Behavioral Implementation Under Incomplete Information∗
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California Institute of Technology
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Authors - Main DIVISION OF THE HUM ANITIES AND SO CI AL SCIENCES CALIFORNIA INSTITUTE OF TECHNOLOGY PASADENA, CALIFORNIA 91125 IMPLEMENTATION THEORY Thomas R. Palfrey � < a: 0 1891 u. "')/,.. () SOCIAL SCIENCE WORKING PAPER 912 September 1995 Implementation Theory Thomas R. Palfrey Abstract This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered. JEL classification numbers: 025, 026 Key words: Implementation Theory, Mechanism Design, Game Theory, Social Choice Implementation Theory* Thomas R. Palfrey 1 Introduction Implementation theory is an area of research in economic theory that rigorously investi gates the correspondence between normative goals and institutions designed to achieve {implement) those goals. More precisely, given a normative goal or welfare criterion for a particular class of allocation pro blems (or domain of environments) it formally char acterizes organizational mechanisms that will guarantee outcomes consistent with that goal, assuming the outcomes of any such mechanism arise from some specification of equilibrium behavior. The approaches to this problem to date lie in the general domain of game theory because, as a matter of definition in the implementation theory litera ture, an institution is modelled as a mechanism, which is essentially a non-cooperative game. Moreover, the specific models of equilibrium behavior -
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 .................................. -
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. -
Stability and Nash Implementation in Matching Markets with Couples
09-017 Stability and Nash Implementation in Matching Markets with Couples Claus-Jochen Haake Bettina Klaus Copyright © 2008 by Claus-Jochen Haake and Bettina Klaus Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It may not be reproduced without permission of the copyright holder. Copies of working papers are available from the author. Stability and Nash Implementation in Matching Markets with Couples∗ Claus-Jochen Haakey Bettina Klausz August 2008 Abstract We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a \double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable. JEL classification: C62, C78, D78, J41. Keywords: Matching with Couples, (Maskin) Monotonicity, Nash Implementation, Sta- bility, Weakly Responsive Preferences. 1 Introduction We consider two-sided matching markets consisting of medical students (graduates, workers) on one side and of residencies jobs, firms) on the other side. In the medical market as well as in many other labor markets, the number of couples with the same professional interests has been growing. Therefore we focus on labor markets in which both members of couples seek positions. Examples of such labor markets with couples are medical markets where each year many medical school graduates seek their first employment as residents or interns. -
Revelation Principles in Multistage Games∗
Revelation Principles in Multistage Games Takuo Sugaya and Alexander Wolitzky Stanford GSB and MIT September 22, 2017 Abstract We study the revelation principle in multistage games for perfect Bayesian equi- libium and sequential equilibrium. The question of whether or not the revelation principle holds is subtle, as expanding players’ opportunities for communication ex- pands the set of consistent beliefs at off-path information sets. In settings with adverse selection but no moral hazard, Nash, perfect Bayesian, and sequential equilibrium are essentially equivalent, and a virtual-implementation version of the revelation principle holds. In general, we show that the revelation principle holds for weak perfect Bayesian equilibrium and for a stronger notion of perfect Bayesian equilibrium introduced by Myerson (1986). Our main result is that the latter notion of perfect Bayesian equilib- rium is outcome-equivalent to sequential equilibrium when the mediator can tremble; this provides a revelation principle for sequential equilibrium. When the mediator cannot tremble, the revelation principle for sequential equilibrium can fail. Preliminary. Comments Welcome. For helpful comments, we thank Drew Fudenberg, Dino Gerardi, Shengwu Li, Roger Myerson, Alessandro Pavan, Harry Pei, Juuso Toikka, and Bob Wilson. 1 Introduction The revelation principle states that any social choice function that can be implemented by any mechanism can also be implemented by a canonical mechanism where communication between players and the mechanism designer or mediator takes a circumscribed form: players communicate only their private information to the mediator, and the mediator communi- cates only recommended actions to the players. This cornerstone of modern microeconomics was developed by several authors in the 1970s and early 1980s, reaching its most general formulation in the principal-agent model of Myerson (1982), which treats one-shot games with both adverse selection and moral hazard. -
The Death of Welfare Economics: History of a Controversy
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Igersheim, Herrade Working Paper The death of welfare economics: History of a controversy CHOPE Working Paper, No. 2017-03 Provided in Cooperation with: Center for the History of Political Economy at Duke University Suggested Citation: Igersheim, Herrade (2017) : The death of welfare economics: History of a controversy, CHOPE Working Paper, No. 2017-03, Duke University, Center for the History of Political Economy (CHOPE), Durham, NC This Version is available at: http://hdl.handle.net/10419/155466 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu The death of welfare economics: History of a controversy by Herrade Igersheim CHOPE Working Paper No. 2017-03 January 2017 Electronic copy available at: https://ssrn.com/abstract=2901574 The death of welfare economics: history of a controversy Herrade Igersheim December 15, 2016 Abstract. -
The Revelation Principle for Mechanism Design with Reporting Costs
The Revelation Principle for Mechanism Design with Reporting Costs ANDREW KEPHART, Duke University VINCENT CONITZER, Duke University The revelation principle is a key tool in mechanism design. It allows the designer to restrict attention to the class of truthful mechanisms, greatly facilitating analysis. This is also borne out in an algorithmic sense, al- lowing certain computational problems in mechanism design to be solved in polynomial time. Unfortunately, when not every type can misreport every other type (the partial verification model), or—more generally— misreporting can be costly, the revelation principle can fail to hold. This also leads to NP-hardness results. The primary contribution of this paper consists of characterizations of conditions under which the revelation principle still holds when misreporting can be costly. (These are generalizations of conditions given earlier for the partial verification case [Green and Laffont 1986; Yu 2011].) We also study associated computational problems. Additional Key Words and Phrases: automated mechanism design, signaling costs, partial verification, rev- elation principle 1. INTRODUCTION Mechanism design concerns making decisions based on the private information of one or more agents, who will not report this information truthfully if they do not see this to be in their interest. The goal is to define a mechanism—a game to be played by the agent(s)—that defines actions for the agents to take and maps these actions to outcomes, such that in equilibrium, the agents’ true types map to outcomes as de- sired. This may, at first, appear to leave us in the unmanageable situation of having to search through all possible games we could define. -
Theory of Mechanism Design
Theory of Mechanism Design Debasis Mishra1 April 14, 2020 1Economics and Planning Unit, Indian Statistical Institute, 7 Shahid Jit Singh Marg, New Delhi 110016, India, E-mail: [email protected] 2 Contents 1 Introduction to Mechanism Design7 1.0.1 Private Information and Utility Transfers................8 1.0.2 Examples in Practice........................... 10 1.1 A General Model of Preferences......................... 11 1.2 Social Choice Functions and Mechanisms.................... 14 1.3 Dominant Strategy Incentive Compatibility................... 16 1.4 Bayesian Incentive Compatibility........................ 18 1.4.1 Failure of revelation principle...................... 21 2 Mechanism Design with Transfers and Quasilinearity 23 2.1 A General Model................................. 24 2.1.1 Allocation Rules............................. 24 2.1.2 Payment Functions............................ 26 2.1.3 Incentive Compatibility.......................... 27 2.1.4 An Example................................ 27 2.1.5 Two Properties of Payments....................... 28 2.1.6 Efficient Allocation Rule is Implementable............... 29 2.2 The Vickrey-Clarke-Groves Mechanism..................... 32 2.2.1 Illustration of the VCG (Pivotal) Mechanism.............. 33 2.2.2 The VCG Mechanism in the Combinatorial Auctions......... 35 2.2.3 The Sponsored Search Auctions..................... 37 2.3 Affine Maximizer Allocation Rules are Implementable............. 38 2.3.1 Public Good Provision.......................... 40 2.3.2 Restricted and Unrestricted Type Spaces................ 41 3 3 Mechanism Design for Selling a Single Object 45 3.1 The Single Object Auction Model........................ 45 3.1.1 The Vickrey Auction........................... 45 3.1.2 Facts from Convex Analysis....................... 46 3.1.3 Monotonicity and Revenue Equivalence................. 49 3.1.4 The Efficient Allocation Rule and the Vickrey Auction....... -
Truthful Revelation Mechanisms for Simultaneous Common Agency Games† 132 Truthful Revelation Mechanisms for Simultaneous Common A
American Economic Journal: Microeconomics 2 (May 2010): 132–190 http://www.aeaweb.org/articles.php?doi 10.1257/mic.2.2.132 = Contents Truthful Revelation Mechanisms for Simultaneous Common Agency Games† 132 Truthful Revelation Mechanisms for Simultaneous Common A. Simple Menu-Auction Example 136 Agency Games† I. The Environment 140 II. Simple Revelation Mechanisms 143 By Alessandro Pavan and Giacomo Calzolari* III. Using Revelation Mechanisms in Applications 150 A. Competition in Nonlinear Tariffs 150 B. Menu Auctions 156 We introduce new revelation mechanisms for simultaneous common C. Moral Hazard 159 agency games which, although they do not always permit a complete IV. Enriched Mechanisms 161 equilibrium characterization, do facilitate the characterization of A. Non-Markov Strategies 161 the equilibrium outcomes that are typically of interest in applica- tions. We then show how these mechanisms can be used in applica- B. Mixed Strategies 163 tions such as menu auctions, competition in nonlinear tariffs, and V. Conclusions 166 moral hazard settings. Lastly, we show how one can enrich the rev- Appendix 1: Take-It-or-Leave-It-Offer Equilibria in the Menu-Auction Example in the Introduction elation mechanisms, albeit at a cost of an increase in complexity, 167 to characterize all possible equilibrium outcomes, including those Appendix 2: Omitted Proofs 168 sustained by non-Markov strategies and or mixed-strategy profiles. REFERENCES 189 / JEL C72, D82, D86 ( ) any economic environments can be modelled as common agency games—that M is, games where multiple principals contract simultaneously and noncoopera- tively with the same agent.1 Despite their relevance for applications, the analysis of these games has been made difficult by the fact that one cannot safely assume that the agent selects a contract with each principal by simply reporting his “type” i.e., his ( exogenous payoff-relevant information . -
Climate Change and Game Theory
Climate Change and Game Theory: a Mathematical Survey Peter John Wood Crawford School The Australian National University CCEP working paper 2.10, October 2010 Abstract This paper examines the problem of achieving global cooperation to reduce greenhouse gas emissions. Contributions to this problem are reviewed from noncooperative game theory, cooperative game theory, and implementation theory. We examine the solutions to games where players have a continuous choice about how much to pollute, and games where players make decisions about treaty participation. The implications of linking cooperation on climate change with cooperation on other issues, such as trade, is also examined. Cooperative and non-cooperative approaches to coalition formation are investigated in order to examine the behaviour of coalitions cooperating on climate change. One way to achieve cooperation is to design a game, known as a mechanism, whose equilibrium corresponds to an optimal outcome. This paper examines some mechanisms that are based on conditional commitments, and their policy implications. These mechanisms could make cooperation on climate change mitigation more likely. Centre for Climate Economics & Policy Crawford School of Economics and Government The Australian National University ccep.anu.edu.au The Centre for Climate Economics & Policy (ccep.anu.edu.au) is an organized research unit at the Crawford School of Economics and Government, The Australian National University. The working paper series is intended to facilitate academic and policy discussion, and the views expressed in working papers are those of the authors. Contact for the Centre: Dr Frank Jotzo, [email protected]. Citation for this report: Wood, P.J. (2010), Climate Change and Game Theory: a Mathematical Survey, CCEP working paper 2.10, Centre for Climate Economics & Policy, Crawford School of Economics and Government, The Australian National University, Canberra. -
Lecture 1: Ascending and Ex Post Incentive Compatible Mechanisms
CS364B: Frontiers in Mechanism Design Lecture #1: Ascending and Ex Post Incentive Compatible Mechanisms∗ Tim Roughgardeny January 8, 2014 1 Introduction These twenty lectures cover advanced topics in mechanism design. They assume familiarity with some of the material covered in the instructor's CS364A course | specifically, lectures 2{4 and 7{9. Recall that mechanism design is the \science of rule-making." The goal is to understand how to design systems with strategic participants | autonomous decision-makers whose objectives are generally different from the the designer's | that have good performance guarantees. For example, a mechanism designer might want to compute a socially efficient allocation of scarce resources or raise significant revenue, while a mechanism participant only cares about its own utility. 2 Course Outline The plan is to cover the following five topics. 1. (6 lectures.) Welfare-maximization in combinatorial auctions: tractable special cases and ascending implementations. 2. (4 lectures.) Welfare-maximization in combinatorial auctions: dominant-strategy ap- proximation mechanisms for NP-hard cases. 3. (3 lectures.) Welfare-maximization in combinatorial auctions: better guarantees for weaker solutions concepts (undominated strategies and Bayes-Nash equilibria). ∗ c 2014, Tim Roughgarden. yDepartment of Computer Science, Stanford University, 462 Gates Building, 353 Serra Mall, Stanford, CA 94305. Email: [email protected]. 1 4. (4 lectures.) The price of anarchy in simple auctions. 5. (3 lectures.) Revenue-maximization in multi-parameter settings. 3 Review: The k-Vickrey Auction Let's recall a basic example from last quarter. Scenario #1: • k identical items (even k = 1 is interesting); • each bidder is unit demand, meaning it only wants one item; • each bidder has a private valuation vi for a item. -
Auction Design in the Presence of Collusion
Theoretical Economics 3 (2008), 383–429 1555-7561/20080383 Auction design in the presence of collusion Gregory Pavlov Department of Economics, University of Western Ontario We study a problem of optimal auction design in the realistic case in which the players can collude both on the way they play in the auction and on their partici- pation decisions. Despite the fact that the principal’s opportunities for extracting payments from the agents in such a situation are limited, we show how the asym- metry of information between the colluding agents can be used to reduce the rev- enue losses from collusion. In a class of environments we show that the principal is even able to achieve the same revenue as when the agents do not collude. For cases in which it is not possible to do so we provide an optimal mechanism in the class of mechanisms with linear and symmetric menus and discuss the po- tential benefits of using asymmetric and nonlinear mechanisms. To address the problem of multiplicity of equilibria we show how the optimal mechanisms can be implemented as uniquely collusion-proof mechanisms. Keywords. Collusion, mechanism design, auctions. JEL classification. C61, D44, D82, L41. 1. Introduction In many environments a revenue-maximizing method of selling scarce goods is to or- ganize an auction.1 However, since an auction exploits competition between the agents to raise the revenue of the seller, it creates strong incentives for collusion between the agents against the seller. In this paper we study a problem of optimal auction design in the realistic case in which the players not only can collude on the way they play in the auction, but also can coordinate their decisions regarding whether to participate in the auction.