Is Japanese Dutch Auction Unreasonable?: A Note on Dutch Auction with Mari
|
|
- Chastity Simmons
- 5 years ago
- Views:
Transcription
1 Is Japanese Dutch Auction Unreasonable?: A Note on Dutch Auction with Mari Minoru Kitahara and Ryo Ogawa February 7, 2006 Dutch auction is a widely used auction system in flower markets, and Japanese flower markets are no exception. However, there is one unique difference in Japanese Dutch auction: it has Mari -stages. In a usual multi-unit Dutch auction, for each round, (i) clock drops continuously from sufficiently high price until a buyer stops the clock, (ii) the buyer gets the goods at the price pointed at by the clock, and then (iii) the auction goes to the next round if there still remain some units. In Japanese Dutch auction, Mari-chū (in the process of Mari) signal appears for a few seconds between (ii) and (iii), while other buyers are allowed to purchase the goods at the same price. In this short note, we investigate the effects of Mari. We find that Japanese Dutch auction seems reasonable in the sense that it speeds up the auction sufficiently at the cost of negligible efficiency loss. 1 Model and Results 1.1 Overall settings There are k units of homogeneous goods and n buyers with their types t independently drawn from U0, 1, which are their private information. Each buyer demands one-unit and is risk-neutral: his payoff is (v(t) the price) 1 {He gets the goods.}. We assume the uniform distribution for the valuation: v(t) = t. The auction system is almost the same as a usual multi-unit Dutch auction but has a Maristage in the first round. (After the Mari-stage, a usual Dutch auction follows.) We focus on simple symmetric equilibrium: there exist βn,k and µ n,k such that (i) type-t buyers stop the clock at βn,k t in the first round, (ii) if the clock stops at βn,k t in the first round, then other buyers participate in Mari if and only if their type t is higher than µ n,k t, and (iii) they play as in a usual Dutch auction from the second round on: if there remain l units and m buyers, then type-t buyers bid m l m t as well known. 1.2 Mari-Stage Modeling Mari-Stage A type- t buyer has stopped the clock at β t. Other n 1 buyers, with their types independently drawn from U0, t), simultaneously decide whether to participate We are grateful to Kuniyoshi Saito, Kiri Sakahara, and Daisuke Shimizu. 1
2 in Mari. If the number of Mari-participants is no more than k 1, then all the participants become winners. Otherwise, k 1 winners are randomly selected among the participants. All winners pay β t for the goods. If there still remain some units after Mari, then the auction goes to the next round Equilibrium Mari-Participation Note that each buyer participates in Mari with probability 1 µ ex ante in the equilibrium. Let E 1 µ,m f(j) m i=0 f(i) mc i (1 µ) i µ m i. Then, if a type-µ t buyer participated in Mari, then his expected payoff would be (µ t β t)e 1 µ,n 2 1 j k 2 + k 1, and otherwise, the payoff would be ( E 1 µ,n 2 µ t n k ) n 1 j µ t 1 j<k 1 Thus, µ is characterized as follows. Proposition 1. If β n k n 1, then µ = 1. Otherwise, µ (uniquely) solves (µ β)e 1 µ,n 2 1 j k 2 + k 1 Proof. See that (1) implies (1 β)e 1 µ,n 2 1 j k 2 + k 1 k 1 j = µe 1 µ,n 2 n 1 j 1 j<k 1. = k 1 n 1. (1) (2) Note that it implies that Mari-participation occurs only if Mari-price is less than n k t n 1 < t. Thus, whether Mari-participation in reality is justified as an equilibrium behavior may not be clear until we investigate the first winner s equilibrium clock-stopping strategy. 1.3 Inefficient Allocation and Speeding Up The expected efficiency loss within this stage is ( 1 t(1 µ)(k 1)E 1 µ,n 1 1 k ) 1 j>k 1. (3) 2 j + 1 If goods are allocated efficiently, then the expected surplus is ( t(k 1) 1 k ). (4) 2n Denote by LR n,k (β) the loss rate (3)/(4) where µ is determined as in Proposition 1. For n = 3 and k = 2, the graph becomes as follows. 2
3 LR Β The expected number of the goods sold within this stage is E 1 µ,n 1 (k 1)1 j>k 1 + j1 j k 1. (5) Similar to LR, denote by RR n,k (β) the reduction rate (5)/(k 1). For n = 3 and k = 2, the graph becomes as follows RR Β Note that to suppress the loss rate below 5%, β should be more than At the same time, to attain the reduction rate of more than 50%, β should be less than These results may make one pessimistic about the good performance in the equilibrium. 1.4 Overall Equilibrium Characterization Suppose that a type-t buyer lowers his bid by small > 0. Then, his payment decreases by in the event he is the first to win the good, the probability of which is t n 1. At the same time, since βt is bid by type-(t /β) buyers, he additionally fails the possibility to be the first winner in the event the highest type among other buyers belongs to (t /β, t, the probability of which is ( /β)(n 1)t n 2, where his probability to win the good decreases from 1 to. In the equilibrium, these potential gains and E 1 µ,n 2 1 j k 2 + k 1 j+1 1 j>k 2 losses from deviation must offset one another. Consequently, the equilibrium β must satisfy: t n 1 = 1 β (n 1)tn 2 {(t βt) (1 E 1 µ,n 2 1 j k 2 + k 1 )}. (6) 3
4 In summary, the equilibrium clock-stopping β n,k and Mari-participation µ n,k are the solution of (1) and (6), which are characterized as follows. Proposition 2. βn,k = n k n, and µ n,k is the (unique) solution of Proof. See that (1) implies (2). E 1 µ,n 2 1 j k 2 + k 1 < n k n 1. = k 1 n n 1 k. (7) Note that βn,k Thus, the equilibrium Mari-price is consistent with Mari-participation. Moreover, the equilibrium performance looks good: β3,2 = 1/3 (0.26, 0.42). It seems very good: LR3,2 = 3.125% and RR3,2 = 75%. This result is not specific for these parameter values. We plot (RR, LR ) below for more broad parameter values, for 2 k 10 and k + 1 n 5k LR van den Berg et al. (2001) reports that k is 5.98 on average in the Aalsmeer Flower Auction. Thus, we may expect more than 80% reduction in exchange for less than 1.5% efficiency loss. 2 Discussions It may be easy to understand the low efficiency-loss result. The expected value of the k 1th highest value among n 1 buyers is n k t. n Thus, β is a marketclearing price on average. As expected by this intuition (and law of large numbers), LR15, %. We are unable to give clear intuition for the high round-reduction result. However, by (7), E 1 µ,n 1 1 j>k 1 1 µ 1 α n where α = k/n, (k 1) (n 1)(1 µ) = n 1 (n 1)µ(1 µ) k 1 n 1 RR (1 µ), (8) µ(1 µ) and for any ɛ > 0, 1 Φ(ɛ n 1) 1/n 0 as n. 4
5 where Φ is the cumulative distribution of N(0, 1). Thus, it seems that µ /α converges to 1 as the market size grows. If so, then since β /α 1 and RR = 1 µ 1 β, RR converges to 1. RR 15, %, as expected by this intuition. Note that in more competitive (i.e., larger α) markets, the pure random allocation, which corresponds to β = 0, leads to larger efficiency loss: for example, LR 3,2 (0) = 25% but LR 11,2 (0) 45%. As indicated by the intuitions above, the equilibrium performances of Mari-stages seem not damaged by the competitiveness: LR 11, % and RR 11, %. 3 Summary Japanese Dutch auction seems reasonable: it speeds up the auction sufficiently in exchange for negligible efficiency loss. It seems more effective for larger or more competitive markets. References van den Berg, Gerald J., van Ours, Jan C. and Pradhan, Menno P. (2001): The Declining Price Anomaly in Dutch Dutch Rose Auctions. American Economic Review 91: Milgrom, Paul and Weber, Robert J. (2000): A Theory of Auctions and Competitive Bidding, II. The Economic Theory of Auctions. P.Klemperer. Cheltenham: Edward Elgar Publishing, Ltd. 2:
Strategy -1- Strategy
Strategy -- Strategy A Duopoly, Cournot equilibrium 2 B Mixed strategies: Rock, Scissors, Paper, Nash equilibrium 5 C Games with private information 8 D Additional exercises 24 25 pages Strategy -2- A
More informationAuctions. Agenda. Definition. Syllabus: Mansfield, chapter 15 Jehle, chapter 9
Auctions Syllabus: Mansfield, chapter 15 Jehle, chapter 9 1 Agenda Types of auctions Bidding behavior Buyer s maximization problem Seller s maximization problem Introducing risk aversion Winner s curse
More information1 Theory of Auctions. 1.1 Independent Private Value Auctions
1 Theory of Auctions 1.1 Independent Private Value Auctions for the moment consider an environment in which there is a single seller who wants to sell one indivisible unit of output to one of n buyers
More informationGames of Incomplete Information ( 資訊不全賽局 ) Games of Incomplete Information
1 Games of Incomplete Information ( 資訊不全賽局 ) Wang 2012/12/13 (Lecture 9, Micro Theory I) Simultaneous Move Games An Example One or more players know preferences only probabilistically (cf. Harsanyi, 1976-77)
More informationStrategy -1- Strategic equilibrium in auctions
Strategy -- Strategic equilibrium in auctions A. Sealed high-bid auction 2 B. Sealed high-bid auction: a general approach 6 C. Other auctions: revenue equivalence theorem 27 D. Reserve price in the sealed
More informationISSN BWPEF Uninformative Equilibrium in Uniform Price Auctions. Arup Daripa Birkbeck, University of London.
ISSN 1745-8587 Birkbeck Working Papers in Economics & Finance School of Economics, Mathematics and Statistics BWPEF 0701 Uninformative Equilibrium in Uniform Price Auctions Arup Daripa Birkbeck, University
More informationSequential Auctions, Price Trends, and Risk Preferences
,, and Risk Preferences Audrey Hu Liang Zou University of Amsterdam/ Tinbergen Institute 15 February, 2015 auctions are market institutions where multiple units of (nearly) identical goods are sold one
More informationPAULI MURTO, ANDREY ZHUKOV
GAME THEORY SOLUTION SET 1 WINTER 018 PAULI MURTO, ANDREY ZHUKOV Introduction For suggested solution to problem 4, last year s suggested solutions by Tsz-Ning Wong were used who I think used suggested
More informationRecalling that private values are a special case of the Milgrom-Weber setup, we ve now found that
Econ 85 Advanced Micro Theory I Dan Quint Fall 27 Lecture 12 Oct 16 27 Last week, we relaxed both private values and independence of types, using the Milgrom- Weber setting of affiliated signals. We found
More informationMicroeconomics Comprehensive Exam
Microeconomics Comprehensive Exam June 2009 Instructions: (1) Please answer each of the four questions on separate pieces of paper. (2) When finished, please arrange your answers alphabetically (in the
More information1 Auctions. 1.1 Notation (Symmetric IPV) Independent private values setting with symmetric riskneutral buyers, no budget constraints.
1 Auctions 1.1 Notation (Symmetric IPV) Ancient market mechanisms. use. A lot of varieties. Widespread in Independent private values setting with symmetric riskneutral buyers, no budget constraints. Simple
More informationLecture 6 Applications of Static Games of Incomplete Information
Lecture 6 Applications of Static Games of Incomplete Information Good to be sold at an auction. Which auction design should be used in order to maximize expected revenue for the seller, if the bidders
More informationSupplemental Materials for What is the Optimal Trading Frequency in Financial Markets? Not for Publication. October 21, 2016
Supplemental Materials for What is the Optimal Trading Frequency in Financial Markets? Not for Publication Songzi Du Haoxiang Zhu October, 06 A Model with Multiple Dividend Payment In the model of Du and
More informationTopics in Contract Theory Lecture 6. Separation of Ownership and Control
Leonardo Felli 16 January, 2002 Topics in Contract Theory Lecture 6 Separation of Ownership and Control The definition of ownership considered is limited to an environment in which the whole ownership
More informationWe examine the impact of risk aversion on bidding behavior in first-price auctions.
Risk Aversion We examine the impact of risk aversion on bidding behavior in first-price auctions. Assume there is no entry fee or reserve. Note: Risk aversion does not affect bidding in SPA because there,
More informationProblem Set 3: Suggested Solutions
Microeconomics: Pricing 3E Fall 5. True or false: Problem Set 3: Suggested Solutions (a) Since a durable goods monopolist prices at the monopoly price in her last period of operation, the prices must be
More informationOctober An Equilibrium of the First Price Sealed Bid Auction for an Arbitrary Distribution.
October 13..18.4 An Equilibrium of the First Price Sealed Bid Auction for an Arbitrary Distribution. We now assume that the reservation values of the bidders are independently and identically distributed
More informationBayesian Nash Equilibrium
Bayesian Nash Equilibrium We have already seen that a strategy for a player in a game of incomplete information is a function that specifies what action or actions to take in the game, for every possibletypeofthatplayer.
More informationAll Equilibrium Revenues in Buy Price Auctions
All Equilibrium Revenues in Buy Price Auctions Yusuke Inami Graduate School of Economics, Kyoto University This version: January 009 Abstract This note considers second-price, sealed-bid auctions with
More informationUCLA Department of Economics Ph.D. Preliminary Exam Industrial Organization Field Exam (Spring 2010) Use SEPARATE booklets to answer each question
Wednesday, June 23 2010 Instructions: UCLA Department of Economics Ph.D. Preliminary Exam Industrial Organization Field Exam (Spring 2010) You have 4 hours for the exam. Answer any 5 out 6 questions. All
More informationProblem Set 3: Suggested Solutions
Microeconomics: Pricing 3E00 Fall 06. True or false: Problem Set 3: Suggested Solutions (a) Since a durable goods monopolist prices at the monopoly price in her last period of operation, the prices must
More informationAuctions That Implement Efficient Investments
Auctions That Implement Efficient Investments Kentaro Tomoeda October 31, 215 Abstract This article analyzes the implementability of efficient investments for two commonly used mechanisms in single-item
More informationwithout transaction costs, all government allocations are equally efficient, since parties will bargain to correct any externality.
0 Auctions The Coase theorem without transaction costs, all government allocations are equally efficient, since parties will bargain to correct any externality. with transaction costs, government may minimize
More informationOptimal Auctions. Game Theory Course: Jackson, Leyton-Brown & Shoham
Game Theory Course: Jackson, Leyton-Brown & Shoham So far we have considered efficient auctions What about maximizing the seller s revenue? she may be willing to risk failing to sell the good she may be
More informationLast-Call Auctions with Asymmetric Bidders
Last-Call Auctions with Asymmetric Bidders Marie-Christin Haufe a, Matej Belica a a Karlsruhe nstitute of Technology (KT), Germany Abstract Favoring a bidder through a Right of First Refusal (ROFR) in
More informationAuction is a commonly used way of allocating indivisible
Econ 221 Fall, 2018 Li, Hao UBC CHAPTER 16. BIDDING STRATEGY AND AUCTION DESIGN Auction is a commonly used way of allocating indivisible goods among interested buyers. Used cameras, Salvator Mundi, and
More informationRecap First-Price Revenue Equivalence Optimal Auctions. Auction Theory II. Lecture 19. Auction Theory II Lecture 19, Slide 1
Auction Theory II Lecture 19 Auction Theory II Lecture 19, Slide 1 Lecture Overview 1 Recap 2 First-Price Auctions 3 Revenue Equivalence 4 Optimal Auctions Auction Theory II Lecture 19, Slide 2 Motivation
More informationFDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.
FDPE Microeconomics 3 Spring 2017 Pauli Murto TA: Tsz-Ning Wong (These solution hints are based on Julia Salmi s solution hints for Spring 2015.) Hints for Problem Set 2 1. Consider a zero-sum game, where
More informationRevenue Equivalence and Income Taxation
Journal of Economics and Finance Volume 24 Number 1 Spring 2000 Pages 56-63 Revenue Equivalence and Income Taxation Veronika Grimm and Ulrich Schmidt* Abstract This paper considers the classical independent
More informationGames with Private Information 資訊不透明賽局
Games with Private Information 資訊不透明賽局 Joseph Tao-yi Wang 00/0/5 (Lecture 9, Micro Theory I-) Market Entry Game with Private Information (-,4) (-,) BE when p < /: (,, ) (-,4) (-,) BE when p < /: (,, )
More informationUp till now, we ve mostly been analyzing auctions under the following assumptions:
Econ 805 Advanced Micro Theory I Dan Quint Fall 2007 Lecture 7 Sept 27 2007 Tuesday: Amit Gandhi on empirical auction stuff p till now, we ve mostly been analyzing auctions under the following assumptions:
More informationOn Existence of Equilibria. Bayesian Allocation-Mechanisms
On Existence of Equilibria in Bayesian Allocation Mechanisms Northwestern University April 23, 2014 Bayesian Allocation Mechanisms In allocation mechanisms, agents choose messages. The messages determine
More informationSignaling in an English Auction: Ex ante versus Interim Analysis
Signaling in an English Auction: Ex ante versus Interim Analysis Peyman Khezr School of Economics University of Sydney and Abhijit Sengupta School of Economics University of Sydney Abstract This paper
More informationAuctions: Types and Equilibriums
Auctions: Types and Equilibriums Emrah Cem and Samira Farhin University of Texas at Dallas emrah.cem@utdallas.edu samira.farhin@utdallas.edu April 25, 2013 Emrah Cem and Samira Farhin (UTD) Auctions April
More informationGame Theory. Lecture Notes By Y. Narahari. Department of Computer Science and Automation Indian Institute of Science Bangalore, India July 2012
Game Theory Lecture Notes By Y. Narahari Department of Computer Science and Automation Indian Institute of Science Bangalore, India July 2012 The Revenue Equivalence Theorem Note: This is a only a draft
More informationNotes on Auctions. Theorem 1 In a second price sealed bid auction bidding your valuation is always a weakly dominant strategy.
Notes on Auctions Second Price Sealed Bid Auctions These are the easiest auctions to analyze. Theorem In a second price sealed bid auction bidding your valuation is always a weakly dominant strategy. Proof
More informationRevenue Equivalence Theorem (RET)
Revenue Equivalence Theorem (RET) Definition Consider an auction mechanism in which, for n risk-neutral bidders, each has a privately know value drawn independently from a common, strictly increasing distribution.
More information6.254 : Game Theory with Engineering Applications Lecture 3: Strategic Form Games - Solution Concepts
6.254 : Game Theory with Engineering Applications Lecture 3: Strategic Form Games - Solution Concepts Asu Ozdaglar MIT February 9, 2010 1 Introduction Outline Review Examples of Pure Strategy Nash Equilibria
More informationBuyback Auctions for Fisheries Management. Guilherme de Freitas, OpenX Ted Groves, UCSD John Ledyard, Caltech Brian Merlob, Caltech
Buyback Auctions for Fisheries Management Guilherme de Freitas, OpenX Ted Groves, UCSD John Ledyard, Caltech Brian Merlob, Caltech Background Many, if not most, national and international fisheries are
More informationMA200.2 Game Theory II, LSE
MA200.2 Game Theory II, LSE Answers to Problem Set [] In part (i), proceed as follows. Suppose that we are doing 2 s best response to. Let p be probability that player plays U. Now if player 2 chooses
More informationMA200.2 Game Theory II, LSE
MA200.2 Game Theory II, LSE Problem Set 1 These questions will go over basic game-theoretic concepts and some applications. homework is due during class on week 4. This [1] In this problem (see Fudenberg-Tirole
More informationClaremont McKenna College. Stochastically Equivalent Sequential Auctions with Multi-Unit Demands. Submitted to. Professor Yaron Raviv.
Claremont McKenna College Stochastically Equivalent Sequential Auctions with Multi-Unit Demands Submitted to Professor Yaron Raviv and Dean Nicholas Warner by Tongjia Shi for Senior Thesis Spring 2015
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationParkes Auction Theory 1. Auction Theory. Jacomo Corbo. School of Engineering and Applied Science, Harvard University
Parkes Auction Theory 1 Auction Theory Jacomo Corbo School of Engineering and Applied Science, Harvard University CS 286r Spring 2007 Parkes Auction Theory 2 Auctions: A Special Case of Mech. Design Allocation
More informationComparing Allocations under Asymmetric Information: Coase Theorem Revisited
Comparing Allocations under Asymmetric Information: Coase Theorem Revisited Shingo Ishiguro Graduate School of Economics, Osaka University 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan August 2002
More informationKIER DISCUSSION PAPER SERIES
KIER DISCUSSION PAPER SERIES KYOTO INSTITUTE OF ECONOMIC RESEARCH http://www.kier.kyoto-u.ac.jp/index.html Discussion Paper No. 657 The Buy Price in Auctions with Discrete Type Distributions Yusuke Inami
More informationCommitment in First-price Auctions
Commitment in First-price Auctions Yunjian Xu and Katrina Ligett November 12, 2014 Abstract We study a variation of the single-item sealed-bid first-price auction wherein one bidder (the leader) publicly
More informationIntroduction to Political Economy Problem Set 3
Introduction to Political Economy 14.770 Problem Set 3 Due date: Question 1: Consider an alternative model of lobbying (compared to the Grossman and Helpman model with enforceable contracts), where lobbies
More informationEfficiency in Decentralized Markets with Aggregate Uncertainty
Efficiency in Decentralized Markets with Aggregate Uncertainty Braz Camargo Dino Gerardi Lucas Maestri December 2015 Abstract We study efficiency in decentralized markets with aggregate uncertainty and
More informationEcon 101A Final exam May 14, 2013.
Econ 101A Final exam May 14, 2013. Do not turn the page until instructed to. Do not forget to write Problems 1 in the first Blue Book and Problems 2, 3 and 4 in the second Blue Book. 1 Econ 101A Final
More informationElements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition
Elements of Economic Analysis II Lecture XI: Oligopoly: Cournot and Bertrand Competition Kai Hao Yang /2/207 In this lecture, we will apply the concepts in game theory to study oligopoly. In short, unlike
More informationMarch 30, Why do economists (and increasingly, engineers and computer scientists) study auctions?
March 3, 215 Steven A. Matthews, A Technical Primer on Auction Theory I: Independent Private Values, Northwestern University CMSEMS Discussion Paper No. 196, May, 1995. This paper is posted on the course
More informationCS711 Game Theory and Mechanism Design
CS711 Game Theory and Mechanism Design Problem Set 1 August 13, 2018 Que 1. [Easy] William and Henry are participants in a televised game show, seated in separate booths with no possibility of communicating
More informationIndependent Private Value Auctions
John Nachbar April 16, 214 ndependent Private Value Auctions The following notes are based on the treatment in Krishna (29); see also Milgrom (24). focus on only the simplest auction environments. Consider
More informationSequential Auctions and Auction Revenue
Sequential Auctions and Auction Revenue David J. Salant Toulouse School of Economics and Auction Technologies Luís Cabral New York University November 2018 Abstract. We consider the problem of a seller
More informationAuctions. Microeconomics II. Auction Formats. Auction Formats. Many economic transactions are conducted through auctions treasury bills.
Auctions Microeconomics II Auctions Levent Koçkesen Koç University Many economic transactions are conducted through auctions treasury bills art work foreign exchange antiques publicly owned companies cars
More informationAuctions 1: Common auctions & Revenue equivalence & Optimal mechanisms. 1 Notable features of auctions. use. A lot of varieties.
1 Notable features of auctions Ancient market mechanisms. use. A lot of varieties. Widespread in Auctions 1: Common auctions & Revenue equivalence & Optimal mechanisms Simple and transparent games (mechanisms).
More informationMA300.2 Game Theory 2005, LSE
MA300.2 Game Theory 2005, LSE Answers to Problem Set 2 [1] (a) This is standard (we have even done it in class). The one-shot Cournot outputs can be computed to be A/3, while the payoff to each firm can
More informationAdverse Selection, Reputation and Sudden Collapses in Securitized Loan Markets
Adverse Selection, Reputation and Sudden Collapses in Securitized Loan Markets V.V. Chari, Ali Shourideh, and Ariel Zetlin-Jones University of Minnesota & Federal Reserve Bank of Minneapolis November 29,
More informationProfit Sharing Auction
Profit Sharing Auction Sandip Sen and Teddy Candale and Susnata Basak athematical &Computer Sciences Department University of Tulsa {sandip, teddy-candale, susnata-basak}@utulsa.edu Abstract Auctions are
More informationRevenue Equivalence and Mechanism Design
Equivalence and Design Daniel R. 1 1 Department of Economics University of Maryland, College Park. September 2017 / Econ415 IPV, Total Surplus Background the mechanism designer The fact that there are
More informationConsider the following (true) preference orderings of 4 agents on 4 candidates.
Part 1: Voting Systems Consider the following (true) preference orderings of 4 agents on 4 candidates. Agent #1: A > B > C > D Agent #2: B > C > D > A Agent #3: C > B > D > A Agent #4: D > C > A > B Assume
More informationAuction Theory: Some Basics
Auction Theory: Some Basics Arunava Sen Indian Statistical Institute, New Delhi ICRIER Conference on Telecom, March 7, 2014 Outline Outline Single Good Problem Outline Single Good Problem First Price Auction
More informationBuy or wait, that is the option
Buy or wait, that is the option The buyer s option in sequential laboratory auctions Philippe Février, Laurent Linnemer and Michael Visser Abstract This paper reports the results from an experiment on
More informationPhD Qualifier Examination
PhD Qualifier Examination Department of Agricultural Economics May 29, 2014 Instructions This exam consists of six questions. You must answer all questions. If you need an assumption to complete a question,
More informationpreferences of the individual players over these possible outcomes, typically measured by a utility or payoff function.
Leigh Tesfatsion 26 January 2009 Game Theory: Basic Concepts and Terminology A GAME consists of: a collection of decision-makers, called players; the possible information states of each player at each
More informationMicroeconomic Theory III Spring 2009
MIT OpenCourseWare http://ocw.mit.edu 14.123 Microeconomic Theory III Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MIT 14.123 (2009) by
More informationUniversity of Hong Kong
University of Hong Kong ECON6036 Game Theory and Applications Problem Set I 1 Nash equilibrium, pure and mixed equilibrium 1. This exercise asks you to work through the characterization of all the Nash
More information6.207/14.15: Networks Lecture 10: Introduction to Game Theory 2
6.207/14.15: Networks Lecture 10: Introduction to Game Theory 2 Daron Acemoglu and Asu Ozdaglar MIT October 14, 2009 1 Introduction Outline Review Examples of Pure Strategy Nash Equilibria Mixed Strategies
More informationProblem Set: Contract Theory
Problem Set: Contract Theory Problem 1 A risk-neutral principal P hires an agent A, who chooses an effort a 0, which results in gross profit x = a + ε for P, where ε is uniformly distributed on [0, 1].
More informationGame Theory Problem Set 4 Solutions
Game Theory Problem Set 4 Solutions 1. Assuming that in the case of a tie, the object goes to person 1, the best response correspondences for a two person first price auction are: { }, < v1 undefined,
More informationAn Experiment on Asymmetric Information in First-Price Common-Value Auctions: The Blessed Winner 1
An Experiment on Asymmetric Information in First-Price Common-Value Auctions: The Blessed Winner 1 Brit Grosskopf Department of Economics University of Exeter Exeter, United Kingdom b.grosskopf@exeter.ac.uk
More informationGathering Information before Signing a Contract: a New Perspective
Gathering Information before Signing a Contract: a New Perspective Olivier Compte and Philippe Jehiel November 2003 Abstract A principal has to choose among several agents to fulfill a task and then provide
More informationOn the benefits of set-asides
On the benefits of set-asides Laurent Lamy (joint with Philippe Jehiel) Paris School of Economics NUS and HKUST, october 2015 Introduction Set-asides: a popular instrument in public procurements: In Japan,
More informationMicroeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 2017
Microeconomic Theory II Preliminary Examination Solutions Exam date: August 7, 017 1. Sheila moves first and chooses either H or L. Bruce receives a signal, h or l, about Sheila s behavior. The distribution
More informationAn Examination of the Efficiency of Resource Allocation Auctions Within Firms 1
An Examination of the Efficiency of Resource Allocation Auctions Within Firms 1 Stanley Baiman 2 Paul Fischer 3 Madhav V. Rajan 4 Richard Saouma 5 December 1, 2006 1 We are indebted to Stefan Reichelstein,
More informationPAULI MURTO, ANDREY ZHUKOV. If any mistakes or typos are spotted, kindly communicate them to
GAME THEORY PROBLEM SET 1 WINTER 2018 PAULI MURTO, ANDREY ZHUKOV Introduction If any mistakes or typos are spotted, kindly communicate them to andrey.zhukov@aalto.fi. Materials from Osborne and Rubinstein
More informationECON 459 Game Theory. Lecture Notes Auctions. Luca Anderlini Spring 2017
ECON 459 Game Theory Lecture Notes Auctions Luca Anderlini Spring 2017 These notes have been used and commented on before. If you can still spot any errors or have any suggestions for improvement, please
More informationPrice Theory of Two-Sided Markets
The E. Glen Weyl Department of Economics Princeton University Fundação Getulio Vargas August 3, 2007 Definition of a two-sided market 1 Two groups of consumers 2 Value from connecting (proportional to
More informationSocial Network Analysis
Lecture IV Auctions Kyumars Sheykh Esmaili Where Are Auctions Appropriate? Where sellers do not have a good estimate of the buyers true values for an item, and where buyers do not know each other s values
More informationEcon 8602, Fall 2017 Homework 2
Econ 8602, Fall 2017 Homework 2 Due Tues Oct 3. Question 1 Consider the following model of entry. There are two firms. There are two entry scenarios in each period. With probability only one firm is able
More informationPractice Problems 2: Asymmetric Information
Practice Problems 2: Asymmetric Information November 25, 2013 1 Single-Agent Problems 1. Nonlinear Pricing with Two Types Suppose a seller of wine faces two types of customers, θ 1 and θ 2, where θ 2 >
More informationTwo hours. To be supplied by the Examinations Office: Mathematical Formula Tables and Statistical Tables THE UNIVERSITY OF MANCHESTER
Two hours MATH20802 To be supplied by the Examinations Office: Mathematical Formula Tables and Statistical Tables THE UNIVERSITY OF MANCHESTER STATISTICAL METHODS Answer any FOUR of the SIX questions.
More informationChapter 3. Dynamic discrete games and auctions: an introduction
Chapter 3. Dynamic discrete games and auctions: an introduction Joan Llull Structural Micro. IDEA PhD Program I. Dynamic Discrete Games with Imperfect Information A. Motivating example: firm entry and
More informationFinancial Economics Field Exam August 2011
Financial Economics Field Exam August 2011 There are two questions on the exam, representing Macroeconomic Finance (234A) and Corporate Finance (234C). Please answer both questions to the best of your
More informationDiscrete models in microeconomics and difference equations
Discrete models in microeconomics and difference equations Jan Coufal, Soukromá vysoká škola ekonomických studií Praha The behavior of consumers and entrepreneurs has been analyzed on the assumption that
More informationSo we turn now to many-to-one matching with money, which is generally seen as a model of firms hiring workers
Econ 805 Advanced Micro Theory I Dan Quint Fall 2009 Lecture 20 November 13 2008 So far, we ve considered matching markets in settings where there is no money you can t necessarily pay someone to marry
More informationAuctions in the wild: Bidding with securities. Abhay Aneja & Laura Boudreau PHDBA 279B 1/30/14
Auctions in the wild: Bidding with securities Abhay Aneja & Laura Boudreau PHDBA 279B 1/30/14 Structure of presentation Brief introduction to auction theory First- and second-price auctions Revenue Equivalence
More informationNotes for Section: Week 7
Economics 160 Professor Steven Tadelis Stanford University Spring Quarter, 004 Notes for Section: Week 7 Notes prepared by Paul Riskind (pnr@stanford.edu). spot errors or have questions about these notes.
More informationApplicant Auction Conference
Applicant Auction Conference Using auctions to resolve string contentions efficiently and fairly in a simple and transparent process Peter Cramton, Chairman Cramton Associates www.applicantauction.com
More informationPROBLEM SET 6 ANSWERS
PROBLEM SET 6 ANSWERS 6 November 2006. Problems.,.4,.6, 3.... Is Lower Ability Better? Change Education I so that the two possible worker abilities are a {, 4}. (a) What are the equilibria of this game?
More informationBayesian games and their use in auctions. Vincent Conitzer
Bayesian games and their use in auctions Vincent Conitzer conitzer@cs.duke.edu What is mechanism design? In mechanism design, we get to design the game (or mechanism) e.g. the rules of the auction, marketplace,
More informationSolution to Assignment 3
Solution to Assignment 3 0/03 Semester I MA6 Game Theory Tutor: Xiang Sun October 5, 0. Question 5, in Tutorial set 5;. Question, in Tutorial set 6; 3. Question, in Tutorial set 7. Solution for Question
More informationResource Allocation Auctions Within Firms
University of Pennsylvania ScholarlyCommons Accounting Papers Wharton Faculty Research 12-2007 Resource Allocation Auctions Within Firms Stanley Baiman University of Pennsylvania Paul E. Fischer University
More informationPh.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017
Ph.D. Preliminary Examination MICROECONOMIC THEORY Applied Economics Graduate Program June 2017 The time limit for this exam is four hours. The exam has four sections. Each section includes two questions.
More informationA simulation study of two combinatorial auctions
A simulation study of two combinatorial auctions David Nordström Department of Economics Lund University Supervisor: Tommy Andersson Co-supervisor: Albin Erlanson May 24, 2012 Abstract Combinatorial auctions
More informationAuction theory. Filip An. U.U.D.M. Project Report 2018:35. Department of Mathematics Uppsala University
U.U.D.M. Project Report 28:35 Auction theory Filip An Examensarbete i matematik, 5 hp Handledare: Erik Ekström Examinator: Veronica Crispin Quinonez Augusti 28 Department of Mathematics Uppsala University
More informationAuctions. Michal Jakob Agent Technology Center, Dept. of Computer Science and Engineering, FEE, Czech Technical University
Auctions Michal Jakob Agent Technology Center, Dept. of Computer Science and Engineering, FEE, Czech Technical University AE4M36MAS Autumn 2015 - Lecture 12 Where are We? Agent architectures (inc. BDI
More informationThe Optimality of Being Efficient. Lawrence Ausubel and Peter Cramton Department of Economics University of Maryland
The Optimality of Being Efficient Lawrence Ausubel and Peter Cramton Department of Economics University of Maryland 1 Common Reaction Why worry about efficiency, when there is resale? Our Conclusion Why
More informationInefficiency of Collusion at English Auctions
Inefficiency of Collusion at English Auctions Giuseppe Lopomo Duke University Robert C. Marshall Penn State University June 17, 2005 Leslie M. Marx Duke University Abstract In its attempts to deter and
More information