades Working Paper 18.01.2021 nº 003 Conventions and the process of market formation: the case of the market for non-prime mortgage-based securities Bruno Höfig Abstract 18.01.2021 nº 003 The article develops the hypothesis that conventions can be key to the development of markets for previously untraded financial assets. It argues that the absence of historical data on the performance of Bruno Höfig Ph.D. in Economics - SOAS, assets may induce agents to form beliefs in ways that University of London preclude the formation of markets for certain financial bhofi[email protected] instruments. Conversely, in the absence of trading, the data on the basis of which agents could revise their The author would like to thank Alfredo Saad-Filho, Pedro beliefs will not be produced, giving rise to a feedback Mendes Loureiro, Camila Alves loop that hinders the process of market-formation. de André, Leonardo Müller, The article contends that one of the ways of Tomás Gotta and Matías Vernengo for comments on overcoming this state is the development of earlier drafts of this article. The conventions about the distribution of future payofs. It usual disclaimers apply. then shows that the emergence of the conventions that credit rating agencies could reliably measure the riskiness of non-prime residential mortgage-securities (RMBSs), and that the FICO score could reliably give a quantitative expression of the creditworthiness of individual borrowers was a crucial enabling condition of the formation of a market for RMBSs in the United States. Keywords: conventional valuation, probability, mortgage-backed securities, credit rating agencies, credit scores. -
Matthew O. Jackson
Matthew O. Jackson Department of Economics Stanford University Stanford, CA 94305-6072 (650) 723-3544, fax: 725-5702, [email protected] http://www.stanford.edu/ jacksonm/ ⇠ Personal: Born 1962. Married to Sara Jackson. Daughters: Emilie and Lisa. Education: Ph.D. in Economics from the Graduate School of Business, Stanford Uni- versity, 1988. Bachelor of Arts in Economics, Summa Cum Laude, Phi Beta Kappa, Princeton University, 1984. Full-Time Appointments: 2008-present, William D. Eberle Professor of Economics, Stanford Univer- sity. 2006-2008, Professor of Economics, Stanford University. 2002-2006, Edie and Lew Wasserman Professor of Economics, California Institute of Technology. 1997-2002, Professor of Economics, California Institute of Technology. 1996-1997, IBM Distinguished Professor of Regulatory and Competitive Practices MEDS department (Managerial Economics and Decision Sci- ences), Kellogg Graduate School of Management, Northwestern Univer- sity. 1995-1996, Mechthild E. Nemmers Distinguished Professor MEDS, Kellogg Graduate School of Management, Northwestern University. 1993-1994 , Professor (MEDS), Kellogg Graduate School of Management, Northwestern University. 1991-1993, Associate Professor (MEDS), Kellogg Graduate School of Man- agement, Northwestern University. 1988-1991, Assistant Professor, (MEDS), Kellogg Graduate School of Man- agement, Northwestern University. Honors : Jean-Jacques La↵ont Prize, Toulouse School of Economics 2020. President, Game Theory Society, 2020-2022, Exec VP 2018-2020. Game Theory Society Fellow, elected 2017. John von Neumann Award, Rajk L´aszl´oCollege, 2015. Member of the National Academy of Sciences, elected 2015. Honorary Doctorate (Doctorat Honoris Causa), Aix-Marseille Universit´e, 2013. Dean’s Award for Distinguished Teaching in Humanities and Sciences, Stanford, 2013. Distinguished Teaching Award: Stanford Department of Economics, 2012. -
Large Games: Structural Robustness
1 Large games: structural robustness Ehud Kalai Northwestern University Forthcoming in The New Palgrave Dictionary of Economics , 2 nd edition, Palgrave Macmillan ABSTRACT In simultaneous-move Bayesian games with many semi-anonymous players all the equilibria are structurally robust. The equilibria survive under structural alterations of the rules of the game and its information structure, even when the game is embedded in bigger games. Structural robustness implies ex-post Nash condition s and a stronger condition of information proofness. It also implies fast learning, self-purification and strong rational expectations in market games. Structurally robust equilibria may be used to model games with highly unspecified structures, such as games played on the web. 0. Background on large games Earlier literature on large (many players) cooperative games is surveyed in Aumann and Shapley (1974). For large strategic games, see Schmeidler (1973) and the follow-up literature on the purification of Nash equilibria. There is also substantial literature on large games with special structures, for example large auctions as reported in Rustichini, Satterthwaite, and Williams (1994). Unlike the above, this survey concentrates on the structural robustness of (general) Bayesian games with many semi-anonymous players, as developed in Kalai (2004, 2005). (For additional notions of robustness in game theory, see Bergemann and Morris, 2005). 1. Main message and examples In simultaneous-move Bayesian games with many semi-anonymous players, all Nash equilibria are structurally robust. The equilibria survive under structural alterations that 2 relax the simultaneous-play assumptions, and permit information transmission, revisions of choices, communication, commitments, delegation, and more. Large economic and political systems and distributive systems such as the Web are examples of environments that give rise to such games. -
Rational Choice As a Toolbox for the Economist: an Interview with Itzhak Gilboa
Erasmus Journal for Philosophy and Economics, Volume 7, Issue 2, Autumn 2014, pp. 116-141. http://ejpe.org/pdf/7-2-int.pdf Rational choice as a toolbox for the economist: an interview with Itzhak Gilboa CATHERINE HERFELD Ludwig-Maximilians-Universität München Itzhak Gilboa (Tel Aviv, 1963) is currently professor of economics at the Eitan Berglas School of Economics at Tel-Aviv University and professor of economics and decision sciences at the Hautes Études Commerciales (HEC) in Paris. He earned undergraduate degrees in mathematics and in economics at Tel Aviv University, where he also obtained his MA and PhD in economics under the supervision of David Schmeidler. Before joining Tel Aviv University in 2004 and the HEC in 2008, Gilboa taught at the J. L. Kellogg Graduate School of Management at Northwestern University, the University of Pennsylvania, and Boston University. Gilboa’s main area of interest is decision-making under uncertainty, focusing on the definition of probability, notions of rationality, non- Bayesian decision models, and related issues. He has published broadly in areas such as decision and game theory, microeconomics, philosophy, social choice theory, and applied mathematics. He has written over 90 articles in these fields. Gilboa has furthermore written a textbook entitled Rational choice (Gilboa 2010a), in which he lays out what he takes to be the main toolbox for studying and improving human decision-making. Additional books include A theory of case-based decisions (Gilboa and Schmeidler 2001), Theory of decision under uncertainty (Gilboa 2009), Making better decisions (Gilboa 2010b), and Case-based predictions (Gilboa and Schmeidler 2012). -
Nancy L. Stokey
March 2021 NANCY L. STOKEY Office Address Home Address Kenneth C. Griffin Department of Economics 320 W. Oakdale Ave., #1903 University of Chicago Chicago, IL 60657 1126 East 59th Street Chicago, IL 60637 Telephone: 773-702-0915 Telephone: 773-477-9640 Fax: 773-702-8490 E-mail: nstokey[at]uchicago.edu Education Doctor of Philosophy in Economics, Harvard University, 1978. Bachelor of Arts in Economics, University of Pennsylvania, 1972. Professional Experience Distinguished Service Professor, 2004-present, University of Chicago; Frederick Henry Prince Professor of Economics, 1997-2004; Professor of Economics, 1990-1996. Visiting Scholar of the Research Department, Federal Reserve Bank of Minneapolis, Fall 2000, Fall 2001, Fall 2002, Fall 2003, Fall 2009, Fall 2010, Fall 2011, Fall 2013, Fall 2018. Harold L. Stuart Professor of Managerial Economics, 1988-90, Department of Managerial Economics and Decision Sciences, Kellogg Graduate School of Management, Northwestern University; Department Chairman, 1987-89; Professor, 1983-87; Associate Professor, 1982-83; Assistant Professor, 1978-82. Visiting Professor of Economics, Department of Economics, University of Chicago, 1983-84. Visiting Professor of Economics, Department of Economics, University of Minnesota, Spring 1983. Visiting Lecturer on Economics, Department of Economics, Harvard University, Fall 1982. Professional Activities and Awards President, Society for the Advancement of Economic Theory (SAET), January 1 – December 31, 2021. American Academy of Arts and Sciences Class III, Section 2 (Economics) Membership Panel, 2019-20. American Academy of Arts and Sciences Class III, Section 2 (Economics) Membership Panel, 2018-19. CME Group-MSRI Prize Committee, 2018-19. Plenary Speaker, Society for Economic Dynamics, Mexico City, June, 2018. Plenary Speaker, Tsinghua Workshop in Macroeconomics, Beijing, June, 2018. -
Large Robust Games 1. Introduction and Examples
LARGE ROBUST GAMES EHUD KALAI Abstract. With many semi-anonymous players, the equilibria of simultaneous- move games are extensively robust. This means that the equilibria survive even if the simultaneous-play assumption is relaxed to allow for a large variety of ex- tensive modifications. Such modification include sequential play with partial and differential revelation of information, commitments and multiple revisions of choices, cheap talk announcements and more. 1. INTRODUCTION AND EXAMPLES 1.1. INTRODUCTION. Games with many players is an old topic in economics and in cooperative game theory. Prominent theorists, including Arrow, Aumann, Debreu, Hildenbrand, Scarf, Shapley, and Shubik, have shown that in large cooper- ative games major modeling difficulties disappear. For example, solution concepts such as the core, competitive equilibrium, and the Shapley value, which in general predict different outcomes for the same game, predict the same outcome when the number of players is large. As a special case, this coincidence offers a cooperative- coalitional foundation for competitive equilibria. For a general survey, see Aumann and Shapley (1974). Less is known about general non-cooperative strategic games with many players. An early study of this subject was Schmeidler (1973), who shows the existence of pure-strategy Nash equilibria in normal-form games with a continuum of anony- mous players. More recently there have been many studies of specific large economic games; see, for example, Mailath and Postlewaite (1990) on bargaining, Rustichini, Sat- terthwaite, and Williams (1994) and Pesendorfer and Swinkels (1997) on auctions, Date:February5,2004. Key words and phrases. anonymous games, Nash equilibrium, Bayesian equilibrium, purifica- tion, robust equilibrium, ex-post Nash, rational expectations equilibrium. -
Chronology of Game Theory
Chronology of Game Theory http://www.econ.canterbury.ac.nz/personal_pages/paul_walker/g... Home | UC Home | Econ. Department | Chronology of Game Theory | Nobel Prize A Chronology of Game Theory by Paul Walker September 2012 | Ancient | 1700 | 1800 | 1900 | 1950 | 1960 | 1970 | 1980 | 1990 | Nobel Prize | 2nd Nobel Prize | 3rd Nobel Prize | 0-500AD The Babylonian Talmud is the compilation of ancient law and tradition set down during the first five centuries A.D. which serves as the basis of Jewish religious, criminal and civil law. One problem discussed in the Talmud is the so called marriage contract problem: a man has three wives whose marriage contracts specify that in the case of this death they receive 100, 200 and 300 respectively. The Talmud gives apparently contradictory recommendations. Where the man dies leaving an estate of only 100, the Talmud recommends equal division. However, if the estate is worth 300 it recommends proportional division (50,100,150), while for an estate of 200, its recommendation of (50,75,75) is a complete mystery. This particular Mishna has baffled Talmudic scholars for two millennia. In 1985, it was recognised that the Talmud anticipates the modern theory of cooperative games. Each solution corresponds to the nucleolus of an appropriately defined game. 1713 In a letter dated 13 November 1713 Francis Waldegrave provided the first, known, minimax mixed strategy solution to a two-person game. Waldegrave wrote the letter, about a two-person version of the card game le Her, to Pierre-Remond de Montmort who in turn wrote to Nicolas Bernoulli, including in his letter a discussion of the Waldegrave solution. -
A Personal Tribute to David Schmeidler's Influence
A Personal Tribute to David Schmeidler’s Influence Peter P. Wakker* UN HOMMAGE PERSONNEL À L’INFLUENCE DE DAVID SCHMEIDLER Keywords: Choquet expected utility, uncertainty, nucleolus Mots clés: espérance d’utilité à la Choquet, incertitude, nucleolus Document téléchargé depuis www.cairn.info - 145.5.176.10 28/02/2020 16:23 © Presses de Sciences Po JEL Codes: D91, C81. This paper describes my relationship with David Schmeidler and how he ins- pired me. My first meeting with David was on August 29, 1984, in a conference on Operations Research in Osnabrück in Germany. Two positive impressions preceded it. First, my colleague PhD student Jean Derks in Nijmegen had once told me enthusiastically about David’s nucleolus cooperative game solution (Schmeidler [1969]). Second, and I could not anticipate how this would change my life, my supervisor and mentor Stef Tijs had given me a copy, that is, a paper copy (of copy of copy of . in those days), of Schmeidler [1982], later published as Schmeidler [1986], [1989]. Stef introduced me to David on August 29, 1984, suggesting I might visit David. David suggested that that might be but kept it short. He was a man of few words, even more then than nowadays. He later attended my lecture on a part of my PhD thesis that led to Wakker [1993], and I guessed that he liked it. Then a 6-week visit was arranged, which took place early 1985. With my Bayesian sympathies I had been learning, the hard way, what a cle- ver and diplomatic Econometrica referee stated as follows: “I urge the author to turn his talents toward nonexpected utility.” My despair had reached a level by that time making me willing to work on just any nonexpected utility model that would come by.