Lecture 10: Auction Mechanisms
|
|
- Brandon Warren
- 5 years ago
- Views:
Transcription
1 Microeconomics I: Game Theory Lecture 10: Auction Mechanisms (see Osborne, 2009, Sect 3.5) Dr. Michael Trost Department of Applied Microeconomics January 17, 2014 Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 1 / 23
2 Auctions An auction is a mechanism for the selling of objects by means of bids submitted by the potential buyers. Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 2 / 23
3 Auctions as allocation mechanisms Auctions are used to allocate economic resources, e.g., work of arts (e.g., The Scream of Edvard Munch for approx. $ 120 mio. in May 2, 2012) Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 3 / 23
4 Auctions as allocation mechanisms Auctions are used to allocate economic resources, e.g., government bonds (e.g., weekly auctions of US Treasury Bills) offshore oil drilling rights (e.g., auction of offshore oil drilling rights in the central Gulf of Mexico in June 20, 2012 ). radio spectrum licenses (e.g., auction of UMTS licenses in 2000 in Germany) merchandise (e.g., online auctions of merchandise in ebay) Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 4 / 23
5 Sealed-bid single-object auctions In this lecture, we restrict ourselves to auctions in which a single object is offered by the auctioneer (so called single-object auctions). the potential buyers submit once and simultaneously a monetary bid for the offered object (so called sealed-bid auctions). Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 5 / 23
6 Auction mechanism An auction mechanism is specific set of rules that determines the course of the auction. These rules stipulate the set of participants of auctions, the set of possible bids the participants are allowed to submit, how a winner is determined by the submitted bids, how much the participants of the auctions must pay for their submitted bids. Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 6 / 23
7 Bidders and bids An auction mechanism is a set of rules which specifies 1 a finite non-empty set I of potential buyers (called bidders) 2 for each bidder i I, a set of possible non-negative real-valued bids b i B i [0, + [. A profile b := (b i ) i I i I B i of bids is a list summarizing the bids submitted by the bidders. Henceforth, the set of all bid profiles is denoted by B := i I B i. Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 7 / 23
8 Winning function An auction mechanism is a set of rules which specifies 3 a winning function w : B (I ) that assigns to each bid profile b := (b i ) i I B a probability vector on I according to which the winner of the auction (i.e., the buyer who receives the object) is chosen. Function w i : B [0, 1] denotes the winning function of bidder i I and gives the probability that i wins the auction if bid profile b B is realized. Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 8 / 23
9 Cost function An auction mechanism is a set of rules which specifies 4 for each bidder i I, a cost function C i : B [0, + [ of bidder i that determines for every bid profile b := (b i ) i I B the payment bidder i must make. Dr. Michael Trost Microeconomics I: Game Theory Lecture 10 9 / 23
10 Auction mechanism Definition 10.1 An auction mechanism A := (I, (B i ) i I, w, (C i ) i I ) consists of the components a finite non-empty set I of bidders, for each bidder i I, a non-empty set B i [0, + [ of possible bids. a winner function w : B (I ) specifying the winner of the auction, for each bidder i I, a cost function C i : B [0, + [ specifying the payment i must settle. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
11 Auctions with free zero-bids An auction mechanism A is said to be an auction with free zero-bids if C i (b) = 0 holds for every bidder i I and for every bid profile b B satisfying b i = 0. This condition says the submission of a bid of zero does not induce any payments for bidders. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
12 Standard auction An auction mechanism A is termed a standard auction whenever the bidder with highest bid is the winner of the auction, and in case there are several bidders who have submitted the highest bid a random device is applied according to which each of them is chosen with the same probability to be the winner of the auction. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
13 Winner set Consider some auction A := (I, (B i ) i I, w, (C i ) i I ). Denote by W (b) the set of possible winners of auction A if bid profile b has been submitted, i.e. W (b) := {i I : w i (b) > 0}. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
14 Standard auction A standard auction is an auction in which 1 the winner set is given by W (b) = {i I : b i b j for every j I } for every bid profile b B. 2 the winning function of every player i I is given by w i (b) := { 1 #W (b) if i W (b), 0 if i / W (b). Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
15 First-price sealed-bid auction A first-price sealed-bid auction is an auction in which every bidder is allowed to submit any non-negative real-valued bid, and the bidder who has submitted the highest bid wins and pays the amount of money she has bid. Bidders who do not win the auction pay nothing. In the case several bidders have submitted the highest bid, a random device is applied according to which each of them is selected with equal probability to be the winner of the auction. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
16 First-price auction EXERCISE: Determine the components of the first-price auction! set of I := bidders set of B bids i := winning w : function cost C function i : Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
17 Second-price sealed-bid auction A second-price sealed-bid auction is an auction in which every bidder is allowed to submit any non-negative realvalued bid, and the bidder who has submitted the highest bid wins and pays the amount of money equal to the second highest bid. Bidder who do not win the auction pay nothing. In case several bidders have submitted the highest bid, a random device is applied according to which each of them is selected with equal probability to be the winner of the auction. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
18 Vickrey auction Second-price sealed bid auctions are also known as Vickrey auctions. Economist William Vickrey was the first who studied properties of this auction form. William Vickrey (June 21, October 11, 1996) received in 1996 the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for fundamental contributions to the economic theory of incentives under asymmetric information. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
19 Vickrey auction EXERCISE: Determine the components of the Vickrey auction! set of I := bidders set of B bids i := winning w : function cost C function i : Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
20 All-pay sealed-bid auction An all-pay sealed-bid auction is an auction in which every bidder is allowed to submit any non-negative real-valued bid, and the bidder who has submitted the highest bid wins. Each bidder must pay the amount of money equal to her submitted bid regardless if she has won the auction, or not. In case several bidders have submitted the highest bid, a random device is applied according to which each of them is selected with equal probability to be the winner of the auction. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
21 All-pay sealed-bid auction EXERCISE: Determine the components of the all-pay sealed-bid auction! set of I := bidders set of B bids i := winning w : function cost C function i : Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
22 Sealed-bid lottery auction A sealed-bid lottery auction is an auction in which every bidder is allowed to submit any non-negative real- valued bid. The winner is chosen by a random device according to which each bidder is selected with the probability equal to the fraction of her bid on the total sum of the bids. In case all bidders have submitted a bid of zero each of them is selected with the same probability to be the winner of the auction. The winner of the auction pays the amount he submitted while the other bidders pay nothing. Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
23 Sealed-bid lottery auction EXERCISE: Determine the components of a sealed-bid lottery auction! Is this auction mechanism a standard auction? set of I := bidders set of B bids i := winning w : function cost C function i : Dr. Michael Trost Microeconomics I: Game Theory Lecture / 23
Introduction: What is Game Theory?
Microeconomics I: Game Theory Introduction: What is Game Theory? (see Osborne, 2009, Sect 1.1) Dr. Michael Trost Department of Applied Microeconomics October 25, 2013 Dr. Michael Trost Microeconomics I:
More informationLecture 3: Nash Equilibrium
Microeconomics I: Game Theory Lecture 3: Nash Equilibrium (see Osborne, 2009, Sect 2.1-2.7) Dr. Michael Trost Department of Applied Microeconomics November 8, 2013 Dr. Michael Trost Microeconomics I: Game
More informationLecture 12: Extensive Games with Perfect Information
Microeconomics I: Game Theory Lecture 12: Extensive Games with Perfect Information (see Osborne, 2009, Sections 5.1,6.1) Dr. Michael Trost Department of Applied Microeconomics January 31, 2014 Dr. Michael
More informationLecture 7: Dominance Concepts
Microeconomics I: Game Theory Lecture 7: Dominance Concepts (see Osborne, 2009, Sect 2.7.8,2.9,4.4) Dr. Michael Trost Department of Applied Microeconomics December 6, 2013 Dr. Michael Trost Microeconomics
More informationSummary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility
Summary Overview of Topics in Econ 30200b: Decision theory: strong and weak domination by randomized strategies, domination theorem, expected utility theorem (consistent decisions under uncertainty should
More informationThe Last Diminisher Method Game Steps
Chapter 3 Notes from The Last Diminisher Method Game Steps Start: randomly assign player order P 1, P 2, P 3,... P N. (For instance, each player could draw a number from a hat, in which there are the numbers
More informationN represents the number of players (at least 3).
Section 5. The last-diminisher method. N represents the number of players (at least 3). First order the players: P1, P2, P3 etc. Basic principle: the first player in each round marks a piece and claims
More informationRULES AND REGULATIONS
RULES AND REGULATIONS 1. About the PowerBall and PowerBall PLUS Games The following are the essential features of the PowerBall and PowerBall PLUS Games as approved by the National Lotteries Commission
More informationebay in the Sky: StrategyProof Wireless Spectrum Auctions
ebay in the Sky: StrategyProof Wireless Spectrum Auctions Xia Zhou, Sorabh Gandhi, Subhash Suri, Heather Zheng Department of Computer Science University of California, Santa Barbara IUSTITIA (Goddess of
More informationThere are several schemes that we will analyze, namely: The Knaster Inheritance Procedure. Cake-Division Procedure: Proportionality
Chapter 13 Fair Division Fair Division Problems When demands or desires of one party are in conflict with those of another; however, objects must be divided or contents must be shared in such a way that
More informationCOMPSCI 223: Computational Microeconomics - Practice Final
COMPSCI 223: Computational Microeconomics - Practice Final 1 Problem 1: True or False (24 points). Label each of the following statements as true or false. You are not required to give any explanation.
More informationGame Theory and Algorithms Lecture 3: Weak Dominance and Truthfulness
Game Theory and Algorithms Lecture 3: Weak Dominance and Truthfulness March 1, 2011 Summary: We introduce the notion of a (weakly) dominant strategy: one which is always a best response, no matter what
More informationSPECIAL: A Strategy-Proof and Efficient Multi-Channel Auction Mechanism for Wireless Networks
2013 Proceedings IEEE INFOCOM SPECIAL: A Strategy-Proof and Efficient Multi-Channel Auction Mechanism for Wireless Networks Tianrong Zhang Fan Wu Chunming Qiao Department of Computer Science and Engineering,
More informationAlgorithmic Game Theory and Applications. Kousha Etessami
Algorithmic Game Theory and Applications Lecture 17: A first look at Auctions and Mechanism Design: Auctions as Games, Bayesian Games, Vickrey auctions Kousha Etessami Food for thought: sponsored search
More informationLecture 6: Basics of Game Theory
0368.4170: Cryptography and Game Theory Ran Canetti and Alon Rosen Lecture 6: Basics of Game Theory 25 November 2009 Fall 2009 Scribes: D. Teshler Lecture Overview 1. What is a Game? 2. Solution Concepts:
More informationRULES AND REGULATIONS
1. ABOUT LOTTO, LOTTO PLUS 1 & LOTTO PLUS 2 1.2 If the Entry is rejected by the Terminal or Site, there is no valid Entry. 1.1 The following are the essential Game features for LOTTO, LOTTO PLUS 1 & LOTTO
More informationMultidimensional Ellsberg: Online Appendix
Multidimensional Ellsberg: Online Appendix Kfir Eliaz and Pietro Ortoleva A Additional analysis of the Lab data Table A.1: Effect of a fixed ambiguous dimension (green). Department of Economics, Tel Aviv
More informationMicroeconomics of Banking: Lecture 4
Microeconomics of Banking: Lecture 4 Prof. Ronaldo CARPIO Oct. 16, 2015 Administrative Stuff Homework 1 is due today at the end of class. I will upload the solutions and Homework 2 (due in two weeks) later
More informationCopyright 2008, Yan Chen
Unless otherwise noted, the content of this course material is licensed under a Creative Commons Attribution Non-Commercial 3.0 License. http://creativecommons.org/licenses/by-nc/3.0/ Copyright 2008, Yan
More informationTopic 1: defining games and strategies. SF2972: Game theory. Not allowed: Extensive form game: formal definition
SF2972: Game theory Mark Voorneveld, mark.voorneveld@hhs.se Topic 1: defining games and strategies Drawing a game tree is usually the most informative way to represent an extensive form game. Here is one
More information14.12 Game Theory Lecture Notes Lectures 10-11
4.2 Game Theory Lecture Notes Lectures 0- Muhamet Yildiz Repeated Games In these notes, we ll discuss the repeated games, the games where a particular smaller game is repeated; the small game is called
More informationMath 152: Applicable Mathematics and Computing
Math 152: Applicable Mathematics and Computing April 16, 2017 April 16, 2017 1 / 17 Announcements Please bring a blue book for the midterm on Friday. Some students will be taking the exam in Center 201,
More informationIntroduction to Game Theory
Introduction to Game Theory Lecture 2 Lorenzo Rocco Galilean School - Università di Padova March 2017 Rocco (Padova) Game Theory March 2017 1 / 46 Games in Extensive Form The most accurate description
More informationA note on k-price auctions with complete information when mixed strategies are allowed
A note on k-price auctions with complete information when mixed strategies are allowed Timothy Mathews and Jesse A. Schwartz y Kennesaw State University September 1, 2016 Abstract Restricting attention
More informationAn extended description of the project:
A brief one paragraph description of your project: - Our project mainly focuses on dividing the indivisible properties. This method is applied in many situation of the real life such as: divorce, inheritance,
More informationCCST9017. Hidden Order in Daily Life:
CCST9017 Hidden Order in Daily Life: A Mathematical Perspective Lecture 4 Shapley Value and Power Indices I Prof. Patrick,Tuen Wai Ng Department of Mathematics, HKU Example 1: An advertising agent approaches
More informationResults of the Austrian Spectrum Auction. Vienna, 21 October 2013
Results of the Austrian Spectrum Auction Vienna, 21 October 2013 1 Cautionary Statement This document contains forward-looking statements. These forward-looking statements are usually accompanied by words
More informationPOLECONOMY THE GAME OF THE UNITED KINGDOM INTRODUCTION
POLECONOMY THE GAME OF THE UNITED KINGDOM INTRODUCTION Poleconorny is a role playing game about money and power where each player is both Tycoon and Politician. As a Tycoon buying and selling some of the
More informationCSCI 699: Topics in Learning and Game Theory Fall 2017 Lecture 3: Intro to Game Theory. Instructor: Shaddin Dughmi
CSCI 699: Topics in Learning and Game Theory Fall 217 Lecture 3: Intro to Game Theory Instructor: Shaddin Dughmi Outline 1 Introduction 2 Games of Complete Information 3 Games of Incomplete Information
More informationFrequency Management in the Environment of the Slovak Republic
Frequency Management in the Environment of the Slovak Republic Milan Mizera Regulatory Authority for Electronic Communications and Postal Services Introduction Frequency spectrum management in Slovakia
More informationA fair division procedure is equitable if each player believes he or she received the same fractional part of the total value.
Math 167 Ch 13 Review 1 (c) Janice Epstein CHAPTER 13 FAIR DIVISION A fair division procedure is equitable if each player believes he or she received the same fractional part of the total value. A fair
More informationECO 463. SimultaneousGames
ECO 463 SimultaneousGames Provide brief explanations as well as your answers. 1. Two people could benefit by cooperating on a joint project. Each person can either cooperate at a cost of 2 dollars or fink
More informationCHAPTER LEARNING OUTCOMES. By the end of this section, students will be able to:
CHAPTER 4 4.1 LEARNING OUTCOMES By the end of this section, students will be able to: Understand what is meant by a Bayesian Nash Equilibrium (BNE) Calculate the BNE in a Cournot game with incomplete information
More informationMarket driven dynamic spectrum allocation over space and time among radio-access. networks: DVB-T and B3G CDMA with heterogeneous terminals
Market driven dynamic spectrum allocation over space and time among radio-access networks: DVB-T and B3G CDMA with heterogeneous terminals Virgilio Rodriguez, Klaus Moessner, Rahim Tafazolli CCSR, The
More informationCONNECTICUT LOTTERY CORPORATION OFFICIAL GAME RULES Connecticut Lucky-4-Life"
CONNECTICUT LOTTERY CORPORATION OFFICIAL GAME RULES Connecticut Lucky-4-Life" Please take notice that the Connecticut Lottery Corporation (CLC) duly adopted, with the advice and consent of the Board of
More informationGame A. Auction Block
Auction Block The purpose of the game is for each player to try to accumulate as much wealth as possible. Each player is given $10,000 at the start of the game. Players roll dice and move around a game
More informationExtensive Games with Perfect Information. Start by restricting attention to games without simultaneous moves and without nature (no randomness).
Extensive Games with Perfect Information There is perfect information if each player making a move observes all events that have previously occurred. Start by restricting attention to games without simultaneous
More informationStudent Name. Student ID
Final Exam CMPT 882: Computational Game Theory Simon Fraser University Spring 2010 Instructor: Oliver Schulte Student Name Student ID Instructions. This exam is worth 30% of your final mark in this course.
More informationCMU Lecture 22: Game Theory I. Teachers: Gianni A. Di Caro
CMU 15-781 Lecture 22: Game Theory I Teachers: Gianni A. Di Caro GAME THEORY Game theory is the formal study of conflict and cooperation in (rational) multi-agent systems Decision-making where several
More informationA fair division procedure is equitable if each player believes he or she received the same fractional part of the total value.
(c) Epstein 2013 Chapter 13: Fair Division P a g e 1 CHAPTER 13: FAIR DIVISION Matthew and Jennifer must split 6 items between the two of them. There is a car, a piano, a Matisse print, a grandfather clock,
More informationfinal examination on May 31 Topics from the latter part of the course (covered in homework assignments 4-7) include:
The final examination on May 31 may test topics from any part of the course, but the emphasis will be on topic after the first three homework assignments, which were covered in the midterm. Topics from
More informationChapter 13. Game Theory
Chapter 13 Game Theory A camper awakens to the growl of a hungry bear and sees his friend putting on a pair of running shoes. You can t outrun a bear, scoffs the camper. His friend coolly replies, I don
More informationDistributed Optimization and Games
Distributed Optimization and Games Introduction to Game Theory Giovanni Neglia INRIA EPI Maestro 18 January 2017 What is Game Theory About? Mathematical/Logical analysis of situations of conflict and cooperation
More informationIncomplete Information. So far in this course, asymmetric information arises only when players do not observe the action choices of other players.
Incomplete Information We have already discussed extensive-form games with imperfect information, where a player faces an information set containing more than one node. So far in this course, asymmetric
More informationBasic Game Theory. Economics Auction Theory. Instructor: Songzi Du. Simon Fraser University. September 7, 2016
Basic Game Theory Economics 383 - Auction Theory Instructor: Songzi Du Simon Fraser University September 7, 2016 ECON 383 (SFU) Basic Game Theory September 7, 2016 1 / 7 Game Theory Game theory studies
More informationChapter 13: Fair Division
October 7, 2013 Motiving Question In 1991 Ivana and Donald Trump divorce. The marital assets included a 45-room mansion in Greenwich, Connecticut; the 118-room Mar-a-Lago mansion in Palm Beach, Florida;
More informationCalifornia State Lottery Commission. Susan S. Kossack, Deputy Director, Marketing
Date: To: California State Lottery Commission From: Joan M. Borucki Director Prepared By: Susan S. Kossack, Deputy Director, Marketing Subject: Item 9(b) Scratchers Game Profiles for Games 597, 598, 599,
More informationFinite games: finite number of players, finite number of possible actions, finite number of moves. Canusegametreetodepicttheextensiveform.
A game is a formal representation of a situation in which individuals interact in a setting of strategic interdependence. Strategic interdependence each individual s utility depends not only on his own
More informationGame Theory. Share information. Evaluate information (obtained from friends, acquaintances and coworkers) Develop trust. Accept or reject friendship
Æ ÇÌ Ë º ÅÁËÀÊ ÈÊÁÄ ¾ ¾¼½¾ Game Theory A social network is not a static structure the individuals in a social network must constantly interact in order to create social capital that reflects how a group
More informationGame theory attempts to mathematically. capture behavior in strategic situations, or. games, in which an individual s success in
Game Theory Game theory attempts to mathematically capture behavior in strategic situations, or games, in which an individual s success in making choices depends on the choices of others. A game Γ consists
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 Mechanism Design Environment Note: This is a only a draft
More informationVALUING SPECTRUM. Michael Honig Department of EECS Northwestern University. Based on a paper with Tom Hazlett. December 2016
VALUING SPECTRUM Michael Honig Department of EECS Northwestern University Based on a paper with Tom Hazlett. Spectrum Crunch 2 Petabytes per month Spectrum Policy is Important 3 Gross inefficiencies still
More informationIncentives and Game Theory
April 15, 2010 This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. Putting Utilitarianism to Work Example Suppose that you and your roomate are considering
More informationSTATE LOTTERIES ACT 1966 LOTTERIES (SET FOR LIFE) RULES
STATE LOTTERIES ACT 1966 LOTTERIES (SET FOR LIFE) RULES This consolidation is of effect as at 27 October 2016. It is provided for convenient reference only and regard should be had to the full text of
More informationAuctions with Manipulative Players
Auctions with Manipulative Players Sujit Prakash Gujar sujit@csa.iisc.ernet.in E-Commerce Lab Department of Computer Science and Automation Indian Institute of Science Bangalore-12 March 16, 2007 Sujit
More informationMath 1070 Sample Exam 2
University of Connecticut Department of Mathematics Math 1070 Sample Exam 2 Exam 2 will cover sections 4.6, 4.7, 5.2, 5.3, 5.4, 6.1, 6.2, 6.3, 6.4, F.1, F.2, F.3 and F.4. This sample exam is intended to
More informationExercises for Introduction to Game Theory SOLUTIONS
Exercises for Introduction to Game Theory SOLUTIONS Heinrich H. Nax & Bary S. R. Pradelski March 19, 2018 Due: March 26, 2018 1 Cooperative game theory Exercise 1.1 Marginal contributions 1. If the value
More informationCHAPTER 7 Probability
CHAPTER 7 Probability 7.1. Sets A set is a well-defined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can
More informationLevel 2. Intermediate. The Scream sells for record price at auction. Warmer
1 Warmer Name ten famous artists and the title of a painting by each of them. Write your answers in the picture frames. 2 Find the information Scan the article to find the information. 1. What is the name
More informationGame Theory and Economics of Contracts Lecture 4 Basics in Game Theory (2)
Game Theory and Economics of Contracts Lecture 4 Basics in Game Theory (2) Yu (Larry) Chen School of Economics, Nanjing University Fall 2015 Extensive Form Game I It uses game tree to represent the games.
More informationDynamic Games: Backward Induction and Subgame Perfection
Dynamic Games: Backward Induction and Subgame Perfection Carlos Hurtado Department of Economics University of Illinois at Urbana-Champaign hrtdmrt2@illinois.edu Jun 22th, 2017 C. Hurtado (UIUC - Economics)
More informationGame Theory and Randomized Algorithms
Game Theory and Randomized Algorithms Guy Aridor Game theory is a set of tools that allow us to understand how decisionmakers interact with each other. It has practical applications in economics, international
More informationSHOPPING MALL THEME OVERVIEW GAME SETUP
SHOPPING MALL 1 of 9 SHOPPING MALL Shopping Mall A Good Portsmanship Game For the piecepack by Michael Schoessow and Stephen Schoessow Based on MarraCash by Stefan Dorra Version #9 Copyright 2006 3-4 Players,
More informationProblem A To and Fro (Problem appeared in the 2004/2005 Regional Competition in North America East Central.)
Problem A To and Fro (Problem appeared in the 2004/2005 Regional Competition in North America East Central.) Mo and Larry have devised a way of encrypting messages. They first decide secretly on the number
More informationIEEE C802.16h-05/020. Proposal for credit tokens based co-existence resolution and negotiation protocol
Project Title Date Submitted IEEE 802.16 Broadband Wireless Access Working Group Proposal for credit tokens based co-existence resolution and negotiation protocol 2005-07-11 Source(s)
More informationMAKE TRADE FAIR GAME Printable Version
MAKE TRADE FAIR GAME Printable Version Welcome to the Make Trade Fair Game! This is a printable version that contains everything you need to play except a pair of dice. The objective of this game is to
More informationSection Summary. Finite Probability Probabilities of Complements and Unions of Events Probabilistic Reasoning
Section 7.1 Section Summary Finite Probability Probabilities of Complements and Unions of Events Probabilistic Reasoning Probability of an Event Pierre-Simon Laplace (1749-1827) We first study Pierre-Simon
More informationChapter 13: Fair Division
October 9, 2013 Last time Adjusted Winner Procedure Knaster s Inheritance procedure Adjusted Winner Procedure Basic Steps in the Adjusted Winner Procedure Step 0: Each party distributes 100 points over
More informationGAME RULES FOR DRAW-BASED GAMES PLAYED INTERACTIVELY. Issue 5 August 2018 INTRODUCTION
GAME RULES FOR DRAW-BASED GAMES PLAYED INTERACTIVELY Issue 5 August 2018 INTRODUCTION These Game Rules have been approved by the Regulator of the National Lottery in accordance with Section 45 of the National
More informationSPECTRUM access networks have recently attracted. Performance and Incentive of Teamwork-based Channel Allocation in Spectrum Access Networks
Performance and Incentive of Teamwork-based Channel Allocation in Spectrum Access Networks Yuchao ZHANG, Ke XU, Haiyang WANG, Jiangchuan LIU, Yifeng ZHONG, Wenlong CHEN Department of Computer Science &
More informationDYNAMIC GAMES. Lecture 6
DYNAMIC GAMES Lecture 6 Revision Dynamic game: Set of players: Terminal histories: all possible sequences of actions in the game Player function: function that assigns a player to every proper subhistory
More informationThe next several lectures will be concerned with probability theory. We will aim to make sense of statements such as the following:
CS 70 Discrete Mathematics for CS Fall 2004 Rao Lecture 14 Introduction to Probability The next several lectures will be concerned with probability theory. We will aim to make sense of statements such
More informationNEW SCRATCHERS AVAILABLE MAY 1
A Sales Guide for Virginia Lottery Retailers May 2018 NEW SCRATCHERS AVAILABLE MAY 1 PLEASE ACTIVATE AND PUT OUT FOR SALE BY MAY 3 CHILLIN' & GRILLIN' EVERY TUESDAY IN MAY WE LL BE GIVING AWAY FIVE $2,000
More informationBANKER S RESPONSIBILITIES. Distribute money at the beginning of the game. Dispense salaries and houses.
BANKER S RESPONSIBILITIES Before play begins, organize all Title Deed cards by color-groups, then shuffle each of the remaining decks of cards. Distribute money at the beginning of the game. Dispense salaries
More informationMAT 155. Key Concept. Notation. Fundamental Counting. February 09, S4.7_3 Counting. Chapter 4 Probability
MAT 155 Dr. Claude Moore Cape Fear Community College Chapter 4 Probability 4 1 Review and Preview 4 2 Basic Concepts of Probability 4 3 Addition Rule 4 4 Multiplication Rule: Basics 4 7 Counting Key Concept
More informationThe topic for the third and final major portion of the course is Probability. We will aim to make sense of statements such as the following:
CS 70 Discrete Mathematics for CS Spring 2006 Vazirani Lecture 17 Introduction to Probability The topic for the third and final major portion of the course is Probability. We will aim to make sense of
More informationSTATE LOTTERIES ACT 1966 LOTTERIES (MONDAY AND WEDNESDAY X LOTTO) RULES
STATE LOTTERIES ACT 1966 LOTTERIES (MONDAY AND WEDNESDAY X LOTTO) RULES This consolidation includes amendments as at 27 October 2016. It is provided for convenient reference only and regard should be had
More informationOrganization Team Team ID# If each of the congruent figures has area 1, what is the area of the square?
1. [4] A square can be divided into four congruent figures as shown: If each of the congruent figures has area 1, what is the area of the square? 2. [4] John has a 1 liter bottle of pure orange juice.
More information4.12 Practice problems
4. Practice problems In this section we will try to apply the concepts from the previous few sections to solve some problems. Example 4.7. When flipped a coin comes up heads with probability p and tails
More informationInstructions [CT+PT Treatment]
Instructions [CT+PT Treatment] 1. Overview Welcome to this experiment in the economics of decision-making. Please read these instructions carefully as they explain how you earn money from the decisions
More informationECON 282 Final Practice Problems
ECON 282 Final Practice Problems S. Lu Multiple Choice Questions Note: The presence of these practice questions does not imply that there will be any multiple choice questions on the final exam. 1. How
More informationLECTURE 26: GAME THEORY 1
15-382 COLLECTIVE INTELLIGENCE S18 LECTURE 26: GAME THEORY 1 INSTRUCTOR: GIANNI A. DI CARO ICE-CREAM WARS http://youtu.be/jilgxenbk_8 2 GAME THEORY Game theory is the formal study of conflict and cooperation
More informationMind Ninja The Game of Boundless Forms
Mind Ninja The Game of Boundless Forms Nick Bentley 2007-2008. email: nickobento@gmail.com Overview Mind Ninja is a deep board game for two players. It is 2007 winner of the prestigious international board
More informationComments filed with the Federal Communications Commission on the Notice of Proposed Rulemaking Transforming the 2.5 GHz Band
Comments filed with the Federal Communications Commission on the Notice of Proposed Rulemaking Transforming the 2.5 GHz Band June 2018 Thomas M. Lenard 409 12 th Street SW Suite 700 Washington, DC 20024
More informationCS510 \ Lecture Ariel Stolerman
CS510 \ Lecture04 2012-10-15 1 Ariel Stolerman Administration Assignment 2: just a programming assignment. Midterm: posted by next week (5), will cover: o Lectures o Readings A midterm review sheet will
More informationStock Trading Game. Rulebook
Stock Trading Game Rulebook Game Concept: Gregorius J. M. Tampubolon Andrew Hedy Tanoto Game Designer: Febndy & Lovita Darwin Artist: FEBNDY & Kevin Reynaldo AQUA TERRA VENTUS PRODUCTION 207 Table of Contents
More information18.S34 (FALL, 2007) PROBLEMS ON PROBABILITY
18.S34 (FALL, 2007) PROBLEMS ON PROBABILITY 1. Three closed boxes lie on a table. One box (you don t know which) contains a $1000 bill. The others are empty. After paying an entry fee, you play the following
More informationTikal 2 4 players aged 10 and up Authors: M. Kiesling / W. Kramer
Tikal 2 4 players aged 10 and up Authors: M. Kiesling / W. Kramer Contents 1 game board 36 terrain hexagons consisting of 15 temple hexagons 10 jungle hexagons 8 treasure hexagons 3 volcano hexagons 24
More informationAuctions as Games: Equilibria and Efficiency Near-Optimal Mechanisms. Éva Tardos, Cornell
Auctions as Games: Equilibria and Efficiency Near-Optimal Mechanisms Éva Tardos, Cornell Yesterday: Simple Auction Games item bidding games: second price simultaneous item auction Very simple valuations:
More informationCastles of Burgundy Rules Summary. Game board: Player board: TERMS
Castles of Burgundy Rules Summary TERMS Game board: Player board: Hex tiles: Silverling (Money) SETUP Silverling x 20, Worker x 30 as general supply (No. unlimited) Sort Hex tiles according to the color
More informationECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly
ECON 2100 Principles of Microeconomics (Summer 2016) Game Theory and Oligopoly Relevant readings from the textbook: Mankiw, Ch. 17 Oligopoly Suggested problems from the textbook: Chapter 17 Questions for
More informationWITH dramatically growing demand of spectrum for new
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64, NO. 2, FEBRUARY 2015 781 Multi-Item Spectrum Auction for Recall-Based Cognitive Radio Networks With Multiple Heterogeneous Secondary Users Changyan Yi
More informationECO 5341 Signaling Games: Another Example. Saltuk Ozerturk (SMU)
ECO 5341 : Another Example and Perfect Bayesian Equilibrium (PBE) (1,3) (2,4) Right Right (0,0) (1,0) With probability Player 1 is. With probability, Player 1 is. cannot observe P1 s type. However, can
More information3. Simultaneous-Move Games
3. Simultaneous-Move Games We now want to study the central question of game theory: how should a game be played. That is, what should we expect about the strategies that will be played in a game. We will
More informationChapter 4. Section 4.1: Divide and Choose Methods. Next: reading homework
Chapter 4 Section 4.1: Divide and Choose Methods Next: reading homework Reading Homework Read Section 4.2 Do problem 22 Next: fair division Fair Division Mathematical way of discussing how to divide resources
More informationGame Theory ( nd term) Dr. S. Farshad Fatemi. Graduate School of Management and Economics Sharif University of Technology.
Game Theory 44812 (1393-94 2 nd term) Dr. S. Farshad Fatemi Graduate School of Management and Economics Sharif University of Technology Spring 2015 Dr. S. Farshad Fatemi (GSME) Game Theory Spring 2015
More informationOBJECT To be the only player left in the game who is not bankrupt.
THE PROPERTY TRADING BOARD GAME RULES THE GAME IN BRIEF MONOPOLY is the game of buying, renting or selling Properties so profitably that players increase their wealth the wealthiest becoming the eventual
More informationSubject: Comments on planned amendment of Gambling Activities Act in Poland.
4 rue de la Presse 1000 Brussels info@eogl.eu Brussels, 29 November 2016 DG Internal Market, Industry, Entrepreneurship and SMEs DG GROW/B/2 N105 4/66 B-1049 Brussels Att: Mr. Giuseppe Cassela Mr. Martin
More informationSuppose Y is a random variable with probability distribution function f(y). The mathematical expectation, or expected value, E(Y) is defined as:
Suppose Y is a random variable with probability distribution function f(y). The mathematical expectation, or expected value, E(Y) is defined as: E n ( Y) y f( ) µ i i y i The sum is taken over all values
More informationComprehensive Rules Document v1.1
Comprehensive Rules Document v1.1 Contents 1. Game Concepts 100. General 101. The Golden Rule 102. Players 103. Starting the Game 104. Ending The Game 105. Kairu 106. Cards 107. Characters 108. Abilities
More information