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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 -
The Shapley Value for Airport and Irrigation Games
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Márkus, Judit; Pintér, Péter Miklós; Radványi, Anna Working Paper The Shapley Value for Airport and Irrigation Games IEHAS Discussion Papers, No. MT-DP - 2012/7 Provided in Cooperation with: Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences Suggested Citation: Márkus, Judit; Pintér, Péter Miklós; Radványi, Anna (2012) : The Shapley Value for Airport and Irrigation Games, IEHAS Discussion Papers, No. MT-DP - 2012/7, ISBN 978-615-5243-00-4, Hungarian Academy of Sciences, Institute of Economics, Centre for Economic and Regional Studies, Budapest This Version is available at: http://hdl.handle.net/10419/108259 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. -
Manuel Alfredo Mosquera Rodríguez's Phd Thesis
UNIVERSIDADE DE SANTIAGO DE COMPOSTELA Departamento de Estatística e Investigación Operativa ESSAYS ON OPERATIONS RESEARCH GAMES AND CAUTIOUS BEHAVIOR Manuel Alfredo Mosquera Rodríguez Santiago de Compostela, February 2007 Supported by the Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia under projects BES-2003-1277, BEC2002- 04102-C02-02, SEJ2005-07637-C02-2 and PGIDIT03PXIC20701PN. Realizado el acto público de defensa y mantenimiento de esta tesis doctoral el día 2 de febrero de 2007, en la Facultad de Matemáticas de la Universidad de Santiago de Compostela, ante el tribunal formado por: Presidente: Dr. D. José Manuel Zarzuelo Zarzosa Vocales: Dr. D. Peter Borm Dr. D. Mark Voorneveld Dr.a D.a Estela Sánchez Rodríguez Secretaria: Dr.a D.a Balbina Virginia Casas Méndez siendo directores la Dr.a D.a María Gloria Fiestras Janeiro y el Dr. D. Ignacio García Jurado, obtu- vo la máxima calificación de SOBRESALIENTE CUM LAUDE. Además, esta tesis ha cumplido los requisitos necesarios para la obtención del DOCTORADO EUROPEO. A Yoli, mis padres y mi hermano. Gracias. Preface Some years ago, I had to decide which bachelor I should take. The Bachelor of Mathematics was not my first option, but because of several reasons I had to choose it. The first year was not fully pleasant because I had in mind to change my studies. However, during that year, I started to discover the world of Mathematics and decided to continue once year more. Year after year, I was more and more interested by the wonderful universe of Mathematics. In my fifth Bachelor’s year, I followed a course in game theory by Ignacio García Jurado. -
Game Theory 2021
More Mechanism Design Game Theory 2021 Game Theory 2021 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss 1 More Mechanism Design Game Theory 2021 Plan for Today In this second lecture on mechanism design we are going to generalise beyond the basic scenario of auctions|as much as we can manage: • Revelation Principle: can focus on direct-revelation mechanisms • formal model of direct-revelation mechanisms with money • incentive compatibility of the Vickrey-Clarke-Groves mechanism • other properties of VCG for special case of combinatorial auctions • impossibility of achieving incentive compatibility more generally Much of this is also (somewhat differently) covered by Nisan (2007). N. Nisan. Introduction to Mechanism Design (for Computer Scientists). In N. Nisan et al. (eds.), Algorithmic Game Theory. Cambridge University Press, 2007. Ulle Endriss 2 More Mechanism Design Game Theory 2021 Reminder Last time we saw four auction mechanisms for selling a single item: English, Dutch, first-price sealed-bid, Vickrey. The Vickrey auction was particularly interesting: • each bidder submits a bid in a sealed envelope • the bidder with the highest bid wins, but pays the price of the second highest bid (unless it's below the reservation price) It is a direct-revelation mechanism (unlike English and Dutch auctions) and it is incentive-compatible, i.e., truth-telling is a dominant strategy (unlike for Dutch and FPSB auctions). Ulle Endriss 3 More Mechanism Design Game Theory 2021 The Revelation Principle Revelation Principle: Any outcome that is implementable in dominant strategies via some mechanism can also be implemented by means of a direct-revelation mechanism making truth-telling a dominant strategy. -
Designing Mechanisms to Make Welfare- Improving Strategies Focal∗
Designing Mechanisms to Make Welfare- Improving Strategies Focal∗ Daniel E. Fragiadakis Peter Troyan Texas A&M University University of Virginia Abstract Many institutions use matching algorithms to make assignments. Examples include the allocation of doctors, students and military cadets to hospitals, schools and branches, respec- tively. Most of the market design literature either imposes strong incentive constraints (such as strategyproofness) or builds mechanisms that, while more efficient than strongly incentive compatible alternatives, require agents to play potentially complex equilibria for the efficiency gains to be realized in practice. Understanding that the effectiveness of welfare-improving strategies relies on the ease with which real-world participants can find them, we carefully design an algorithm that we hypothesize will make such strategies focal. Using a lab experiment, we show that agents do indeed play the intended focal strategies, and doing so yields higher overall welfare than a common alternative mechanism that gives agents dominant strategies of stating their preferences truthfully. Furthermore, we test a mech- anism from the field that is similar to ours and find that while both yield comparable levels of average welfare, our algorithm performs significantly better on an individual level. Thus, we show that, if done carefully, this type of behavioral market design is a worthy endeavor that can most promisingly be pursued by a collaboration between institutions, matching theorists, and behavioral and experimental economists. JEL Classification: C78, C91, C92, D61, D63, Keywords: dictatorship, indifference, matching, welfare, efficiency, experiments ∗We are deeply indebted to our graduate school advisors Fuhito Kojima, Muriel Niederle and Al Roth for count- less conversations and encouragement while advising us on this project. -
An Approach to N-Person Cooperative Games
Undergraduate Thesis MAJOR IN MATHEMATICS Faculty of Mathematics University of Barcelona AN APPROACH TO N-PERSON COOPERATIVE GAMES Eric` L´opez Ramiro [email protected] Advisor: Dr. Josep Vives Dept. of Probability, Logic and Statistics Barcelona, January 18, 2016 This page intentionally left blank. Abstract This work is an overview on n-person cooperative games in Game Theory, the mathemat- ical theory of interactive decision situations characterized by a group of agents, each of whom has to make a decision based on their own preferences on the set of outcomes. These situations are called games, agents are players and decisions are strategies. By focusing on Cooperative Game Theory, we analyze concepts such as coalition formation, equilibrium, stability, fairness and the most important proposed solution concepts. Keywords: Cooperative Game Theory, Cooperative game, Shapley value, nucleolus, core, bankruptcy problem, airport problem, indices of power, voting games. Resum Aquest treball tracta sobre els jocs n-personals cooperatius en Teoria de Jocs, la branca de les matem`atiquesque estudia i analitza les interaccions entre una s`erie d'agents que han de prendre una decisi´o,segons les seves prefer`enciessobre el conjunt de possibles resultats dels jocs. En centrar-nos en la Teoria de Jocs Cooperatius, analitzarem conceptes com la formaci´ode coalicions, l'equilibri, la just´ıciai les propostes de conceptes de solucions m´es importants. i Acknowledgements For his continuous help and patient guidance throughout the development of this thesis, I would like to express my deep gratitude, first of all, to my advisor, Dr. Josep Vives. Without his encouragement, persistent advice and useful corrections, this would not have been possible. -
Strategyproof Exchange with Multiple Private Endowments
Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence Strategyproof Exchange with Multiple Private Endowments Taiki Todo, Haixin Sun, Makoto Yokoo Dept. of Informatics Kyushu University Motooka 744, Fukuoka, JAPAN ftodo, sunhaixin, [email protected] Abstract efficient and individually rational. Moreover, it is the only We study a mechanism design problem for exchange rule that satisfies those three properties (Ma 1994). Due to economies where each agent is initially endowed with these advantages, TTC has been attracting much attention a set of indivisible goods and side payments are not al- from both economists and computer scientists. lowed. We assume each agent can withhold some en- In this paper we consider exchange economies where each dowments, as well as misreport her preference. Under this assumption, strategyproofness requires that for each agent is endowed with a set of multiple goods, instead of agent, reporting her true preference with revealing all a single good. Under that model, Pareto efficiency, indi- her endowments is a dominant strategy, and thus implies vidual rationality, and strategyproofness cannot be simulta- individual rationality. Our objective in this paper is to neously satisfied (Sonmez¨ 1999). Therefore, one main re- analyze the effect of such private ownership in exchange search direction on exchanges with multiple endowments is economies with multiple endowments. As fundamental to achieve strategyproof rules that guarantee a limited notion results, we first show that the revelation principle holds of efficiency. In particular, Papai´ (2003) defined a class of under a natural assumption and that strategyproofness exchange rules and gave a characterization by strategyproof- and Pareto efficiency are incompatible even under the ness and individual rationality with some other weak effi- lexicographic preference domain. -
Proportionality and Strategyproofness in Multiwinner Elections
Session 43: Social Choice Theory 3 AAMAS 2018, July 10-15, 2018, Stockholm, Sweden Proportionality and Strategyproofness in Multiwinner Elections Dominik Peters University of Oxford Oxford, UK [email protected] ABSTRACT focussed on cases where there are no parties, and preferences are Multiwinner voting rules can be used to select a fixed-size com- expressed directly over the candidates [23]. The latter setting allows mittee from a larger set of candidates. We consider approval-based for applications in areas outside the political sphere, such as in committee rules, which allow voters to approve or disapprove can- group recommendation systems. didates. In this setting, several voting rules such as Proportional To formalise the requirement of proportionality in this party-free Approval Voting (PAV) and Phragmén’s rules have been shown to setting, it is convenient to consider the case where input preferences produce committees that are proportional, in the sense that they are given as approval ballots: each voter reports a set of candidates proportionally represent voters’ preferences; all of these rules are that they find acceptable. Even for this simple setting, there isa strategically manipulable by voters. On the other hand, a generalisa- rich variety of rules that exhibit different behaviour [31], and this tion of Approval Voting gives a non-proportional but strategyproof setting gives rise to a rich variety of axioms. voting rule. We show that there is a fundamental tradeoff between One natural way of selecting a committee of k candidates when these two properties: we prove that no multiwinner voting rule can given approval ballots is to extend Approval Voting (AV): for each simultaneously satisfy a weak form of proportionality (a weakening of the m candidates, count how many voters approve them (their of justified representation) and a weak form of strategyproofness. -
The Shapley Value for Airport and Irrigation Games
MPRA Munich Personal RePEc Archive The Shapley value for airport and irrigation games Judit M´arkus and Mikl´os Pint´er and Anna Radv´anyi 2011 Online at https://mpra.ub.uni-muenchen.de/30031/ MPRA Paper No. 30031, posted 10. April 2011 08:26 UTC The Shapley value for airport and irrigation games∗ Judit M´arkus,Mikl´osPint´eryand Anna Radv´anyi Corvinus University of Budapest April 2, 2011 Abstract In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree prob- lems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games (Littlechild and Thompson, 1977) is a subclass of irrigation games. The Shapley value (Shapley, 1953) is probably the most popular solution concept for transferable util- ity cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's (Shapley, 1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irri- gation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. -
Relaxing Strategyproofness in One-Sided Matching
Relaxing Strategyproofness in One-sided Matching TIMO MENNLE and SVEN SEUKEN University of Zurich We consider the one-sided matching problem, where agents must be matched to indivisible ob- jects. Our first result is a novel characterization of strategyproof mechanisms by three intuitive axioms. Furthermore, we introduce partial strategyproofness, a new relaxation of strategyproof- ness that bridges the gap between full and weak strategyproofness. Partial strategyproofness finds application in the incentive analysis of non-strategyproof mechanisms, such as Probabilistic Serial, different variants of the Boston mechanism, and hybrid mechanisms. In this letter, we summarize the main results from [Mennle and Seuken 2014a] and demonstrate how they can be used for the design and analysis of matching mechanisms.1 Categories and Subject Descriptors: J.4.a [Social and Behavioral Sciences]: Economics General Terms: Economics; Theory Additional Key Words and Phrases: Matching, Mechanism Design, Strategyproofness 1. INTRODUCTION The (probabilistic) one-sided matching problem is concerned with the allocation of indivisible goods to self-interested agents with privately known preferences in domains where monetary transfers are not permitted. Such problems often arise in situations that are of great importance to peoples' lives. For example, students must be matched to schools, teachers to training programs, or tenants to houses. Strategyproof mechanisms, such as Random Serial Dictatorship (RSD), are ap- pealing because they make truthful reporting a dominant strategy for all agents. Participation in the mechanism becomes an easy task as there is no need for delib- eration about the best response, thus reducing cognitive costs for the agents and (likely) endowing the mechanism with correct information about agents' preferences. -
Specification Faithfulness in Networks with Rational Nodes
Specification Faithfulness in Networks with Rational Nodes Jeffrey Shneidman, David C. Parkes Division of Engineering and Applied Sciences, Harvard University, 33 Oxford Street, Cambridge MA 02138 {jeffsh, parkes}@eecs.harvard.edu ABSTRACT drive up their “contributed computation” credit [15]. There It is useful to prove that an implementation correctly follows is interesting work documenting the “free rider” problem [1] a specification. But even with a provably correct implemen- and the “tragedy of the commons” [12] in a data centric peer tation, given a choice, would a node choose to follow it? This to peer setting. paper explores how to create distributed system specifica- This behavior can be classified as a type of failure, which tions that will be faithfully implemented in networks with should stand independently from other types of failures in rational nodes, so that no node will choose to deviate. Given distributed systems and is indicative of an underlying in- a strategyproof centralized mechanism, and given a network centive problem in a system’s design when run on a network of nodes modeled as having rational-manipulation faults, with rational nodes. Whereas traditional failure models are we provide a proof technique to establish the incentive-, overcome by relying on redundancy, rational manipulation communication-, and algorithm-compatibility properties that can also be overcome with design techniques such as prob- guarantee that participating nodes are faithful to a sug- lem partitioning, catch-and-punish, and incentives. In such gested specification. As a case study, we apply our methods a network one can state a strong claim about the faithfulness to extend the strategyproof interdomain routing mechanism of each node’s implementation. -
Fair Sharing: the Shapley Value for Ride-Sharing and Routing Games
Fair Sharing: The Shapley Value for Ride-Sharing and Routing Games Chaya Levinger1, Noam Hazon1, and Amos Azaria1 Department of Computer Science, Ariel University, Israel [email protected] fnoamh,[email protected] Abstract. Ride-sharing services are gaining popularity and are crucial for a sus- tainable environment. A special case in which such services are most applicable, is the last mile variant. In this variant it is assumed that all the passengers are positioned at the same origin location (e.g. an airport), and each have a different destination. One of the major issues in a shared ride is fairly splitting of the ride cost among the passengers. In this paper we use the Shapley value, which is one of the most significant solu- tion concepts in cooperative game theory, for fairly splitting the cost of a shared ride. We consider two scenarios. In the first scenario there exists a fixed prior- ity order in which the passengers are dropped-off (e.g. elderly, injured etc.), and we show a method for efficient computation of the Shapley value in this setting. Our results are also applicable for efficient computation of the Shapley value in routing games. In the second scenario there is no predetermined priority order. We show that the Shapley value cannot be efficiently computed in this setting. However, extensive simulations reveal that our approach for the first scenario can serve as an excellent proxy for the second scenario, outperforming other known proxies. 1 Introduction On-demand ride-sharing services, which group together passengers with similar itineraries, can be of significant social and environmental benefit, by reducing travel costs, road congestion and CO2 emissions.