1 Competition Policy Implications from Game Theory
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Monopolistic Competition in General Equilibrium: Beyond the CES Evgeny Zhelobodko, Sergey Kokovin, Mathieu Parenti, Jacques-François Thisse
Monopolistic competition in general equilibrium: Beyond the CES Evgeny Zhelobodko, Sergey Kokovin, Mathieu Parenti, Jacques-François Thisse To cite this version: Evgeny Zhelobodko, Sergey Kokovin, Mathieu Parenti, Jacques-François Thisse. Monopolistic com- petition in general equilibrium: Beyond the CES. 2011. halshs-00566431 HAL Id: halshs-00566431 https://halshs.archives-ouvertes.fr/halshs-00566431 Preprint submitted on 16 Feb 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. WORKING PAPER N° 2011 - 08 Monopolistic competition in general equilibrium: Beyond the CES Evgeny Zhelobodko Sergey Kokovin Mathieu Parenti Jacques-François Thisse JEL Codes: D43, F12, L13 Keywords: monopolistic competition, additive preferences, love for variety, heterogeneous firms PARIS-JOURDAN SCIENCES ECONOMIQUES 48, BD JOURDAN – E.N.S. – 75014 PARIS TÉL. : 33(0) 1 43 13 63 00 – FAX : 33 (0) 1 43 13 63 10 www.pse.ens.fr CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE – ECOLE DES HAUTES ETUDES EN SCIENCES SOCIALES ÉCOLE DES PONTS PARISTECH – ECOLE NORMALE SUPÉRIEURE – INSTITUT NATIONAL DE LA RECHERCHE AGRONOMIQUE Monopolistic Competition in General Equilibrium: Beyond the CES∗ Evgeny Zhelobodko† Sergey Kokovin‡ Mathieu Parenti§ Jacques-François Thisse¶ 13th February 2011 Abstract We propose a general model of monopolistic competition and derive a complete characterization of the market equilibrium using the concept of Relative Love for Variety. -
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. -
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 .................................. -
Game Theoretic Interaction and Decision: a Quantum Analysis
games Article Game Theoretic Interaction and Decision: A Quantum Analysis Ulrich Faigle 1 and Michel Grabisch 2,* 1 Mathematisches Institut, Universität zu Köln, Weyertal 80, 50931 Köln, Germany; [email protected] 2 Paris School of Economics, University of Paris I, 106-112, Bd. de l’Hôpital, 75013 Paris, France * Correspondence: [email protected]; Tel.: +33-144-07-8744 Received: 12 July 2017; Accepted: 21 October 2017; Published: 6 November 2017 Abstract: An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result, cooperation systems, decision systems and quantum systems all become visible as manifestations of special interaction systems. The treatment of the theory is purely mathematical and does not require any special knowledge of physics. It is shown how standard notions in cooperative game theory arise naturally in this context. In particular, states of general interaction systems are seen to arise as linear superpositions of pure quantum states and Fourier transformation to become meaningful. Moreover, quantum games fall into this framework. Finally, a theory of Markov evolution of interaction states is presented that generalizes classical homogeneous Markov chains to the present context. Keywords: cooperative game; decision system; evolution; Fourier transform; interaction system; measurement; quantum game 1. Introduction In an interaction system, economic (or general physical) agents interact pairwise, but do not necessarily cooperate towards a common goal. However, this model arises as a natural generalization of the model of cooperative TU games, for which already Owen [1] introduced the co-value as an assessment of the pairwise interaction of two cooperating players1. -
Chapter 5 Perfect Competition, Monopoly, and Economic Vs
Chapter Outline Chapter 5 • From Perfect Competition to Perfect Competition, Monopoly • Supply Under Perfect Competition Monopoly, and Economic vs. Normal Profit McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. From Perfect Competition to Picking the Quantity to Maximize Profit Monopoly The Perfectly Competitive Case P • Perfect Competition MC ATC • Monopolistic Competition AVC • Oligopoly P* MR • Monopoly Q* Q Many Competitors McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Picking the Quantity to Maximize Profit Characteristics of Perfect The Monopoly Case Competition P • a large number of competitors, such that no one firm can influence the price MC • the good a firm sells is indistinguishable ATC from the ones its competitors sell P* AVC • firms have good sales and cost forecasts D • there is no legal or economic barrier to MR its entry into or exit from the market Q* Q No Competitors McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. McGraw -Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. 1 Monopoly Monopolistic Competition • The sole seller of a good or service. • Monopolistic Competition: a situation in a • Some monopolies are generated market where there are many firms producing similar but not identical goods. because of legal rights (patents and copyrights). • Example : the fast-food industry. McDonald’s has a monopoly on the “Happy Meal” but has • Some monopolies are utilities (gas, much competition in the market to feed kids water, electricity etc.) that result from burgers and fries. -
The Three Types of Collusion: Fixing Prices, Rivals, and Rules Robert H
University of Baltimore Law ScholarWorks@University of Baltimore School of Law All Faculty Scholarship Faculty Scholarship 2000 The Three Types of Collusion: Fixing Prices, Rivals, and Rules Robert H. Lande University of Baltimore School of Law, [email protected] Howard P. Marvel Ohio State University, [email protected] Follow this and additional works at: http://scholarworks.law.ubalt.edu/all_fac Part of the Antitrust and Trade Regulation Commons, and the Law and Economics Commons Recommended Citation The Three Types of Collusion: Fixing Prices, Rivals, and Rules, 2000 Wis. L. Rev. 941 (2000) This Article is brought to you for free and open access by the Faculty Scholarship at ScholarWorks@University of Baltimore School of Law. It has been accepted for inclusion in All Faculty Scholarship by an authorized administrator of ScholarWorks@University of Baltimore School of Law. For more information, please contact [email protected]. ARTICLES THE THREE TYPES OF COLLUSION: FIXING PRICES, RIVALS, AND RULES ROBERTH. LANDE * & HOWARDP. MARVEL** Antitrust law has long held collusion to be paramount among the offenses that it is charged with prohibiting. The reason for this prohibition is simple----collusion typically leads to monopoly-like outcomes, including monopoly profits that are shared by the colluding parties. Most collusion cases can be classified into two established general categories.) Classic, or "Type I" collusion involves collective action to raise price directly? Firms can also collude to disadvantage rivals in a manner that causes the rivals' output to diminish or causes their behavior to become chastened. This "Type 11" collusion in turn allows the colluding firms to raise prices.3 Many important collusion cases, however, do not fit into either of these categories. -
Tough Talk, Cheap Talk, and Babbling: Government Unity, Hawkishness
Tough Talk, Cheap Talk, and Babbling: Government Unity, Hawkishness and Military Challenges By Matthew Blake Fehrs Department of Political Science Duke University Date:_____________________ Approved: ___________________________ Joseph Grieco, Supervisor __________________________ Alexander Downes __________________________ Peter Feaver __________________________ Chris Gelpi __________________________ Erik Wibbels Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Political Science in the Graduate School of Duke University 2008 ABSTRACT Tough Talk, Cheap Talk, and Babbling: Government Unity, Hawkishness and Military Challenges By Matthew Blake Fehrs Department of Political Science Duke University Date:_____________________ Approved: ___________________________ Joseph Grieco, Supervisor __________________________ Alexander Downes __________________________ Peter Feaver __________________________ Chris Gelpi __________________________ Erik Wibbels An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Political Science in the Graduate School of Duke University 2008 Copyrighted by Matthew Blake Fehrs 2008 Abstract A number of puzzles exist regarding the role of domestic politics in the likelihood of international conflict. In particular, the sources of incomplete information remain under-theorized and the microfoundations deficient. This study will examine the role that the unity of the government and the views of the government towards the use of force play in the targeting of states. The theory presented argues that divided dovish governments are particularly likely to suffer from military challenges. In particular, divided governments have difficulty signaling their intentions, taking decisive action, and may appear weak. The theory will be tested on a new dataset created by the author that examines the theory in the context of international territorial disputes. -
Forward Guidance: Communication, Commitment, Or Both?
Forward Guidance: Communication, Commitment, or Both? Marco Bassetto July 25, 2019 WP 2019-05 https://doi.org/10.21033/wp-2019-05 *Working papers are not edited, and all opinions and errors are the responsibility of the author(s). The views expressed do not necessarily reflect the views of the Federal Reserve Bank of Chicago or the Federal Federal Reserve Bank of Chicago Reserve Federal Reserve System. Forward Guidance: Communication, Commitment, or Both?∗ Marco Bassettoy July 25, 2019 Abstract A policy of forward guidance has been suggested either as a form of commitment (\Odyssean") or as a way of conveying information to the public (\Delphic"). I an- alyze the strategic interaction between households and the central bank as a game in which the central bank can send messages to the public independently of its actions. In the absence of private information, the set of equilibrium payoffs is independent of the announcements of the central bank: forward guidance as a pure commitment mechanism is a redundant policy instrument. When private information is present, central bank communication can instead have social value. Forward guidance emerges as a natural communication strategy when the private information in the hands of the central bank concerns its own preferences or beliefs: while forward guidance per se is not a substitute for the central bank's commitment or credibility, it is an instrument that allows policymakers to leverage their credibility to convey valuable information about their future policy plans. It is in this context that \Odyssean forward guidance" can be understood. ∗I thank Gadi Barlevy, Jeffrey Campbell, Martin Cripps, Mariacristina De Nardi, Fernando Duarte, Marco Del Negro, Charles L. -
Collusion Constrained Equilibrium
Theoretical Economics 13 (2018), 307–340 1555-7561/20180307 Collusion constrained equilibrium Rohan Dutta Department of Economics, McGill University David K. Levine Department of Economics, European University Institute and Department of Economics, Washington University in Saint Louis Salvatore Modica Department of Economics, Università di Palermo We study collusion within groups in noncooperative games. The primitives are the preferences of the players, their assignment to nonoverlapping groups, and the goals of the groups. Our notion of collusion is that a group coordinates the play of its members among different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that meet this requirement need not exist. We instead introduce the weaker notion of collusion constrained equilibrium. This al- lows groups to put positive probability on alternatives that are suboptimal for the group in certain razor’s edge cases where the set of incentive compatible plans changes discontinuously. These collusion constrained equilibria exist and are a subset of the correlated equilibria of the underlying game. We examine four per- turbations of the underlying game. In each case,we show that equilibria in which groups choose the best alternative exist and that limits of these equilibria lead to collusion constrained equilibria. We also show that for a sufficiently broad class of perturbations, every collusion constrained equilibrium arises as such a limit. We give an application to a voter participation game that shows how collusion constraints may be socially costly. Keywords. Collusion, organization, group. JEL classification. C72, D70. 1. Introduction As the literature on collective action (for example, Olson 1965) emphasizes, groups often behave collusively while the preferences of individual group members limit the possi- Rohan Dutta: [email protected] David K. -
Interim Correlated Rationalizability
Interim Correlated Rationalizability The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Dekel, Eddie, Drew Fudenberg, and Stephen Morris. 2007. Interim correlated rationalizability. Theoretical Economics 2, no. 1: 15-40. Published Version http://econtheory.org/ojs/index.php/te/article/view/20070015 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:3196333 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Theoretical Economics 2 (2007), 15–40 1555-7561/20070015 Interim correlated rationalizability EDDIE DEKEL Department of Economics, Northwestern University, and School of Economics, Tel Aviv University DREW FUDENBERG Department of Economics, Harvard University STEPHEN MORRIS Department of Economics, Princeton University This paper proposes the solution concept of interim correlated rationalizability, and shows that all types that have the same hierarchies of beliefs have the same set of interim-correlated-rationalizable outcomes. This solution concept charac- terizes common certainty of rationality in the universal type space. KEYWORDS. Rationalizability, incomplete information, common certainty, com- mon knowledge, universal type space. JEL CLASSIFICATION. C70, C72. 1. INTRODUCTION Harsanyi (1967–68) proposes solving games of incomplete -
Tacit Collusion in Oligopoly"
Tacit Collusion in Oligopoly Edward J. Green,y Robert C. Marshall,z and Leslie M. Marxx February 12, 2013 Abstract We examine the economics literature on tacit collusion in oligopoly markets and take steps toward clarifying the relation between econo- mists’analysis of tacit collusion and those in the legal literature. We provide examples of when the economic environment might be such that collusive pro…ts can be achieved without communication and, thus, when tacit coordination is su¢ cient to elevate pro…ts versus when com- munication would be required. The authors thank the Human Capital Foundation (http://www.hcfoundation.ru/en/), and especially Andrey Vavilov, for …nancial support. The paper bene…tted from discussions with Roger Blair, Louis Kaplow, Bill Kovacic, Vijay Krishna, Steven Schulenberg, and Danny Sokol. We thank Gustavo Gudiño for valuable research assistance. [email protected], Department of Economics, Penn State University [email protected], Department of Economics, Penn State University [email protected], Fuqua School of Business, Duke University 1 Introduction In this chapter, we examine the economics literature on tacit collusion in oligopoly markets and take steps toward clarifying the relation between tacit collusion in the economics and legal literature. Economists distinguish between tacit and explicit collusion. Lawyers, using a slightly di¤erent vocabulary, distinguish between tacit coordination, tacit agreement, and explicit collusion. In hopes of facilitating clearer communication between economists and lawyers, in this chapter, we attempt to provide a coherent resolution of the vernaculars used in the economics and legal literature regarding collusion.1 Perhaps the easiest place to begin is to de…ne explicit collusion. -
1 SAYING and MEANING, CHEAP TALK and CREDIBILITY Robert
SAYING AND MEANING, CHEAP TALK AND CREDIBILITY Robert Stalnaker In May 2003, the U.S. Treasury Secretary, John Snow, in response to a question, made some remarks that caused the dollar to drop precipitously in value. The Wall Street Journal sharply criticized him for "playing with fire," and characterized his remarks as "dumping on his own currency", "bashing the dollar," and "talking the dollar down". What he in fact said was this: "When the dollar is at a lower level it helps exports, and I think exports are getting stronger as a result." This was an uncontroversial factual claim that everyone, whatever his or her views about what US government currency policy is or should be, would agree with. Why did it have such an impact? "What he has done," Alan Blinder said, "is stated one of those obvious truths that the secretary of the Treasury isn't supposed to say. When the secretary of the Treasury says something like that, it gets imbued with deep meaning whether he wants it to or not." Some thought the secretary knew what he was doing, and intended his remarks to have the effect that they had. ("I think he chose his words carefully," said one currency strategist.) Others thought that he was "straying from the script," and "isn't yet fluent in the delicate language of dollar policy." The Secretary, and other officials, followed up his initial remarks by reiterating that the government's policy was to support a strong dollar, but some still saw his initial remark as a signal that "the Bush administration secretly welcomes the dollar's decline."1 The explicit policy statements apparently lacked credibility.