Robust 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 ................................................ -
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 -
Three Essays in Mechanism Design
THREE ESSAYS IN MECHANISM DESIGN Andrei Rachkov A DISSERTATION PRESENTED TO THE FACULTY OF PRINCETON UNIVERSITY IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY RECOMMENDED FOR ACCEPTANCE BY THE DEPARTMENT OF ECONOMICS Adviser: Stephen Morris January 2013 c Copyright by Andrei Rachkov, 2012. All rights reserved. iii Abstract In the first and second chapters we study whether the current trend of using stronger solution concepts is justified for the optimal mechanism design. In the first chapter, we take a simple auction model and allow for type-dependent outside options. We argue that Bayesian foundation for dominant strategy mechanisms is valid when symmetry conditions are satisfied. This contrasts with monotonicity constraints used before in the literature. In the second chapter we develop the idea further by looking into the practical application of type-dependency of outside options in auctions - namely, a possibility of collusion between agents. We show that in this environment for a certain range of primitives no maxmin foundation for dominant strategy mechanisms will exist. Finally, in the last chapter we study a voting environment and non-transferable utility mechanism design. We argue that strategic voting as opposed to truthful voting may lead to higher total welfare through better realization of preference intensities in the risky environment. We also study optimal mechanisms rules, that are sufficiently close to the first best for the uniform distribution, and argue that strategic voting may be a proxy for information transmission if the opportunities to communicate preference intensities are scarce. iv Acknowledgments To my mother who imbued me with a strong sense of fairness and my father who taught me to always strive for the ideal. -
Multi-Pose Interactive Linkage Design Teaser
EUROGRAPHICS 2019 / P. Alliez and F. Pellacini Volume 38 (2019), Number 2 (Guest Editors) Multi-Pose Interactive Linkage Design Teaser G. Nishida1 , A. Bousseau2 , D. G. Aliaga1 1Purdue University, USA 2Inria, France a) b) e) f) Fixed bodies Moving bodies c) d) Figure 1: Interactive design of a multi-pose and multi-body linkage. Our system relies on a simple 2D drawing interface to let the user design a multi-body object including (a) fixed bodies, (b) moving bodies (green and purple shapes), (c) multiple poses for each moving body to specify the desired motion, and (d) a desired region for the linkage mechanism. Then, our system automatically generates a 2.5D linkage mechanism that makes the moving bodies traverse all input poses in a desired order without any collision (e). The system also automatically generates linkage parts ready for 3D printing and assembly (f). Please refer to the accompanying video for a demonstration of the sketching interface and animations of the resulting mechanisms. Abstract We introduce an interactive tool for novice users to design mechanical objects made of 2.5D linkages. Users simply draw the shape of the object and a few key poses of its multiple moving parts. Our approach automatically generates a one-degree-of- freedom linkage that connects the fixed and moving parts, such that the moving parts traverse all input poses in order without any collision with the fixed and other moving parts. In addition, our approach avoids common linkage defects and favors compact linkages and smooth motion trajectories. Finally, our system automatically generates the 3D geometry of the object and its links, allowing the rapid creation of a physical mockup of the designed object. -
Computing in Mechanism Design∗
Computing in Mechanism Design¤ Tuomas Sandholm Computer Science Department Carnegie Mellon University Pittsburgh, PA 15213 1. Introduction Computational issues in mechanism design are important, but have received insufficient research interest until recently. Limited computing hinders mechanism design in several ways, and presents deep strategic interactions between com- puting and incentives. On the bright side, the vast increase in computing power has enabled better mechanisms. Perhaps most interestingly, limited computing of the agents can be used as a tool to implement mechanisms that would not be implementable among computationally unlimited agents. This chapter briefly reviews some of the key ideas, with the goal of alerting the reader to the importance of these issues and hopefully spurring future research. I will discuss computing by the center, such as an auction server or vote aggregator, in Section 2. Then, in Section 3, I will address the agents’ computing, be they human or software. 2. Computing by the center Computing by the center plays significant roles in mechanism design. In the following three subsections I will review three prominent directions. 2.1. Executing expressive mechanisms As algorithms have advanced drastically and computing power has increased, it has become feasible to field mecha- nisms that were previously impractical. The most famous example is a combinatorial auction (CA). In a CA, there are multiple distinguishable items for sale, and the bidders can submit bids on self-selected packages of the items. (Sometimes each bidder is also allowed to submit exclusivity constraints of different forms among his bids.) This increase in the expressiveness of the bids drastically reduces the strategic complexity that bidders face. -
Supermodular Mechanism Design
Theoretical Economics 5(2010),403–443 1555-7561/20100403 Supermodular mechanism design L M Department of Economics, University of Texas This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded ra- tionality. This approach is a tool for constructing supermodular mechanisms, i.e., mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes—as opposed to strate- gic complementarities—then this mechanism can be converted into a supermod- ular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilib- rium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences. K.Implementation,mechanisms,multipleequilibriumproblem,learn- ing, strategic complementarities, supermodular games. JEL .C72,D78,D83. 1. I For the economist designing contracts, taxes, or other institutions, there is a dilemma between the simplicity of a mechanism and the multiple equilibrium problem. On the one hand, simple mechanisms often restrict attention to the “right” equilibria. In public good contexts, for example, most tax schemes overlook inefficient equilibrium situa- tions, provided that one equilibrium outcome is a social optimum. -
Formation of Coalition Structures As a Non-Cooperative Game
Formation of coalition structures as a non-cooperative game Dmitry Levando, ∗ Abstract We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative si- multaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and has two outcomes: an alloca- tion of players over coalitions and a payoff for every player. Coalition structures of a game are described by Young diagrams. They serve to enumerate coalition structures and allocations of players over them. For every coalition structure a player has a set of finite strategies. A player chooses a coalition structure and a strategy. A (social) mechanism eliminates conflicts in individual choices and produces final coalition structures. Every final coalition structure is a non-cooperative game. Mixed equilibrium always exists and consists arXiv:2107.00711v1 [cs.GT] 1 Jul 2021 of a mixed strategy profile, payoffs and equilibrium coalition struc- tures. We use a maximum coalition size to parametrize the family ∗Moscow, Russian Federation, independent. No funds, grants, or other support was received. Acknowledge: Nick Baigent, Phillip Bich, Giulio Codognato, Ludovic Julien, Izhak Gilboa, Olga Gorelkina, Mark Kelbert, Anton Komarov, Roger Myerson, Ariel Rubinstein, Shmuel Zamir. Many thanks for advices and for discussion to participants of SIGE-2015, 2016 (an earlier version of the title was “A generalized Nash equilibrium”), CORE 50 Conference, Workshop of the Central European Program in Economic Theory, Udine (2016), Games 2016 Congress, Games and Applications, (2016) Lisbon, Games and Optimization at St Etienne (2016). All possible mistakes are only mine. E-mail for correspondence: dlevando (at) hotmail.ru. -
Chapter on Automated Mechanism Design
Chapter 6 Automated Mechanism Design Mechanism design has traditionally been a manual endeavor. The designer uses experience and intuition to hypothesize that a certain rule set is desirable in some ways, and then tries to prove that this is the case. Alternatively, the designer formulates the mechanism design problem mathemat- ically and characterizes desirable mechanisms analytically in that framework. These approaches have yielded a small number of canonical mechanisms over the last 40 years, the most significant of which we discussed in Chapter 4. Each of these mechanisms is designed for a class of settings and a specific objective. The upside of these mechanisms is that they do not rely on (even probabilistic) information about the agents' preferences (e.g. Vickrey-Clarke-Groves mechanisms), or they can be easily applied to any probability distribution over the preferences (e.g. the dAGVA mechanism, the Myerson auction, and the Maskin-Riley multi-unit auction). However, these general mechanisms also have significant downsides: ² The most famous and most broadly applicable general mechanisms, VCG and dAGVA, only maximize social welfare. If the designer is self-interested, as is the case in many electronic commerce settings, these mechanisms do not maximize the designer's objective. ² The general mechanisms that do focus on a self-interested designer are only applicable in very restricted settings. For example, Myerson's expected revenue maximizing auction is for selling a single item, and Maskin and Riley's expected revenue maximizing auction is for selling multiple identical units of an item. ² Even in the restricted settings in which these mechanisms apply, the mechanisms only allow for payment maximization. -
Lectures in Contract Theory1
Lectures in Contract Theory1 Steve Tadelis and Ilya Segal2 UC Berkeley and Stanford University Preliminary and Incomplete December 2005 1These notes were prepared for a second year graduate course in Contract theory at Stanford University (Econ 282/291) and UC Berkeley (Econ 206). They are preliminary and incomplete. Thanks also to Debbie Johnston for typing the first version and to Scott Hemphill for excellent research assistance. 2Copyright c 1998-2005 by Steven Tadelis and Ilya Segal. All rights reserved. No part of these° notes may be reproduced in any form by any electronuic or mechanical means without writen permission from the author. Contents IIntroduction 5 0.1Tradewithsmallnumbersofagents............... 6 0.2 Incentives ............................. 7 0.3BoundedRationality....................... 8 0.4Contracts,Mechanisms,Institutions............... 8 II Hidden Information 10 1 The Principal-Agent Model 12 1.1Setup................................ 12 1.1.1 Preferences........................ 12 1.1.2 Contracting........................ 13 1.2Single-CrossingandtheMonotonicityofChoice........ 13 1.3TheFullInformationBenchmark................ 16 1.4TheRevelationPrinciple..................... 18 1.5SolutionwithTwoTypes..................... 20 1.5.1 ManyDiscreteTypes................... 24 1.6SolutionwithaContinuumofTypes.............. 25 1.6.1 TheRelaxedProblem................... 28 1.6.2 Whattodoifmonotonicitybinds(technical)...... 31 1.7ApplicationsoftheModel.................... 32 1.7.1 SecondDegreePriceDiscrimination..........