Three Essays in Mechanism Design
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On Games of Strategic Experimentation Dinah Rosenberg, Antoine Salomon, Nicolas Vieille
On Games of Strategic Experimentation Dinah Rosenberg, Antoine Salomon, Nicolas Vieille To cite this version: Dinah Rosenberg, Antoine Salomon, Nicolas Vieille. On Games of Strategic Experimentation. 2010. hal-00579613 HAL Id: hal-00579613 https://hal.archives-ouvertes.fr/hal-00579613 Preprint submitted on 24 Mar 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. On Games of Strategic Experimentation Dinah Rosenberg∗, Antoine Salomon† and Nicolas Vieille‡ December 15, 2010 Abstract We focus on two-player, two-armed bandit games. We analyze the joint effect on the informational spillovers between the players of the correlation between the risky arms, and the extent to which one’s experimentation results are publicly disclosed. Our main results only depend on whethert informational shocks bring good or bad news. In the latter case, there is a sense in which the marginal value of these informational spillovers is zero. Strategic experimentation issues are prevalent in most situations of social learning. In such setups, an agent may learn useful information by experimenting himself, or possibly, by observ- ing other agents. Typical applications include dynamic R&D (see e.g. Moscarini and Squin- tani (2010), Malueg and Tsutsui (1997)), competition in an uncertain environment (MacLennan (1984)), financial contracting (Bergemann and Hege (2005) ), etc. -
Hierarchies of Ambiguous Beliefs∗
Hierarchies of Ambiguous Beliefs∗ David S. Ahny August 2006 Abstract We present a theory of interactive beliefs analogous to Mertens and Zamir [31] and Branden- burger and Dekel [10] that allows for hierarchies of ambiguity. Each agent is allowed a compact set of beliefs at each level, rather than just a single belief as in the standard model. We propose appropriate definitions of coherency and common knowledge for our types. Common knowledge of coherency closes the model, in the sense that each type homeomorphically encodes a compact set of beliefs over the others' types. This space universally embeds every implicit type space of ambiguous beliefs in a beliefs-preserving manner. An extension to ambiguous conditional probability systems [4] is presented. The standard universal type space and the universal space of compact continuous possibility structures are epistemically identified as subsets. JEL classification: C72; D81 Keywords: ambiguity, Knightian uncertainty, Bayesian games, universal type space 1 Introduction The idea of a player's type introduced by Harsanyi [19] provides a useful and compact represen- tation of the interactive belief structures that arise in a game, encoding a player's beliefs on some \primitive" parameter of uncertainty, her belief about the others' beliefs, their beliefs about her belief about their beliefs, and so on. Mertens and Zamir [31], hereafter MZ, constructed a universal type space encoding all internally consistent streams of beliefs, ensuring that Bayesian games with Harsanyi types lose no analytic generality.1 ∗NOTICE: this is the author's version of a work that was accepted for publication in Journal of Economic Theory. -
How Three Beginning Social Studies Teachers Enact Personal Practical Theories
UNDERSTANDING THE RELATIONSHIP BETWEEN BELIEFS ABOUT DEMOCRACY AND PRACTICE: HOW THREE BEGINNING SOCIAL STUDIES TEACHERS ENACT PERSONAL PRACTICAL THEORIES A dissertation submitted to the Kent State University College of Education, Health, and Human Services in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Andrew L. Hostetler August 2012 © Copyright 2012, by Andrew L. Hostetler All Rights Reserved ii A dissertation written by Andrew L. Hostetler B.S., Kent State University, 2002 M.Ed., Ashland University, 2008 Ph.D., Kent State University, 2012 Approved by _________________________, Director, Doctoral Dissertation Committee Alicia R. Crowe _________________________, Member, Doctoral Dissertation Committee Todd S. Hawley _________________________, Member, Doctoral Dissertation Committee Susan V. Iverson Accepted by _________________________, Director, School of Teaching, Learning and Curriculum Alexa L. Sandmann Studies _________________________, Dean, College of Education, Health and Human Services Daniel F. Mahony iii HOSTETLER, ANDREW L., Ph.D., August 2012 TEACHING, LEARNING, AND CURRICULUM STUDIES UNDERSTANDING THE RELATIONSHIP BETWEEN BELIEFS ABOUT DEMOCRACY AND PRACTICE: HOW THREE BEGINNING SOCIAL STUDIES TEACHERS ENACT PERSONAL PRACTICAL THEORIES (332 pp.) Director of Dissertation: Alicia R. Crowe, Ph.D. This study addressed the gap between teacher beliefs studies that claim beliefs of teachers influence practice and the recommendations for democratic practice presented in much of the literature -
Norms, Repeated Games, and the Role of Law
Norms, Repeated Games, and the Role of Law Paul G. Mahoneyt & Chris William Sanchiricot TABLE OF CONTENTS Introduction ............................................................................................ 1283 I. Repeated Games, Norms, and the Third-Party Enforcement P rob lem ........................................................................................... 12 88 II. B eyond T it-for-Tat .......................................................................... 1291 A. Tit-for-Tat for More Than Two ................................................ 1291 B. The Trouble with Tit-for-Tat, However Defined ...................... 1292 1. Tw o-Player Tit-for-Tat ....................................................... 1293 2. M any-Player Tit-for-Tat ..................................................... 1294 III. An Improved Model of Third-Party Enforcement: "D ef-for-D ev". ................................................................................ 1295 A . D ef-for-D ev's Sim plicity .......................................................... 1297 B. Def-for-Dev's Credible Enforceability ..................................... 1297 C. Other Attractive Properties of Def-for-Dev .............................. 1298 IV. The Self-Contradictory Nature of Self-Enforcement ....................... 1299 A. The Counterfactual Problem ..................................................... 1300 B. Implications for the Self-Enforceability of Norms ................... 1301 C. Game-Theoretic Workarounds ................................................ -
Lecture Notes General Equilibrium Theory: Ss205
LECTURE NOTES GENERAL EQUILIBRIUM THEORY: SS205 FEDERICO ECHENIQUE CALTECH 1 2 Contents 0. Disclaimer 4 1. Preliminary definitions 5 1.1. Binary relations 5 1.2. Preferences in Euclidean space 5 2. Consumer Theory 6 2.1. Digression: upper hemi continuity 7 2.2. Properties of demand 7 3. Economies 8 3.1. Exchange economies 8 3.2. Economies with production 11 4. Welfare Theorems 13 4.1. First Welfare Theorem 13 4.2. Second Welfare Theorem 14 5. Scitovsky Contours and cost-benefit analysis 20 6. Excess demand functions 22 6.1. Notation 22 6.2. Aggregate excess demand in an exchange economy 22 6.3. Aggregate excess demand 25 7. Existence of competitive equilibria 26 7.1. The Negishi approach 28 8. Uniqueness 32 9. Representative Consumer 34 9.1. Samuelsonian Aggregation 37 9.2. Eisenberg's Theorem 39 10. Determinacy 39 GENERAL EQUILIBRIUM THEORY 3 10.1. Digression: Implicit Function Theorem 40 10.2. Regular and Critical Economies 41 10.3. Digression: Measure Zero Sets and Transversality 44 10.4. Genericity of regular economies 45 11. Observable Consequences of Competitive Equilibrium 46 11.1. Digression on Afriat's Theorem 46 11.2. Sonnenschein-Mantel-Debreu Theorem: Anything goes 47 11.3. Brown and Matzkin: Testable Restrictions On Competitve Equilibrium 48 12. The Core 49 12.1. Pareto Optimality, The Core and Walrasian Equiilbria 51 12.2. Debreu-Scarf Core Convergence Theorem 51 13. Partial equilibrium 58 13.1. Aggregate demand and welfare 60 13.2. Production 61 13.3. Public goods 62 13.4. Lindahl equilibrium 63 14. -
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 -
Personality and Marital Surplus
IZA DP No. 4945 Personality and Marital Surplus Shelly Lundberg May 2010 DISCUSSION PAPER SERIES Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor Personality and Marital Surplus Shelly Lundberg University of Washington, University of Bergen and IZA Discussion Paper No. 4945 May 2010 IZA P.O. Box 7240 53072 Bonn Germany Phone: +49-228-3894-0 Fax: +49-228-3894-180 E-mail: [email protected] Any opinions expressed here are those of the author(s) and not those of IZA. Research published in this series may include views on policy, but the institute itself takes no institutional policy positions. The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA Discussion Paper No. 4945 May 2010 ABSTRACT Personality and Marital Surplus* This paper uses data from the German Socio-economic Panel Study to examine the relationship between psychological traits, in particular personality, and the formation and dissolution of marital and cohabiting partnerships. -
Game Theory for Signal Processing in Networks
Game Theory for Signal Processing in Networks Giacomo Bacci, Samson Lasaulce, Walid Saad, and Luca Sanguinetti Abstract In this tutorial, the basics of game theory are introduced along with an overview of its most recent and emerging applications in signal processing. One of the main features of this contribution is to gather in a single paper some fundamental game-theoretic notions and tools which, over the past few years, have become widely spread over a large number of papers. In particular, both strategic-form and coalition-form games are described in details while the key connections and differences betweenthemareoutlined.Moreover,aparticularattention is also devoted to clarify the connections between strategic-form games and distributed optimization and learning algorithms. Beyond an introduction to the basic concepts andmainsolutionapproaches,severalcarefullydesigned examples are provided to allow a better understanding of how to apply the described tools. I. INTRODUCTION game theory (GT) is a branch of mathematics that enables the modeling and analysis of the interactions between several decision-makers (called players) who can have conflicting or common objectives. A game is a situation in which the benefit or cost achieved by each player from an interactive situation depends, not only on its own decisions, but also on those taken by the other players. For example, the time a car driver needs to get back home generally depends not only on the route he/she chooses but also on the decisions taken by the other drivers. Therefore, in a game, the actions and objectives of the players are tightly coupled.Untilveryrecently,GThas been used only marginally in signal processing (SP), with notable examples being some applications in robust detection and estimation [1] as well as watermarking [2] (in which the watermarking problem is seen as a game between the data embedder and the attacker). -
Homo Economicus: Why the Economy Cannot Be Divorced from Its Governance
RESTRAINING THE GENUINE HOMO ECONOMICUS: WHY THE ECONOMY CANNOT BE DIVORCED FROM ITS GOVERNANCE STERGIOS SKAPERDAS CESIFO WORKING PAPER NO. 901 CATEGORY 2: PUBLIC CHOICE APRIL 2003 An electronic version of the paper may be downloaded • from the SSRN website: www.SSRN.com • from the CESifo website: www.CESifo.de CESifo Working Paper No. 901 RESTRAINING THE GENUINE HOMO ECONOMICUS: WHY THE ECONOMY CANNOT BE DIVORCED FROM ITS GOVERNANCE Abstract The Homo economicus of traditional economics is far from being completely self-interested, rational, or as individualistic as he is purported to be; he will haggle to death over price but will not take what he wants by force. Implicitly, he is assumed to behave ruthlessly within a welldefined bubble of sainthood. Based on a simple model, I first examine what occurs when this assumption is relaxed and genuine, amoral Homo economici interact. Productivity can be inversely related to compensation; a longer shadow of the future can intensify conflict; and, more competition among providers of protection reduces welfare. The patently inefficient outcomes that follow call for restraining self-interest, for finding ways to govern markets. I then review some of the different ways of creating restraints, from the traditional social contract, to the hierarchical domination of kings and lords, to modern forms of governance. Checks and balances, wider representation, the bureaucratic form of organization, and other ingredients of modern governance can partly be thought of as providing restraints to the dark side of self-interest. Though highly imperfect, these restraints are better than the alternative, which typically involves autocratic, amateurish, and corrupt rule. -
Games in Coalitional Form 1
GAMES IN COALITIONAL FORM EHUD KALAI Forthcoming in the New Palgrave Dictionary of Economics, second edition Abstract. How should a coalition of cooperating players allocate payo¤s to its members? This question arises in a broad range of situations and evokes an equally broad range of issues. For example, it raises technical issues in accounting, if the players are divisions of a corporation, but involves issues of social justice when the context is how people behave in society. Despite the breadth of possible applications, coalitional game theory o¤ers a uni…ed framework and solutions for addressing such questions. This brief survey presents some of its major models and proposed solutions. 1. Introduction In their seminal book, von Neumann and Morgenstern (1944) introduced two theories of games: strategic and coalitional. Strategic game theory concentrates on the selection of strategies by payo¤-maximizing players. Coalitional game theory concentrates on coalition formation and the distribution of payo¤s. The next two examples illustrate situations in the domain of the coalitional approach. 1.1. Games with no strategic structure. Example 1. Cost allocation of a shared facility. Three municipalities, E, W, and S, need to construct water puri…cation facilities. Costs of individual and joint facilities are described by the cost function c: c(E) = 20, c(W ) = 30, and c(S) = 50; c(E; W ) = 40, c(E; S) = 60, and c(W; S) = 80; c(E; W; S) = 80. For example, a facility that serves the needs of W and S would cost $80 million. The optimal solution is to build, at the cost of 80, one facility that serves all three municipalities. -
Egalitarianism in Mechanism Design∗
Egalitarianism in Mechanism Design∗ Geoffroy de Clippely This Version: January 2012 Abstract This paper examines ways to extend egalitarian notions of fairness to mechanism design. It is shown that the classic properties of con- strained efficiency and monotonicity with respect to feasible options become incompatible, even in quasi-linear settings. An interim egali- tarian criterion is defined and axiomatically characterized. It is applied to find \fair outcomes" in classical examples of mechanism design, such as cost sharing and bilateral trade. Combined with ex-ante utilitari- anism, the criterion characterizes Harsanyi and Selten's (1972) interim Nash product. Two alternative egalitarian criteria are proposed to il- lustrate how incomplete information creates room for debate as to what is socially desirable. ∗The paper beneficiated from insightful comments from Kfir Eliaz, Klaus Nehring, David Perez-Castrillo, Kareen Rozen, and David Wettstein. Financial support from the National Science Foundation (grant SES-0851210) is gratefully acknowledged. yDepartment of Economics, Brown University. Email: [email protected] 1. INTRODUCTION Developments in the theory of mechanism design, since its origin in the sev- enties, have greatly improved our understanding of what is feasible in envi- ronments involving agents that hold private information. Yet little effort has been devoted to the discussion of socially desirable selection criteria, and the computation of incentive compatible mechanisms meeting those criteria in ap- plications. In other words, extending the theory of social choice so as to make it applicable in mechanism design remains a challenging topic to be studied. The present paper makes some progress in that direction, with a focus on the egalitarian principle. -
Market Design and Walrasian Equilibrium†
Market Design and Walrasian Equilibriumy Faruk Gul, Wolfgang Pesendorfer and Mu Zhang Princeton University February 2020 Abstract We establish the existence of Walrasian equilibrium for economies with many dis- crete goods and possibly one divisible good. Our goal is not only to study Walrasian equilibria in new settings but also to facilitate the use of market mechanisms in resource allocation problems such as school choice or course selection. We consider all economies with quasilinear gross substitutes preferences but allow agents to have limited quantities of the divisible good (limited transfers economies). We also consider economies without a divisible good (nontransferable utility economies). We show the existence and efficiency of Walrasian equilibrium in limited transfers economies and the existence and efficiency of strong (Walrasian) equilibrium in nontransferable utility economies. Finally, we show that various constraints on minimum and maximum levels of consumption and aggregate constraints of the kind that are relevant for school choice/course selection problems can be accommodated by either incorporating these constraints into individual preferences or by incorporating a suitable production technology into nontransferable utility economies. y This research was supported by grants from the National Science Foundation. 1. Introduction In this paper, we establish the existence of Walrasian equilibrium in economies with many discrete goods and either with a limited quantity of one divisible good or without any divisible goods. Our goal is not only to study Walrasian equilibria in new settings but also to facilitate the use of market mechanisms in resource allocation problems such as school choice or course selection. To this end, we develop techniques for analyzing al- location problems in economies with or without transfers and for incorporating additional constraints into allocation rules.