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INSTITUTE FOR MATHEMATICAL BEHAVIORAL SCIENCES CONFERENCE: LUCE AND RAIFFA AFTER 50 YEARS: WHAT IS NEXT? January 25 – 27, 2008 Friday, January 25 LOCATION: DOHENY BEACH A – STUDENT CENTER (LEVEL 1)__ 2:00 – 2:10 Opening Remarks by DONALD SAARI, Director of IMBS 2:10 – 2:50 Discussion by DUNCAN LUCE AND HOWARD RAIFFA 2:50 – 3:40 TOM SCHELLING, Professor, School of Public Policy, U. of Maryland Title to be announced 3:40 – 4:00 Discussion 4:00 – 4:30 ROGER MYERSON, Professor, Dept. of Economic, U. of Chicago “Discussion on the evolution of non-cooperative game theory in the 1950s and the state of the art today”. 4:30 – 4:40 General Discussion 4:40 – 5:20 LLOYD SHAPLEY, Prof. Emeritus of Mathematics and Economics, UCLA “RHO Stability: A New Solution Concept for Cooperative Games” Saturday, January 26 LOCATION: LUCE CONFERENCE ROOM, SOCIAL SCIENCE PLAZA A 2112 9:00 – 9:50 ERIC MASKIN. Professor, Dept. of Economics, Princeton University “Mechanism Design: How to Implement Social Goals” 9:50 – 10:00 Discussion 10:00 – 10:50 EHUD KALAI, Professor, Department of Managerial Economics & Decision Sciences, Kellogg School of Management, Northwestern University “Perspectives on Game Science” 10:50 – 11:00 Discussion 11:00 – 11:20 BREAK in SSPA 2142 11:20 – 12:10 AVINASH DIXIT, Professor, Department of Economics, Princeton “The achievements and future of game theory: A user’s perspective” Luce-Raiffa Conference Page 2 12:10 – 12:20 Discussion 12:20 – 2:00 LUNCH BREAK 2:00 – 2:50 SIMON LEVIN, Professor, Ecology & Evolutionary Biology, Princeton “Games, Groups, Norms and Societies”\ 2:50 – 3:00 Discussion 3:00 – 3:20 BREAK in SSPA 2142 3:20 – 4:10 ROBERT WILSON, Professor, Graduate School of Business, Stanford University “Evolution of Game Theory into Multi-Person Decision Theory” 4:10 – 4:20 Discussion Sunday, January 27 LOCATION: LUCE CONFERENCE ROOM, SOCIAL SCIENCE PLAZA A 2112 9:00 – 9:50 KEN BINMORE, Professor, Dept. of Economics, U. College of London “Making Decisions in Large Worlds” 9:50 – 10:00 Discussion 10:00 – 10:50 CHARLES PLOTT, Professor, Economics & Political Sciences, Cal Tech “Information Aggregation Mechanisms: Design, Testing and Application” .

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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.
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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.
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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 LászlóCollege, 2015. Member of the National Academy of Sciences, elected 2015. Honorary Doctorate (Doctorat Honoris Causa), Aix-Marseille Université, 2013. Dean’s Award for Distinguished Teaching in Humanities and Sciences, Stanford, 2013. Distinguished Teaching Award: Stanford Department of Economics, 2012.
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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.
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Curriculum Vitae 03/97
CURRICULUM VITAE April 2006 Ehud Kalai, Ph.D. Home Office 1110 N. Lake Shore Dr., Apt. 23S Department of Managerial Economics and Decision Sciences Chicago, IL 60611 Kellogg School of Management Phone: (847) 571-1097 Northwestern University, Evanston, Illinois, 60208 Fax: (312) 482-9772 (847) 491-7017; fax (847) 467-3646 e-mail: [email protected] Born, December 7, 1942, Tel Aviv, Israel Education Cornell University, Ithaca, New York: Ph.D. in Mathematics (1972); MS in Statistics (1971). University of California, Berkeley: A.B. in Mathematics (1967). Permanent Academic Positions 09/75-present Kellogg School of Management, Northwestern University: Visiting Assistant Professor (9/75-9/76), Associate Professor (9/76-9/78), Professor (9/78-9/82), The Charles E. Morrison Professor of Decision Sciences (9/82-9/2001); The James J. O'Connor Distinguished Professor of Decision and Game Sciences (9/2001 - present). 03/90-present Professor of Mathematics (courtesy), Department of Mathematics, CAS, Northwestern University. 10/72-9/75 Assistant Professor, Department of Statistics, Tel Aviv University. Editorial Positions Editor and founder, Games and Economic Behavior, Academic Press, 1988- . Member of the Editorial Board of the International Journal of Game Theory, Physica Verlag, 1984- . Member of the Editorial Board of Mathematical Social Sciences, North-Holland, 1980-1993. Associate Editor, The Journal of Economic Theory, Academic Press, Inc., 1980-1988. Other Positions President of the Game Theory Society, 2003-2006 Co Founder and Executive Vice President of the Game Theory Society, 1998-2003 Director of the Kellogg Center for Strategic Decision-Making, 1995- . Founding organizer of the Nancy L.
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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.
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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.
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Side Payments Among Players
Review of Economic Studies (2005) 72, 543–566 0034-6527/05/00220543$02.00 c 2005 The Review of Economic Studies Limited Endogenous Games and Mechanisms: Side Payments Among Players MATTHEW O. JACKSON and SIMON WILKIE California Institute of Technology First version received August 2002; final version accepted May 2004 (Eds.) We characterize the outcomes of games when players may make binding offers of strategy contingent side payments before the game is played. This does not always lead to efficient outcomes, despite complete information and costless contracting. The characterizations are illustrated in a series of examples, including voluntary contribution public good games, Cournot and Bertrand oligopoly, principal–agent problems, and commons games, among others. 1. INTRODUCTION Game theory and mechanism design are powerful tools that have become essential in the modelling of economic interactions. Generally, in modelling interactions from public goods contributions to imperfect competition among firms, the game being played or mechanism being designed is viewed in isolation. That is, we usually treat the game as being fixed from the players’ perspective. The analysis of many games viewed in such isolation leads to a prediction of an inefficient outcome, since in many contexts there are externalities present. For instance voluntary public goods contributions games and commons games have well-known free rider problems and equilibria that are Pareto inefficient. Similar results hold for many other games, such as those with imperfect competition or production externalities such as pollution. In practice, however, we often see players side contracting to improve efficiency. For instance, large donors often match the donations of other donors in contributions games.
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Olivier Gossner Qualifications Positions Visiting Positions
Feb. 2018 Olivier Gossner Born 04/04/1969 Qualiﬁcations 2004 Habilitation a` diriger les recherches 1996 Ph.D. Thesis, Universite´ Paris 6, summa cum laude 1995 Agregation´ de mathemathiques´ 1989–1993 Ecole Normale Superieure´ , Mathematics, Paris Positions 2014– CREST, CNRS, Economics Department, Ecole polytechnique 2008– London School of Economics, Department of Mathematics 2005–2014 PjSE, CNRS, Paris School of Economics 1998–2005 THEMA, CNRS, Universite´ Paris Nanterre 1996–1998 CORE, Universite´ Catholique de Louvain Visiting positions 2005–2008 MEDS, Kellogg School of Management, Northwestern University 2004–2005 Institute of Advanced Studies, Jerusalem Publications Articles in peer reviewed journals “A normalized value for information purchases”, with Antonio Cabrales and Roberto Serrano, Journal of Economic Theory, 170:266-288, 2017 “The complexity of interacting automata”, with Penelope´ Hernandez´ and Ron Peretz Interna- tional Journal of Game Theory, 45:461-496, 2016 “Finite-sample exact tests for linear regressions with bounded dependent variables”, with Karl Schlag, Journal of Econometrics, 177: 75-94, 2013 “Entropy and the value of information to investors”, with Antonio Cabrales and Roberto Ser- rano, American Economic Review 103: 360-377, 2013 “Performing best when it matters most: evidence from professional tennis”, with Julio Gonzalez-D´ ´ıas and Brian Rogers, Journal of Economic Behavior and Organizations 84: 767- 781, 2012 “Reasoning-based introspection”, with Elias Tsakas, Theory and Decision 73: 513-523, 2012 “Impermanent
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Ex-Post Stability in Large Games (Draft, Comments Welcome)
EX-POST STABILITY IN LARGE GAMES (DRAFT, COMMENTS WELCOME) EHUD KALAI Abstract. The equilibria of strategic games with many semi-anonymous play- ers have a strong ex-post Nash property. Even with perfect hindsight about the realized types and selected actions of all his opponents, no player has an incentive to revise his own chosen action. This is illustrated for normal form and for one shot Baysian games with statistically independent types, provided that a certain continuity condition holds. Implications of this phenomenon include strong robustness properties of such equilibria and strong puriﬁcation result for large anonymous games. 1. Introduction and Summary In a one-shot game with many semi-anonymous players all the equilibria are approximately ex-post Nash. Even with perfect hindsight about the realized types and actions of all his opponents, no player regrets, or has an incentive to unilaterally change his own selected action. This phenomenon holds for normal form games and for one shot Bayesian games with statistically independent types, provided that the payoﬀ functions are continuous. Moreover, the ex-post Nash property is obtained uniformly, simultaneously for all the equilibria of all the games in certain large classes, at an exponential rate in the number of players. When restricted to normal form games, the above means that with probability close to one, the play of any mixed strategy equilibrium must produce a vector of pure strategies that is an epsilon equilibrium of the game. At an equilibrium of a Bayesian game, the vector of realized pure actions must be an epsilon equilibrium of the complete information game in which the realized vector of player types is common knowledge.
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David Schmeidler, Professor
David Schmeidler, Professor List of Publications and Discussion Papers: Articles in Journals David Schmeidler, Competitive equilibria in markets with a continuum of traders and incomplete preferences, Econometrica, Vol. 37, 578-86 (1969). David Schmeidler, The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, Vol. 17, 1163-70 (1969). David Schmeidler, Fatou's Lemma in several dimensions, Proc. Amer. Math. Soc., Vol. 24, 300-6 (1970). David Schmeidler, A condition for the completeness of partial preference relations, Econometrica, Vol. 39, 403-4 (1971). David Schmeidler, Cores of exact games, I, J. Math. Anal. and Appl., Vol. 40, 214- 25 (1972). David Schmeidler, On set correspondences into uniformly convex Banach spaces, Proc. Amer. Math. Soc., Vol. 34, 97-101(1972). David Schmeidler, A remark on the core of an atomless economy, Econometrica, Vol. 40, 579-80 (1972). David Schmeidler and Karl Vind, Fair net trades, Econometrica, Vol. 40, 637-42 (1972). Jaques Dreze, Joan Gabszewicz, David Schmeidler and Karl Vind, Cores and prices in an exchange economy with an atomless sector, Econometrica, Vol. 40, 1091-108 (1972). David Schmeidler, Equilibrium points of non-atomic games, Journal of Statistical Physics, Vol. 7, 295-301 (1973). Werner Hildenbrand, David Schmeidler and Shmuel Zamir, Existence of approximate equilibria and cores, Econometrica, Vol. 41, 1159-66 (1973). Elisha A. Pazner and David Schmeidler, A difficulty in the concept of fairness, Review of Economic Studies, Vol. 41, 441-3 (1974). Elisha A. Pazner and David Schmeidler, Competitive analysis under complete ignorance, International Economic Review, Vol. 16, 246-57 (1975). Elisha A. Pazner and David Schmeidler, Social contract theory and ordinal distributive equity, Journal of Public Economics, Vol.
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Group Incentive Compatible Mechanism Yielding Core Allocations*
JOURNAL OF ECONOMICTHEORY 20, 13-22 (1979) A Group Incentive Compatible Mechanism Yielding Core Allocations* EHUD KALAI Department of Managerial Economics and Decision Sciences, Northwestern University, Evanston, Illinois 60201 ANDREW POSTLEWAITE Department of Economics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801 AND JOHN ROBERTS Department of Managerial Economics and Decision Sciences, Northwestern University, Evanston, INinois 60201 Received July 24, 1978 The possibilities for achieving desirable standards of economic performance in a decentralized, incentive compatible manner have recently received widespread research attention. Perhaps the most notable contribution in this area has been the remarkable paper by Groves and Ledyard [7]. They devised a mechanism for allocating resources in economies with public goods which gives agents broad opportunities for strategic behavior but under which Nash equilibrium results in Pareto optimal allocations. These allocations resulting from the Groves-Ledyard rules are not, however, guaranteed to be individually rational, so some agents may end up worse off under the operation of the mechanism than at their initial endowment points. Further, the mechanism is not group incentive compatible: if even two agents can coordinate their choices of messages, then the Nash equilibria are no longer stable and inefficiency may result [3]. * Support for Postlewaite’s and Roberts’ research was provided by the National Science Foundation through grants to the University of Illinois and to Northwestern University. Kalai’s research was supported by a grant from the Graduate School of Management, Northwestern University. 13 OO22-0531/79/01OO13-10$2.00/O Copyright 0 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
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