Empirical Strategy-Proofness∗
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Equilibrium Refinements
Equilibrium Refinements Mihai Manea MIT Sequential Equilibrium I In many games information is imperfect and the only subgame is the original game. subgame perfect equilibrium = Nash equilibrium I Play starting at an information set can be analyzed as a separate subgame if we specify players’ beliefs about at which node they are. I Based on the beliefs, we can test whether continuation strategies form a Nash equilibrium. I Sequential equilibrium (Kreps and Wilson 1982): way to derive plausible beliefs at every information set. Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 2 / 38 An Example with Incomplete Information Spence’s (1973) job market signaling game I The worker knows her ability (productivity) and chooses a level of education. I Education is more costly for low ability types. I Firm observes the worker’s education, but not her ability. I The firm decides what wage to offer her. In the spirit of subgame perfection, the optimal wage should depend on the firm’s beliefs about the worker’s ability given the observed education. An equilibrium needs to specify contingent actions and beliefs. Beliefs should follow Bayes’ rule on the equilibrium path. What about off-path beliefs? Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 3 / 38 An Example with Imperfect Information Courtesy of The MIT Press. Used with permission. Figure: (L; A) is a subgame perfect equilibrium. Is it plausible that 2 plays A? Mihai Manea (MIT) Equilibrium Refinements April 13, 2016 4 / 38 Assessments and Sequential Rationality Focus on extensive-form games of perfect recall with finitely many nodes. An assessment is a pair (σ; µ) I σ: (behavior) strategy profile I µ = (µ(h) 2 ∆(h))h2H: system of beliefs ui(σjh; µ(h)): i’s payoff when play begins at a node in h randomly selected according to µ(h), and subsequent play specified by σ. -
Draft Abstract
SN 1327-8231 ECONOMICS, ECOLOGY AND THE ENVIRONMENT WORKING PAPER NO. 38 Neglected Features of the Safe Minimum Standard: Socio-economic and Institutional Dimensions by IRMI SEIDL AND CLEM TISDELL March 2000 THE UNIVERSITY OF QUEENSLAND ISSN 1327-8231 WORKING PAPERS ON ECONOMICS, ECOLOGY AND THE ENVIRONMENT Working Paper No. 38 Neglected Features of the Safe Minimum Standard: Socio-Economic and Institutional Dimensions by Irmi Seidl1 and Clem Tisdell2 March 2000 © All rights reserved 1 Irmi Seidl, Institut fuer Umweltwissenschaften, University of Zuerich, Winterthurerstr. 190, CH-8057, Zuerich, Switzerland. Email: [email protected] 2 School of Economics, The University of Queensland, Brisbane QLD 4072, Australia Email: [email protected] WORKING PAPERS IN THE SERIES, Economics, Ecology and the Environment are published by the School of Economics, University of Queensland, 4072, Australia, as follow up to the Australian Centre for International Agricultural Research Project 40 of which Professor Clem Tisdell was the Project Leader. Views expressed in these working papers are those of their authors and not necessarily of any of the organisations associated with the Project. They should not be reproduced in whole or in part without the written permission of the Project Leader. It is planned to publish contributions to this series over the next few years. Research for ACIAR project 40, Economic impact and rural adjustments to nature conservation (biodiversity) programmes: A case study of Xishuangbanna Dai Autonomous Prefecture, Yunnan, China was sponsored by the Australian Centre for International Agricultural Research (ACIAR), GPO Box 1571, Canberra, ACT, 2601, Australia. The research for ACIAR project 40 has led in part, to the research being carried out in this current series. -
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 -
OR-M5-Ktunotes.In .Pdf
CHAPTER – 12 Decision Theory 12.1. INTRODUCTION The decisions are classified according to the degree of certainty as deterministic models, where the manager assumes complete certainty and each strategy results in a unique payoff, and Probabilistic models, where each strategy leads to more than one payofs and the manager attaches a probability measure to these payoffs. The scale of assumed certainty can range from complete certainty to complete uncertainty hence one can think of decision making under certainty (DMUC) and decision making under uncertainty (DMUU) on the two extreme points on a scale. The region that falls between these extreme points corresponds to the concept of probabilistic models, and referred as decision-making under risk (DMUR). Hence we can say that most of the decision making problems fall in the category of decision making under risk and the assumed degree of certainty is only one aspect of a decision problem. The other way of classifying is: Linear or non-linear behaviour, static or dynamic conditions, single or multiple objectives.KTUNOTES.IN One has to consider all these aspects before building a model. Decision theory deals with decision making under conditions of risk and uncertainty. For our purpose, we shall consider all types of decision models including deterministic models to be under the domain of decision theory. In management literature, we have several quantitative decision models that help managers identify optima or best courses of action. Complete uncertainty Degree of uncertainty Complete certainty Decision making Decision making Decision-making Under uncertainty Under risk Under certainty. Before we go to decision theory, let us just discuss the issues, such as (i) What is a decision? (ii) Why must decisions be made? (iii) What is involved in the process of decision-making? (iv) What are some of the ways of classifying decisions? This will help us to have clear concept of decision models. -
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. -
VCTAL Game Theory Module.Docx
Competition or Collusion? Game Theory in Security, Sports, and Business A CCICADA Homeland Security Module James Kupetz, Luzern County Community College [email protected] Choong-Soo Lee, St. Lawrence University [email protected] Steve Leonhardi, Winona State University [email protected] 1/90 Competition or Collusion? Game Theory in Security, Sports, and Business Note to teachers: Teacher notes appear in dark red in the module, allowing faculty to pull these notes off the teacher version to create a student version of the module. Module Summary This module introduces students to game theory concepts and methods, starting with zero-sum games and then moving on to non-zero-sum games. Students learn techniques for classifying games, for computing optimal solutions where known, and for analyzing various strategies for games in which no optimal solution exists. Finally, students have the opportunity to transfer what they’ve learned to new game-theoretic situations. Prerequisites Students should be able to use the skills learned in High School Algebra 1, including the ability to graph linear equations, find points of intersection, and algebraically solve systems of two linear equations in two unknowns. Knowledge of basic probability (such as should be learned by the end of 9th grade) is also required; experience with computing expected value would be helpful, but can be taught as part of the module. No computer programming experience is required or involved, although students with some programming knowledge may be able to adapt their knowledge to optional projects. Suggested Uses This module can be used with students in grades 10-14 in almost any class, but is best suited to students in mathematics, economics, political science, or computer science courses. -
Informational Size and Incentive Compatibility
Econometrica, Vol. 70, No. 6 (November, 2002), 2421–2453 INFORMATIONAL SIZE AND INCENTIVE COMPATIBILITY By Richard McLean and Andrew Postlewaite1 We examine a general equilibrium model with asymmetrically informed agents. The presence of asymmetric information generally presents a conflict between incentive com- patibility and Pareto efficiency. We present a notion of informational size and show that the conflict between incentive compatibility and efficiency can be made arbitrarily small if agents are of sufficiently small informational size. Keywords: Incentive compatibility, mechanism design, incomplete information. 1 introduction The incompatibility of Pareto efficiency and incentive compatibility is a central theme in economics and game theory. The issues associated with this incompatibility are particularly important in the design of resource allocation mechanisms in the presence of asymmetrically informed agents where the need to acquire information from agents in order to compute efficient outcomes and the incentives agents have to misrepresent that information for personal gain come into conflict. Despite a large literature that focuses on these issues, there has been little work aimed at understanding those situations in which informational asymmetries are quantitatively important. Virtually every transaction is characterized by some asymmetry of information: any investor who buys or sells a share of stock generally knows something rel- evant to the value of the share that is not known to the person on the other side of the transaction. In order to focus on more salient aspects of the problem, many models (rightly) ignore the incentive problems associated with informa- tional asymmetries in the belief that, for the problem at hand, agents are “infor- mationally small.” However, few researchers have investigated the circumstances under which an analysis that ignores these incentive problems will yield results similar to those obtained when these problems are fully accounted for. -
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. -
Agency Business Cycles
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Golosov, Michail Ju.; Menzio, Guido Article Agency business cycles Theoretical Economics Provided in Cooperation with: The Econometric Society Suggested Citation: Golosov, Michail Ju.; Menzio, Guido (2020) : Agency business cycles, Theoretical Economics, ISSN 1555-7561, Wiley, Hoboken, NJ, Vol. 15, Iss. 1, pp. 123-158, http://dx.doi.org/10.3982/TE3379 This Version is available at: http://hdl.handle.net/10419/217101 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. https://creativecommons.org/licenses/by-nc/4.0/ www.econstor.eu Theoretical Economics 15 (2020), 123–158 1555-7561/20200123 Agency business cycles Mikhail Golosov Department of Economics, University of Chicago and NBER Guido Menzio Department of Economics, New York University and NBER We develop a theory of endogenous and stochastic fluctuations in economic ac- tivity. -
Game Theory and Strictly Determined Games • Zero-Sum Game - a Game in Which the Payoff to One Party Results in an Equal Loss to the Other
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166 - Week in Review #11 Section 9.4 - Game Theory and Strictly Determined Games • Zero-sum Game - a game in which the payoff to one party results in an equal loss to the other. • The entries in a payoff matrix represent the earnings of the row player. • Maximin Strategy 1. For each row of the payoff matrix, find the smallest entry in that row and underline it. 2. Find the largest underlined number and note the row that it is in. This row gives the row player’s “best” move. • Minimax Strategy 1. For each column of the payoff matrix, find the largest entry in that column and circle it. 2. Find the smallest circled number and note the column that it is in. This column gives the column player’s “best” move. • Strictly Determined Game - A strictly determined game has the following properties: 1. There is an entry in the payoff matrix that is simultaneously the smallest entry in its row and the largest entry in its column (i.e., there is one entry that is both underlined and circles at the same time). This entry is called the saddle point for the game. 2. The optimal strategy for the row player is precisely the maximin strategy and is the row containing the saddle point. The optimal strategy for the column player is the minimax strategy and is the column containing the saddle point. • The saddle point of a strictly determined game is also referred to as the value of the game. -
2.2 Production Function
13 MM VENKATESHWARA OPEN UNIVERSITY MICROECONOMIC THEORY www.vou.ac.in MICROECONOMIC THEORY MICROECONOMIC MICROECONOMIC THEORY MA [MEC-102] VENKATESHWARA OPEN UNIVERSITYwww.vou.ac.in MICROECONOMIC THEORY MA [MEC-102] BOARD OF STUDIES Prof Lalit Kumar Sagar Vice Chancellor Dr. S. Raman Iyer Director Directorate of Distance Education SUBJECT EXPERT Bhaskar Jyoti Neog Assistant Professor Dr. Kiran Kumari Assistant Professor Ms. Lige Sora Assistant Professor Ms. Hage Pinky Assistant Professor CO-ORDINATOR Mr. Tauha Khan Registrar Authors Dr. S.L. Lodha, (Units: 1.2, 1.4, 1.6, 1.7, 5.2, 5.3.1, 5.4, 9.4, 10.2, 10.3, 10.3.2) © Dr. S.L. Lodha, 2019 D.N. Dwivedi, (Units: 1.3, 1.5, 1.8, 2.2-2.4, 3.2-3.3, 3.4.1-3.4.2, 4.2-4.4, 5.3, 5.5-5.6, 6.2-6.4, 6.5.2-6.7, 7.2-7.4, 8.2-8.5.2, 8.6, 9.2-9.3, 10.2.1-10.2.2) © D.N. Dwivedi, 2019 Dr. Renuka Sharma & Dr. Kiran Mehta, (Units: 3.4.3-3.4.5, 7.5, 8.7) © Dr. Renuka Sharma & Dr. Kiran Mehta, 2019 Vikas Publishing House (Units: 1.0-1.1, 1.9-1.13, 2.0-2.1, 2.5-2.9, 3.0-3.1, 3.4, 3.5-3.9, 4.0-4.1, 4.5-4.9, 5.0-5.1, 5.7-5.11, 6.0-6.1, 6.5-6.5.1, 6.8-6.12, 7.0-7.1, 7.6-7.10, 8.0-8.1, 8.5.3, 8.8-8.12, 9.0-9.1, 9.5-9.9, 10.0-10.1, 10.3.1, 10.4-10.8) © Reserved, 2019 All rights reserved.