# CMSC 474, Introduction to Game Theory Analyzing Normal-Form Games

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 CMSC 474, Introduction to Game Theory Analyzing Normal-Form Games Mohammad T. Hajiaghayi University of Maryland

2 Some Comments about Normal-Form Games Only two kinds of strategies in the normal-form game representation: Pure strategy: just a single action Mixed strategy: probability distribution over pure strategies i.e., choose an action at random from the probability distribution The normal-form game representation may see very restricted No such thing as a conditional strategy (e.g., cross the bay if the temperature is above 70) No temperature or anything else to observe However much more complicated games can be mapped into normal-form games Each pure strategy is a description of what you ll do in every situation you might ever encounter in the game In later sessions, we see more examples C D C 3, 3 0, 5 D 5, 0 1, 1

3 How to reason about games? In single-agent decision theory, look at an optimal strategy Maximize the agent s expected payoff in its environment With multiple agents, the best strategy depends on others choices Deal with this by identifying certain subsets of outcomes called solution concepts This second chapter of the book discusses two solution concepts: Pareto optimality Nash equilibrium Chapter 3 will discuss several others

4 Pareto Optimality A strategy profile s Pareto dominates a strategy profile s if no agent gets a worse payoff with s than with s, i.e., u i (s) u i (s ) for all i, at least one agent gets a better payoff with s than with s, i.e., u i (s) > u i (s ) for at least one i A strategy profile s is Pareto optimal (or Pareto efficient) if there s no strategy profile s' that Pareto dominates s Every game has at least one Pareto optimal profile Always at least one Pareto optimal profile in which the strategies are pure Proof: Find a pure strategy profile with the highest payoff p for agent 1 (note that no pure or mixed strategy can have a higher payoff than p for agent 1). Now among all pure strategy profiles for which agent 1 has payoff p, find the one with highest payoff for agent 2 and recurse; the pure strategy profile at the end is Pareto optimal. Is a pure strategy with maximum sum of payoffs is a Pareto optimal one? Yes but we leave the proof as an exercise.

5 Examples C D C 3, 3 0, 5 The Prisoner s Dilemma D 5, 0 1, 1 (D,C) is Pareto optimal: no profile gives player 1 a higher payoff (C, D) is Pareto optimal: no profile gives player 2 a higher payoff (C,C) is Pareto optimal: no profile gives both players a higher payoff (D,D) isn t Pareto optimal: (C,C) Pareto dominates it Which Side of the Road (Left,Left) and (Right,Right) are Pareto optimal In common-payoff games, all Pareto optimal strategy profiles have the same payoffs If (Left,Left) had payoffs (2,2), then (Right,Right) wouldn t be Pareto optimal Left Right Left 1, 1 0, 0 Right 0, 0 1, 1

6 Best Response Suppose agent i knows how the others are going to play Then i has an ordinary optimization problem: maximize expected utility We ll use s i to mean a strategy profile for all of the agents except i s i = (s 1,, s i 1, s i+1,, s n ) Let s i be any strategy for agent i. Then (s i, s i ) = (s 1,, s i 1, s i, s i+1,, s n ) s i is a best response to s i if for every strategy s i available to agent i, u i (s i, s i ) u i (s i, s i ) There is always at least one best response A best response s i is unique if u i (s i, s i ) > u i (s i, s i ) for every s i s i

7 Best Response Given s i, there are only two possibilities: (1) i has a pure strategy s i that is a unique best response to s i (2) i has infinitely many best responses to s i Proof. Suppose (1) is false. Then there are two possibilities: Case 1: s i isn t unique, i.e., 2 strategies are best responses to s i Then they all must have the same expected utility Otherwise, they aren t all best Thus any mixture of them is also a best response Case 2: s i isn t pure, i.e., it s a mixture of k > 2 actions The actions correspond to pure strategies, so this reduces to Case 1 Theorem: Always there exists a pure best response s i to s i Proof. In both (1) and (2) above, there should be one pure best response.

8 Example Suppose we modify the Prisoner s Dilemma to give Agent 1 another possible action: Suppose 2 s strategy is to play action C What are 1 s best responses? Suppose 2 s strategy is to play action D What are 1 s best responses? C D C 3, 3 0, 5 D 5, 0 1, 1 E 3, 3 1, 3

9 Nash Equilibrium s = (s 1,, s n ) is a Nash equilibrium if for every i, s i is a best response to s i Every agent s strategy is a best response to the other agents strategies No agent can do better by unilaterally changing his/her strategy Theorem (Nash, 1951): Every game with a finite number of agents and actions has at least one Nash equilibrium Left Right In Which Side of the Road, (Left,Left) and (Right,Right) are Nash equilibria Left 1, 1 0, 0 Right 0, 0 1, 1 In the Prisoner s Dilemma, (D,D) is a Nash equilibrium Ironically, it s the only pure-strategy profile that isn t Pareto optimal C D C 3, 3 0, 5 D 5, 0 1, 1

10 Strict Nash Equilibrium A Nash equilibrium s = (s 1,..., s n ) is strict if for every i, s i is the only best response to s i i.e., any agent who unilaterally changes strategy will do worse Recall that if a best response is unique, it must be pure It follows that in a strict Nash equilibrium, all of the strategies are pure But if a Nash equilibrium is pure, it isn t necessarily strict Which of the following Nash equilibria are strict? Why? C D C 3, 3 0, 5 C D C 3, 3 0, 4 Left Right Left 1, 1 0, 0 Left Right Left 1, 1 0, 0 Right 0, 0 1, 1 D 5, 0 1, 1 D 4, 0 1, 1 Right 0, 0 1, 1 Center 0, 0 1, ½

11 Weak Nash Equilibrium If a Nash equilibrium s isn t strict, then it is weak At least one agent i has more than one best response to s i If a Nash equilibrium includes a mixed strategy, then it is weak If a mixture of k => 2 actions is a best response to s i, then any other mixture of the actions is also a best response If a Nash equilibrium consists only of pure strategies, it might still be weak Left Right Weak Nash equilibria are less stable than strict Nash equilibria If a Nash equilibrium is weak, then at least one agent has infinitely many best responses, and only one of them is in s Left 1, 1 0, 0 Right 0, 0 1, 1 Center 0, 0 1, ½

### Analytic Preliminaries for Social Acceptability of Legal Norms &

Analytic Preliminaries for Social Acceptability of John Asker February 7, 2013 Yale Law School Roadmap Build on case studies of environments where extra-legal norms are at least as important as formal

### Game theory (Sections )

Game theory (Sections 17.5-17.6) Game theory Game theory deals with systems of interacting agents where the outcome for an agent depends on the actions of all the other agents Applied in sociology, politics,

### EC493f Review Sheet 1

Econ 493f Law and Economics Spring 2017 1 Identify and/or Define: a. Codex of Hammurabi l. Dominant Strategy b. Marginal Cost m. Nash Equilibrium c. Net Benefit n. Optimal Crime Rate d. Expected Penalty

### Do not open this exam until told to do so. Solution

Do not open this exam until told to do so. Department of Economics College of Social and Applied Human Sciences K. Annen, Fall 003 Final (Version): Intermediate Microeconomics (ECON30) Solution Final (Version

### ECN 3103 INDUSTRIAL ORGANISATION

ECN 3103 INDUSTRIAL ORGANISATION 5. Game Theory Mr. Sydney Armstrong Lecturer 1 The University of Guyana 1 Semester 1, 2016 OUR PLAN Analyze Strategic price and Quantity Competition (Noncooperative Oligopolies)

### Analyze different types of non zero sum games. Hawk vs. Dove game. Advertising problem. Problem of companies polluting the environment.

Unit 3 GME THEORY Lesson 31 Learning Objective: nalyze different types of non zero sum games Hawk vs. game. dvertising problem. Problem of companies polluting the environment. Rationalizability or Iterative

### MOT Seminar. John Musacchio 4/16/09

Game Theory MOT Seminar John Musacchio johnm@soe.ucsc.edu 4/16/09 1 Who am I? John Musacchio Assistant Professor in ISTM Joined January 2005 PhD from Berkeley in Electrical l Engineering i Research Interests

### Lecture 21: Strategic Interaction and Game Theory

Lecture 2: Strategic Interaction and Game Theory EC DD & EE / Manove Strategic Interaction p What types of firms are most likely to engage in costly rent-seeking? EC DD & EE / Manove Monopoly>Rent Seeking

### Matching: The Theory. Muriel Niederle Stanford and NBER. October 5, 2011

Matching: The Theory Muriel Niederle Stanford and NBER October 5, 2011 NRMP match variations: Couples: Submit rank oders over pairs of programs, and must be matched to two positions Applicants who match

### AGEC 3333 Practice Questions for Exam 3 Fall Semester, 2009 Set A: Material From Chapter 10, Pages ,

(1) (from page 108) Match each industry description with the proper identification by drawing a line between the description and identification. a market with many buyers and sellers with roughly equal

### ECON 230D2-002 Mid-term 1. Student Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

ECON 230D2-002 Mid-term 1 Name Student Number MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Scenario 12.3: Suppose a stream is discovered whose

### PRICE OF ANARCHY: QUANTIFYING THE INEFFICIENCY OF EQUILIBRIA. Zongxu Mu

PRICE OF ANARCHY: QUANTIFYING THE INEFFICIENCY OF EQUILIBRIA Zongxu Mu The Invisible Hand Equilibria and Efficiency Central to free market economics The Wealth of Nations (Smith, 1776) led by an invisible

### Managerial Economics & Business Strategy. Game Theory: Inside Oligopoly

Managerial Economics & Business Strategy Chapter 10 Game Theory: Inside Oligopoly Revised 2/12 by DF McGraw-Hill/Irwin Copyright Copyright 2006 by The 2006 McGraw-Hill by The McGraw-Hill Companies, Inc.

### Welfare Economics. The Edgeworth Box. The Basic Theorem. Some Basic Assumptions

Welfare Economics The Edgeworth Box The Basic Theorem The basic theorem in welfare economics: A market, exchange, economy will achieve efficient resource allocation. We intend to show the basics of that

### Collusion. Sotiris Georganas. February Sotiris Georganas () Collusion February / 31

Collusion Sotiris Georganas February 2012 Sotiris Georganas () Collusion February 2012 1 / 31 Outline 1 Cartels 2 The incentive for cartel formation The scope for collusion in the Cournot model 3 Game

### Oligopoly. Quantity Price(per year) 0 \$120 2,000 \$100 4,000 \$80 6,000 \$60 8,000 \$40 10,000 \$20 12,000 \$0

Oligopoly 1. Markets with only a few sellers, each offering a product similar or identical to the others, are typically referred to as a. monopoly markets. b. perfectly competitive markets. c. monopolistically

### CSCI 3210: Computational Game Theory. Inefficiency of Equilibria & Routing Games Ref: Ch 17, 18 [AGT]

CSCI 3210: Computational Game Theory Inefficiency of Equilibria & Routing Games Ref: Ch 17, 18 [AGT] Mohammad T. Irfan Email: mirfan@bowdoin.edu Web: www.bowdoin.edu/~mirfan Split or steal game u NE outcome

### Information Acquisition and Price Discrimination

Information Acquisition and Price Discrimination Farshad Fatemi Sharif University of Technology ffatemi@sharif.edu We consider a Hotelling model of price competition where firms may acquire costly information

### Chapter 9: Static Games and Cournot Competition

Chapter 9: Static Games and Cournot Competition Learning Objectives: Students should learn to:. The student will understand the ideas of strategic interdependence and reasoning strategically and be able

### Chapter 12. A Game Theoretic Approach to Strategic Behavior

Chapter 12 A Game Theoretic Approach to Strategic Behavior Chapter Outline An Introduction to the Theory of Games Prisoner s Dilemma Nash Equilibrium Maximin Strategy Strategies for Repeated Play Sequential

### Models of Language Evolution

Models of Language Evolution Session 4: 2014/11/19 Organizational Matters 22.10 Language Evolution - Overview 29.10 Language Evolution - Protolanguage 12.11 Models of Language Evolution 19.11 26.11 Evolutionary

### Chapter 5: A Closed-Economy One-Period Macroeconomic Model

Chapter 5: A Closed-Economy One-Period Macroeconomic Model Introduce the government. Construct closed-economy one-period macroeconomic model, which has: (i) representative consumer; (ii) representative

### ECON 230-D2-002 Version 2. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

ECON 230-D2-002 Version 2 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The two largest auto manufacturers, Toyota and GM, have experimented

### Price-Fixing and. Repeated Games. Collusion and cartels. Recent events. Collusion and cartels 2. Cartels. Recent cartel violations 2

Collusion and cartels Price-Fixing and What is a cartel? attempt to enforce market discipline and reduce competition between a group of suppliers cartel members agree to coordinate their actions prices

### Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry s output.

Topic 8 Chapter 13 Oligopoly and Monopolistic Competition Econ 203 Topic 8 page 1 Oligopoly: How do firms behave when there are only a few competitors? These firms produce all or most of their industry

### Advanced Topics in Computer Science 2. Networks, Crowds and Markets. Fall,

Advanced Topics in Computer Science 2 Networks, Crowds and Markets Fall, 2012-2013 Prof. Klara Kedem klara@cs.bgu.ac.il Office 110/37 Office hours by email appointment The textbook Chapters from the book

### Price of anarchy in auctions & the smoothness framework. Faidra Monachou Algorithmic Game Theory 2016 CoReLab, NTUA

Price of anarchy in auctions & the smoothness framework Faidra Monachou Algorithmic Game Theory 2016 CoReLab, NTUA Introduction: The price of anarchy in auctions COMPLETE INFORMATION GAMES Example: Chicken

### Oligopoly Pricing. EC 202 Lecture IV. Francesco Nava. January London School of Economics. Nava (LSE) EC 202 Lecture IV Jan / 13

Oligopoly Pricing EC 202 Lecture IV Francesco Nava London School of Economics January 2011 Nava (LSE) EC 202 Lecture IV Jan 2011 1 / 13 Summary The models of competition presented in MT explored the consequences

### Note on webpage about sequential ascending auctions

Econ 805 Advanced Micro Theory I Dan Quint Fall 2007 Lecture 20 Nov 13 2007 Second problem set due next Tuesday SCHEDULING STUDENT PRESENTATIONS Note on webpage about sequential ascending auctions Everything

### Applied Welfare Economics

Economics Monika Köppl - Turyna Department of Economics ISCTE-IUL Summer 2014/2015 Introduction We will have lectures and problem solving sessions (usually one per two lectures) Attendance is generally

### An Experiment on Prisoner s Dilemma with Confirmed Proposals

An Experiment on Prisoner s Dilemma with Confirmed Proposals Giuseppe Attanasi * Toulouse School of Economics (LERNA), France Aurora García Gallego LEE, Universitat Jaume I, Castellón, Spain Nikolaos Georgantzís

### Game Theory & Firms. Jacob LaRiviere & Justin Rao April 20, 2016 Econ 404, Spring 2016

Game Theory & Firms Jacob LaRiviere & Justin Rao April 20, 2016 Econ 404, Spring 2016 What is Game Theory? Game Theory Intuitive Definition: Theory of strategic interaction Technical Definition: Account

### Exam #2 (100 Points Total) Answer Key

Exam #2 (100 Points Total) Answer Key 1. A Pareto efficient outcome may not be good, but a Pareto inefficient outcome is in some meaningful sense bad. (a) (5 points) Give an example or otherwise explain,

### The Robust Price of Anarchy of Altruistic Games

The Robust Price of Anarchy of Altruistic Games Po-An Chen 1, Bart de Keijzer 2, David Kempe 1, and Guido Schäfer 2,3 1 Department of Computer Science, University of Southern California, USA, {poanchen,

### Modeling of competition in revenue management Petr Fiala 1

Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize

### Principles of Microeconomics Assignment 8 (Chapter 10) Answer Sheet. Class Day/Time

1 Principles of Microeconomics Assignment 8 (Chapter 10) Answer Sheet Name Class Day/Time Questions of this homework are in the next few pages. Please find the answer of the questions and fill in the blanks

### Welfare Economics. Philip A. Viton. May 17, Philip A. Viton CRP 781 () Welfare May 17, / 1

Welfare Economics Philip A. Viton May 17, 2012 Philip A. Viton CRP 781 () Welfare May 17, 2012 1 / 1 Economic Systems An economic system is a set of institutional arrangements for the exchange of goods

### Some relationships between evolutionary stability criteria in games

Economics Letters 57 (1997) 45 50 Some relationships between evolutionary stability criteria in games Martin Dufwenberg a,b, * a Center for Economic Research, Tilburg University, Tilburg, Netherlands b

### On the Reputation of Agent-based Web Services

On the Reputation of Agent-based Web Services Babak Khosravifar, Jamal Bentahar, Ahmad Moazin, and Philippe Thiran 2 Concordia University, Canada, 2 University of Namur, Belgium b khosr@encs.concordia.ca,

### Incentives in Crowdsourcing: A Game-theoretic Approach

Incentives in Crowdsourcing: A Game-theoretic Approach ARPITA GHOSH Cornell University NIPS 2013 Workshop on Crowdsourcing: Theory, Algorithms, and Applications Incentives in Crowdsourcing: A Game-theoretic

### Chapter 13. Game Theory. Gaming and Strategic Decisions. Noncooperative v. Cooperative Games

Chapter 13 Game Theory Gaming and Strategic Decisions Game theory tries to determine optimal strategy for each player Strategy is a rule or plan of action for playing the game Optimal strategy for a player

### STRATEGY. Here we suppose a game with one other player. The other player could be another firm, another person, or the industry.

STRATEGY Strategy deals with managerial decisions when other firms (or persons) change their behavior in response to your behavior. For example, in the last section we learned that demand for a firm s

### Mutual Benefits as Incentives for

Mutual Benefits as Incentives for Transboundary Water Cooperation? An Analysis of Negative and Positive Externality Problems Ines Dombrowsky / Dept. of Economics London, May 6, 2006 Content (1) The problem

### Econ 201 Review Notes - Part 3

Econ 201 Review Notes - Part 3 This is intended as a supplement to the lectures and section. It is what I would talk about in section if we had more time. After the first three chapters where we talked

### Chapter 13 Outline. Challenge: Intel and AMD s Advertising Strategies. An Overview of Game Theory. An Overview of 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

### #1: Monopolistic Competition

Answers: #1: Monopolistic Competition MC-1. d. All of the terms describe economically breaking even MC-2. c. Economic profits will attract competition MC-3. d. Economically breaking even means you just

### 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen November 7, Lecture 22

Monopoly. Principles of Microeconomics, Fall Chia-Hui Chen November, Lecture Monopoly Outline. Chap : Monopoly. Chap : Shift in Demand and Effect of Tax Monopoly The monopolist is the single supply-side

### 29/02/2016. Market structure II- Other types of imperfect competition. What Is Monopolistic Competition? OTHER TYPES OF IMPERFECT COMPETITION

Market structure II- Other types of imperfect competition OTHER TYPES OF IMPERFECT COMPETITION Characteristics of Monopolistic Competition Monopolistic competition is a market structure in which many firms

### SUPERGAMES IN ELECTRICITY MARKETS: BEYOND THE NASH EQUILIBRIUM CONCEPT

SUPERGAMES IN ELECTRICITY MARKETS: BEYOND THE NASH EQUILIBRIUM CONCEPT Pedro Correia, Thomas Overbye, Ian Hiskens Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign

### Monopolistic Competition Oligopoly Duopoly Monopoly. The further right on the scale, the greater the degree of monopoly power exercised by the firm.

Oligopoly Monopolistic Competition Oligopoly Duopoly Monopoly The further right on the scale, the greater the degree of monopoly power exercised by the firm. Imperfect competition refers to those market

### INDUSTRIAL ECONOMICS, WITH APPLICATIONS TO E-COMMERCE An Option for MSc Economics and MSc E-Commerce Autumn Term 2003

School of Economics, Mathematics and Statistics INDUSTRIAL ECONOMICS, WITH APPLICATIONS TO E-COMMERCE An Option for MSc Economics and MSc E-Commerce Autumn Term 2003 1. Strategic Interaction and Oligopoly

### Oligopoly is a market structure in which Natural or legal barriers prevent the entry of new firms. A small number of firms compete.

CHAPTER 15: OLIGOPOLY What Is Oligopoly? Oligopoly is a market structure in which Natural or legal barriers prevent the entry of new firms. A small number of firms compete. Barriers to Entry Either natural

### Principles of Economics: Seminar 1 - Game Theory

Principles of Economics: Seminar 1 - Game Theory July 18, 2017 Principles of Economics: Seminar 1 - Game Theory July 18, 2017 1 / 20 What is a game? Definition: A game is any situation involving two or

### A Better-Response Strategy for Self-Interested Planning Agents

Applied Intelligence manuscript No. (will be inserted by the editor) A Better-Response Strategy for Self-Interested Planning Agents Jaume Jordán Alejandro Torreño Mathijs de Weerdt Eva Onaindia Received:

### Lecture 13(ii) Announcements. 1. Application of Game Theory: Duopoly (The one-shot game case)

Lecture 13(ii) Announcements Check out Final Exam OneStop Page at the very bottom of Moodle One stop shopping for all your final preparation needs, including questions from previous finals. 1. Application

### 11. Oligopoly. Literature: Pindyck and Rubinfeld, Chapter 12 Varian, Chapter 27

11. Oligopoly Literature: Pindyck and Rubinfeld, Chapter 12 Varian, Chapter 27 04.07.2017 Prof. Dr. Kerstin Schneider Chair of Public Economics and Business Taxation Microeconomics Chapter 11 Slide 1 Chapter

### THE LIKELIHOOD OF TRADE PATTERN CHANGES

THE LIKELIHOOD OF TRADE PATTERN CHANGES Lisandro Abrego University of Warwick Raymond Riezman University of Iowa John Whalley Universities of Warwick and Western Ontario and NBER December 2002 Abstract

### Coordination in the Presence of Asset Markets 1

Coordination in the Presence of Asset Markets 1 Shimon Kogan Anthony M. Kwasnica Roberto Weber McCombs School of Business, University of Texas at Austin Smeal College of Business, The Pennsylvania State

### Common-Pool Resources (Ch 34) and Public Goods (Ch 36)

Common-Pool Resources (Ch 34) and (Ch 36) Final Exam Details 20 hours of OH between now and final Review Session: Saturday, 3/12, 4-6pm, NH 1006 Final exam: Tuesday, March 15, 12-3pm, here Format: 12 15

### HIERARCHICAL decision making problems arise naturally

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 5, NO. 3, JULY 2008 377 Mechanism Design for Single Leader Stackelberg Problems and Application to Procurement Auction Design Dinesh Garg and

### ECON 8010 (Spring 2013) Exam 3

ECON 8010 (Spring 2013) Exam 3 Name Multiple Choice Questions: (4 points each) 1. Nash s Existence Theorem states that A. an equilibrium exists in any game of incomplete information, but never exists in

### Umbrella Branding Can Leverage Reputation, but only with Market Power. May 19, Eric B. Rasmusen

Umbrella Branding Can Leverage Reputation, but only with Market Power May 19, 2012 Eric B. Rasmusen Dan R. and Catherine M. Dalton Professor, Department of Business Economics and Public Policy, Kelley

### Damaged Durable Goods: Mitigating the Time Inconsistency Problem

JEL Codes: D0, L0 1. Introduction World Review of Business Research Vol. 2. No. 6. November 2012. Pp. 84 99 Damaged Durable Goods: Mitigating the Time Inconsistency Problem Xiaojing (Joanne) MA * In this

### CHAPTER 13 Oligopoly and Monopolistic Competition

CHPTER 13 Oligopoly and Monopolistic Competition CHPTER OUTLINE 13.1 Market Structures 13.2 Game Theory Single-Period, Two-Firm, Quantity-Setting Game Why Firms Do Not Cooperate in a Single-Period Game

### Technological Investment Games Among Wireless Telecommunications Service Providers

INTERNATIONAL JOURNAL OF NETWORK MANAGEMENT Int. J. Network Mgmt 2008; 00:1 6 [Version: 2008/03/18 v1.00] Technological Investment Games Among Wireless Telecommunications Service Providers Patrick Maillé

### EVALUATING ALLOCATIONS OF FREEDOM

EVALUATING ALLOCATIONS OF FREEDOM Itai Sher University of Minnesota Conference on Normative Ethics and Welfare Economics Becker Friedman Institute University of Chicago October 24, 2014 Conflict of Freedoms

### Economics 101A (Lecture 19) Stefano DellaVigna

Economics 101A (Lecture 19) Stefano DellaVigna November 9, 2004 Outline 1. Monopoly 2. Price Discrimination 3. Oligopoly? 4. Game Theory 1 Profit Maximization: Monopoly Monopoly. Firm maximizes profits,

### Speed and Quality of Collective Decision Making: Incentives for Information Provision

Speed and Quality of Collective Decision Making: Incentives for Information Provision Hans Peter GRÜNER University of Mannheim and CEPR, London Elisabeth SCHULTE University of Mannheim June 2009 Abstract

### Noncooperative Game Theory For Industrial Organization: An Introduction and Overview. by Drew Fudenberg and Jean Tirole Number 445 April 1987

Noncooperative Game Theory For Industrial Organization: An Introduction and Overview by Drew Fudenberg and Jean Tirole Number 445 April 1987 Digitized by the Internet Archive in 2011 with funding from

### Bargaining and Power in Networks

Chapter 12 Bargaining and Power in Networks In our analysis of economic transactions on networks, particularly the model in Chapter 11, we considered how a node s position in a network affects its power

### Eco 685 Graphs, Tables, and Definitions

Eco 685 Graphs, Tables, and Definitions David L. Kelly 1 1 Department of Economics, University of Miami dkelly@miami.edu Fall, 2017 Introduction Introduction Managerial Economics Definition Definition

### A COMMITMENT FOLK THEOREM

A COMMITMENT FOLK THEOREM ADAM TAUMAN KALAI, EHUD KALAI, EHUD LEHRER, AND DOV SAMET Abstract. Real world players often increase their payoffs by voluntarily committing to play a fixed strategy, prior to

### An Introduction to Game Theory: Applications in Environmental Economics and Public Choice with Mathematical Appendix

Western Kentucky University From the SelectedWorks of Matt Bogard August, 2012 An Introduction to Game Theory: Applications in Environmental Economics and Public Choice with Mathematical Appendix Matt

### Universitat Autònoma de Barcelona Department of Applied Economics

Universitat Autònoma de Barcelona Department of Applied Economics Annual Report Endogenous R&D investment when learning and technological distance affects absorption capacity Author: Jorge Luis Paz Panizo

### Tilburg University. The repeated lake game Brock, W.A.; de Zeeuw, Aart. Published in: Economics Letters. Publication date: Link to publication

Tilburg University The repeated lake game Brock, W.A.; de Zeeuw, Aart Published in: Economics Letters Publication date: 2002 Link to publication Citation for published version (APA): Brock, W. A., & de

### Comm295 Midterm Review Package. October, Content:

Managerial Economics Comm295 Midterm Review Package October, 20 2014 Supply and Demand Elasticity Regression Analysis Consumer Choice Production Cost Concepts Profit Maximization Perfect Competition Monopoly

### Recall from last time. Econ 410: Micro Theory. Cournot Equilibrium. The plan for today. Comparing Cournot, Stackelberg, and Bertrand Equilibria

Slide Slide 3 Recall from last time A Nash Equilibrium occurs when: Econ 40: Micro Theory Comparing Cournot, Stackelberg, and Bertrand Equilibria Monday, December 3 rd, 007 Each firm s action is a best

### Econ Economics of Public Sector HW #1 Suggested Solutions.

Econ 411-1 Economics of Public Sector HW #1 Suggested Solutions. by Anna Rubinchik-Pessach October 7, 1 Problem 1: Chapter 5, q.4 Cash-for-Clunkers Program The goal of the EPA policy is to limit emission

### Technology selection for electric drive production with a game theoretic approach Gisela Lanza 1,a, Johannes Stoll 1,b, Sven Gerbe 1,c

Advanced Materials Research Online: 2013-09-04 ISSN: 1662-8985, Vol. 769, pp 303-310 doi:10.4028/www.scientific.net/amr.769.303 2013 Trans Tech Publications, Switzerland Technology selection for electric

### Advanced Microeconomics Theory. Chapter 8: Game Theory and Imperfect Competition

Advanced Microeconomics Theory Chapter 8: Game Theory and Imperfect Competition Outline Game Theory Tools Bertrand Model of Price Competition Cournot Model of Quantity Competition Product Differentiation

### Why and How Should the Government Subsidize Education? February 13, 2008

Why and How Should the Government Subsidize Education? February 13, 2008 Human Capital Model To keep things simple and flexible, lets use the following version of the human capital model 2 periods everyone

### We survey different models, techniques, and some recent results to tackle machine scheduling

PRODUCTION AND OPERATIONS MANAGEMENT Vol. 16, No. 4, July-August 2007, pp. 437 454 issn 1059-1478 07 1604 437\$1.25 POMS 2007 Production and Operations Management Society Games and Mechanism Design in Machine

### Oligopoly Equilibria à la Stackelberg in Pure Exchange Economies 1

Oligopoly Equilibria à la Stackelberg in Pure Exchange Economies 1 Ludovic A. Julien Fabrice Tricou * * 1 2 3 1 Introduction The concept of oligopoly competition introduced by Stackelberg (1934) has mainly

### Final Exam: ECON-100A Intermediate Microeconomics Bob Baden Section I: Answer at least two questions (answer all parts of the questions you choose)

Final Exam: ECON-100A Intermediate Microeconomics Bob Baden Section I: Answer at least two questions (answer all parts of the questions you choose) Question 1: (16 points) Donald Fribble is a stamp collector.

### Lecture 22. Oligopoly & Monopolistic Competition

Lecture 22. Oligopoly & Monopolistic Competition Course Evaluations on Thursday: Be sure to bring laptop, smartphone, or tablet with browser, so that you can complete your evaluation in class. Oligopoly

### Lecture 11 Imperfect Competition

Lecture 11 Imperfect Competition Business 5017 Managerial Economics Kam Yu Fall 2013 Outline 1 Introduction 2 Monopolistic Competition 3 Oligopoly Modelling Reality The Stackelberg Leadership Model Collusion

### Negotiation and Task Sharing Among Autonomous Agents in Cooperative Domains

Abstract Research in Distributed Artificial Intelligence is concerned with how automated agents can be designed to interact effectively. One important capability that could aid inter-agent cooperation

### Notes on Introduction to Contract Theory

Notes on Introduction to Contract Theory John Morgan Haas School of Business and Department of Economics University of California, Berkeley 1 Overview of the Course This is a readings course. The lectures

### Selected brief answers for review questions for first exam, Fall 2006 AGEC 350 Don't forget, you may bring a 3x5" notecard to the exam.

1 Selected brief answers for review questions for first exam, Fall 2006 AGEC 350 Don't forget, you may bring a 3x5" notecard to the exam. These are brief answers intended to help you find the complete

### 2007 Thomson South-Western

BETWEEN MONOPOLY AND PERFECT COMPETITION Imperfect competition refers to those market structures that fall between perfect competition and pure monopoly. Imperfect competition includes industries in which

### Signaling, Screening, and Sequential Equilibrium

Chapter Signaling, Screening, and Sequential Equilibrium 2-Player Signaling Games Informed and uninformed players Let the buyer beware Three varieties of market failure, and one variety of market success

### A Short Course in Intermediate Microeconomics with Calculus

A Short Course in Intermediate Microeconomics with Calculus This book provides a concise treatment of the core concepts of microeconomic theory at the intermediate level with calculus integrated into the

### First-Price Path Auctions

First-Price Path Auctions Nicole Immorlica MIT CS&AI Laboratory Cambridge, MA 2139 nickle@csail.mit.edu Evdokia Nikolova MIT CS&AI Laboratory Cambridge, MA 2139 enikolova@csail.mit.edu David Karger MIT

### Stackelberg or Cournot Equilibria", Games and Economic Behavior, 2, 29-46, 1990.

Hamilton, Jonathan H., and Steven M. Slutsky, "Endogenous Timing in Duopoly Games: Stackelberg or Cournot Equilibria", Games and Economic Behavior, 2, 29-46, 1990. Kahana, Nava, "Do Multiplant Labor-Managed

Bidding for Sponsored Link Advertisements at Internet Search Engines Benjamin Edelman Portions with Michael Ostrovsky and Michael Schwarz Industrial Organization Student Seminar September 2006 Project

### ASSIGNMENT 4. Read all of the following information before starting the Assignment:

ASSIGNMENT 4 Principles of Economics EC 110-001 June 28, 2007 Name: } {{ } by writing my name i swear by the honor code Read all of the following information before starting the Assignment: You are not

### Benefits of Learning in Negotiation

Benefits of Learning in Negotiation Dajun Zeng Katia Sycara The Robotics Institute Carnegie Mellon University, Pittsburgh, PA 15213 Voice: (412) 268-8815 Fax: (412) 268-5569 Dajun.Zeng@cs.cmu.edu katia@cs.cmu.edu

### Extensive Games with Imperfect Information

Extensive Games with Imperfect Information Jeff Rowley Abstract This document will draw heavily on definitions presented in Osborne; An Introduction to Game Theory and, for later definitions, Jehle & Reny;

### Chapter 15 Oligopoly

Goldwasser AP Microeconomics Chapter 15 Oligopoly BEFORE YOU READ THE CHAPTER Summary This chapter explores oligopoly, a market structure characterized by a few firms producing a product that mayor may

### Review of Economic Studies, Ltd.

Review of Economic Studies, Ltd. Provision of Public Goods: Fully Implementing the Core through Private Contributions Author(s): Mark Bagnoli and Barton L. Lipman Source: The Review of Economic Studies,