Uniqueness and Symmetry in Bargaining Theories of Justice
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Slope Takers in Anonymous Markets"
Slope Takers in Anonymous Markets Marek Weretka,y 29th May 2011 Abstract In this paper, we study interactions among large agents trading in anonymous markets. In such markets, traders have no information about other traders’payo¤s, identities or even submitted orders. To trade optimally, each trader estimates his own price impact from the available data on past prices as well as his own trades and acts optimally, given such a simple (residual supply) representation of the residual mar- ket. We show that in a Walrasian auction, which is known to have a multiplicity of Nash equilibria that if all traders independently estimate and re-estimate price im- pacts, market interactions converge to a particular Nash equilibrium. Consequently, anonymity and learning argument jointly provide a natural selection argument for the Nash equilibrium in a Walrasian auction. We then study the properties of such focal equilibrium. JEL clasi…cation: D43, D52, L13, L14 Keywords: Walrasian Auction, Anonymous Thin Markets, Price impacts 1 Introduction Many markets, e.g., markets for …nancial assets are anonymous. In such markets inform- ation of each individual trader is restricted to own trades and commonly observed market price. Traders have no information about other traders’payo¤s, identities or submitted or- ders. The archetypical framework to study anonymous markets, a competitive equilibrium I would like to thank Paul Klemperer, Margaret Meyer, Peyton Young and especially Marzena Rostek for helpful conversations. yUniversity of Wisconsin-Madison, Department of Economics, 1180 Observatory Drive, Madison, WI 53706. E-mail: [email protected]. 1 assumes the following preconditions 1) all traders freely and optimally adjust traded quant- ities to prices; 2) trade occurs in centralized anonymous markets; and 3) individual traders are negligible and hence treat prices parametrically. -
Fair Division Michael Meurer Boston Univeristy School of Law
Boston University School of Law Scholarly Commons at Boston University School of Law Faculty Scholarship 1999 Fair Division Michael Meurer Boston Univeristy School of Law Follow this and additional works at: https://scholarship.law.bu.edu/faculty_scholarship Part of the Gaming Law Commons Recommended Citation Michael Meurer, Fair Division, 47 Buffalo Law Review 937 (1999). Available at: https://scholarship.law.bu.edu/faculty_scholarship/530 This Article is brought to you for free and open access by Scholarly Commons at Boston University School of Law. It has been accepted for inclusion in Faculty Scholarship by an authorized administrator of Scholarly Commons at Boston University School of Law. For more information, please contact [email protected]. BOSTON UNIVERSITY SCHOOL OF LAW WORKING PAPER SERIES, LAW & ECONOMICS WORKING PAPER NO. 99-10 FAIR DIVISION MICHAEL MEURER THIS PAPER APPEARS IN 47 BUFFALO LAW REVIEW 937 AND IS REPRINTED BY PERMISSION OF THE AUTHOR AND BUFFALO LAW REVIEW This paper can be downloaded without charge at: The Boston University School of Law Working Paper Series Index: http://www.bu.edu/law/faculty/papers The Social Science Research Network Electronic Paper Collection: http://papers.ssrn.com/paper.taf?abstract_id=214949 BOOK REVIEW Fair Division † MICHAEL J. MEURER appearing in 47 BUFFALO LAW REVIEW 937-74 (1999) INTRODUCTION Fair division is a fundamental issue of legal policy. The law of remedies specifies damages and rules of contribution that apportion liability among multiple defendants.1 Probate law specifies -
Lecture Notes
GRADUATE GAME THEORY LECTURE NOTES BY OMER TAMUZ California Institute of Technology 2018 Acknowledgments These lecture notes are partially adapted from Osborne and Rubinstein [29], Maschler, Solan and Zamir [23], lecture notes by Federico Echenique, and slides by Daron Acemoglu and Asu Ozdaglar. I am indebted to Seo Young (Silvia) Kim and Zhuofang Li for their help in finding and correcting many errors. Any comments or suggestions are welcome. 2 Contents 1 Extensive form games with perfect information 7 1.1 Tic-Tac-Toe ........................................ 7 1.2 The Sweet Fifteen Game ................................ 7 1.3 Chess ............................................ 7 1.4 Definition of extensive form games with perfect information ........... 10 1.5 The ultimatum game .................................. 10 1.6 Equilibria ......................................... 11 1.7 The centipede game ................................... 11 1.8 Subgames and subgame perfect equilibria ...................... 13 1.9 The dollar auction .................................... 14 1.10 Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem ... 15 2 Strategic form games 17 2.1 Definition ......................................... 17 2.2 Nash equilibria ...................................... 17 2.3 Classical examples .................................... 17 2.4 Dominated strategies .................................. 22 2.5 Repeated elimination of dominated strategies ................... 22 2.6 Dominant strategies .................................. -
Endgame Solving
Endgame Solving: The Surprising Breakthrough that Enabled Superhuman Two-Player No- Limit Texas Hold 'em Play Sam Ganzfried Assistant Professor, Computer Science, Florida International University, Miami FL PhD, Computer Science Department, Carnegie Mellon University, 2015 [email protected] 1 2 3 4 5 Milestones • Opponent Modelling in Poker, Billings et.al., ‘98 • Abstraction Methods for Game-Theoretic Poker, Shi/Littman, ‘00 • Approximating Game-Theoretic Optimal Strategies for Full-scale Poker, Billings et.al., ‘03 • Optimal Rhode Island Poker, Gilpin/Sandholm, ‘05 • Annual Computer Poker Competition ‘06-Present • EGT/automated abstraction algorithms, Gilpin/Sandholm ‘06-‘08 • Regret Minimization in Games with Incomplete Information, Zinkevich et.al., ‘07 • Man vs. Machine limit Texas hold ‘em competitions ‘08-’09 • Computer Poker & Imperfect Information Symposium/Workshop ‘12-Present • Heads-up Limit Hold'em Poker is Solved, Bowling et.al., ‘15 • Brains vs. AI no-limit Texas hold ‘em competition ’15 • First Computer Poker Tutorial ‘16 • DeepStack: Expert-Level Artificial Intelligence in No-Limit Poker ’17 • Second Brains vs. AI no-limit Texas hold ‘em competition ‘17 6 Scope and applicability of game theory • Strategic multiagent interactions occur in all fields – Economics and business: bidding in auctions, offers in negotiations – Political science/law: fair division of resources, e.g., divorce settlements – Biology/medicine: robust diabetes management (robustness against “adversarial” selection of parameters in MDP) – Computer -
Implementation Theory*
Chapter 5 IMPLEMENTATION THEORY* ERIC MASKIN Institute for Advanced Study, Princeton, NJ, USA TOMAS SJOSTROM Department of Economics, Pennsylvania State University, University Park, PA, USA Contents Abstract 238 Keywords 238 1. Introduction 239 2. Definitions 245 3. Nash implementation 247 3.1. Definitions 248 3.2. Monotonicity and no veto power 248 3.3. Necessary and sufficient conditions 250 3.4. Weak implementation 254 3.5. Strategy-proofness and rich domains of preferences 254 3.6. Unrestricted domain of strict preferences 256 3.7. Economic environments 257 3.8. Two agent implementation 259 4. Implementation with complete information: further topics 260 4.1. Refinements of Nash equilibrium 260 4.2. Virtual implementation 264 4.3. Mixed strategies 265 4.4. Extensive form mechanisms 267 4.5. Renegotiation 269 4.6. The planner as a player 275 5. Bayesian implementation 276 5.1. Definitions 276 5.2. Closure 277 5.3. Incentive compatibility 278 5.4. Bayesian monotonicity 279 * We are grateful to Sandeep Baliga, Luis Corch6n, Matt Jackson, Byungchae Rhee, Ariel Rubinstein, Ilya Segal, Hannu Vartiainen, Masahiro Watabe, and two referees, for helpful comments. Handbook of Social Choice and Welfare, Volume 1, Edited by K.J Arrow, A.K. Sen and K. Suzumura ( 2002 Elsevier Science B. V All rights reserved 238 E. Maskin and T: Sj'str6m 5.5. Non-parametric, robust and fault tolerant implementation 281 6. Concluding remarks 281 References 282 Abstract The implementation problem is the problem of designing a mechanism (game form) such that the equilibrium outcomes satisfy a criterion of social optimality embodied in a social choice rule. -
The Role of Self-Interest in Elite Bargaining
The role of self-interest in elite bargaining Brad L. LeVecka,b, D. Alex Hughesa,c, James H. Fowlera,c,d, Emilie Hafner-Burtona,c, and David G. Victora,1 aLaboratory on International Law and Regulation, School of International Relations and Pacific Studies, cDepartment of Political Science, and dDivision of Medical Genetics, University of California, San Diego, La Jolla, CA 92093; and bDepartment of Political Science, University of California, Merced, CA 95343 Edited by David G. Rand, Yale University, New Haven, CT, and accepted by the Editorial Board November 11, 2014 (received for review May 28, 2014) One of the best-known and most replicated laboratory results in evident in less experienced populations (16, 17). Some research behavioral economics is that bargainers frequently reject low has examined whether leaders are psychologically or physiolog- offers, even when it harms their material self-interest. This finding ically different from nonelite populations—for example, research could have important implications for international negotiations on anxiety levels in leaders (18) and work on how leaders may be on many problems facing humanity today, because models of selected for skills in coordination, leadership, and followership international bargaining assume exactly the opposite: that policy (19). The few existing studies that have empirically examined makers are rational and self-interested. However, it is unknown actual decision making by elites in highly particular roles—such whether elites who engage in diplomatic bargaining will similarly as professional tennis players, soccer players, and traders—sug- reject low offers because past research has been based almost gest that, through a combination of learning and attrition, elites exclusively on convenience samples of undergraduates, members are more likely to exhibit self-interested, profit-maximizing be- of the general public, or small-scale societies rather than highly havior than their less experienced counterparts (20–23). -
Publications of Agnes Cseh
Publications of Agnes Cseh This document lists all peer-reviewed publications of Agnes Cseh, Chair for Algorithm Engineering, Hasso Plattner Institute, Potsdam, Germany. This listing was automatically generated on October 6, 2021. An up-to-date version is available online at hpi.de/friedrich/docs/publist/cseh.pdf. Journal articles [1] Cseh, Á., Juhos, A., Pairwise Preferences in the Stable Marriage Problem. In: ACM Transactions on Economics and Computation (TEAC) 9, pp. 1–28, 2021. [2] Cseh, Á., Kavitha, T., Popular matchings in complete graphs. In: Algorithmica, pp. 1–31, 2021. [3] Andersson, T., Cseh, Á., Ehlers, L., Erlanson, A., Organizing time exchanges: Lessons from matching markets. In: American Economic Journal: Microeconomics 13, pp. 338–73, 2021. [4] Cseh, Á., Fleiner, T., The Complexity of Cake Cutting with Unequal Shares. In: ACM Transactions on Algorithms 16, pp. 1–21, 2020. An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional share. In this article, we investigate the problem of proportional division with unequal shares, where each player is entitled to receive a predetermined portion of the cake. Our main contribution is threefold. First we present a protocol for integer demands, which delivers a proportional solution in fewer queries than all known proto- cols. -
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. -
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. -
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. -
Bounded Rationality in Bargaining Games: Do Proposers Believe That Responders Reject an Equal Split?
No. 11 UNIVERSITY OF COLOGNE WORKING PAPER SERIES IN ECONOMICS BOUNDED RATIONALITY IN BARGAINING GAMES: DO PROPOSERS BELIEVE THAT RESPONDERS REJECT AN EQUAL SPLIT? BEN GREINER Department of Economics University of Cologne Albertus-Magnus-Platz D-50923 Köln Germany http://www.wiso.uni-koeln.de Bounded Rationality in Bargaining Games: Do Proposers Believe That Responders Reject an Equal Split?∗ Ben Greiner† June 19, 2004 Abstract Puzzled by the experimental results of the ’impunity game’ by Bolton & Zwick (1995) we replicate the game and alter it in a systematic manner. We find that although almost nobody actually rejects an offered equal split in a bargaining game, proposers behave as if there would be a considerably large rejection rate for equal splits. This result is inconsistent with existing models of economic decision making. This includes models of selfish play- ers as well as models of social utility and reciprocity, even when combined with erroneous decision making. Our data suggests that subjects fail to foresee their opponent’s decision even for one step in our simple bargaining games. We consider models of bounded rational decision making such as rules of thumb as explanations for the observed behavioral pattern. Keywords: ultimatum game, dictator game, impunity game, social utility, bounded rationality JEL Classification: C72, C92, D3 ∗I thank Bettina Bartels, Hakan Fink and Ralica Gospodinova for research assistance, the Strategic Interaction Group at MPI Jena for comments and serving as pilot participants, especially Susanne B¨uchner, Sven Fischer, Katinka Pantz and Carsten Schmidt for support in the conduction of the experiment, and Werner G¨uth, Axel Ockenfels, Ro’i Zultan, participants at the European ESA Meeting in Erfurt and at the Brown Bag seminars in Jena and Cologne for discussions and valuable comments. -
Partisan Gerrymandering and the Construction of American Democracy
0/-*/&4637&: *ODPMMBCPSBUJPOXJUI6OHMVFJU XFIBWFTFUVQBTVSWFZ POMZUFORVFTUJPOT UP MFBSONPSFBCPVUIPXPQFOBDDFTTFCPPLTBSFEJTDPWFSFEBOEVTFE 8FSFBMMZWBMVFZPVSQBSUJDJQBUJPOQMFBTFUBLFQBSU $-*$,)&3& "OFMFDUSPOJDWFSTJPOPGUIJTCPPLJTGSFFMZBWBJMBCMF UIBOLTUP UIFTVQQPSUPGMJCSBSJFTXPSLJOHXJUI,OPXMFEHF6OMBUDIFE ,6JTBDPMMBCPSBUJWFJOJUJBUJWFEFTJHOFEUPNBLFIJHIRVBMJUZ CPPLT0QFO"DDFTTGPSUIFQVCMJDHPPE Partisan Gerrymandering and the Construction of American Democracy In Partisan Gerrymandering and the Construction of American Democracy, Erik J. Engstrom offers an important, historically grounded perspective on the stakes of congressional redistricting by evaluating the impact of gerrymandering on elections and on party control of the U.S. national government from 1789 through the reapportionment revolution of the 1960s. In this era before the courts supervised redistricting, state parties enjoyed wide discretion with regard to the timing and structure of their districting choices. Although Congress occasionally added language to federal- apportionment acts requiring equally populous districts, there is little evidence this legislation was enforced. Essentially, states could redistrict largely whenever and however they wanted, and so, not surpris- ingly, political considerations dominated the process. Engstrom employs the abundant cross- sectional and temporal varia- tion in redistricting plans and their electoral results from all the states— throughout U.S. history— in order to investigate the causes and con- sequences of partisan redistricting. His analysis