CSCI 3210: Computational Game Theory. Inefficiency of Equilibria & Routing Games Ref: Ch 17, 18 [AGT]
|
|
- Clyde McCoy
- 6 years ago
- Views:
Transcription
1 CSCI 3210: Computational Game Theory Inefficiency of Equilibria & Routing Games Ref: Ch 17, 18 [AGT] Mohammad T. Irfan Web: Split or steal game u NE outcome vs. socially best/optimal outcome Tony Payoff matrix Split Split $33K, $33K Steal $66K, $0+fr. Lucy Steal $0+fr., $66K $0, $0 1
2 Prisoner's "dilemma" game u Again: NE outcome vs socially optimal outcome Suspect 2 Suspect 1 Payoff matrix Not Confess Confess Not Confess 1, 1 10, 0 Confess 0, 10 5, 5 Costs (negative of payoffs) Measuring the inefficiency of NE u What is the objective function to compare different outcomes? u Utilitarian u Egalitarian u How to deal with multiplicity of NE? u Inefficiency of which NE? u Price of anarchy vs. price of stability 2
3 Price of Anarchy (PoA) u PoA = Worst objective function value of a NE Objective function value of optimal outcome Price of Stability (PoS) u PoS = Best objective function value of a NE Objective function value of optimal outcome 3
4 Example u Calculate PoA and PoS Suspect 2 Suspect 1 Payoff matrix Not Confess Confess Not Confess 1, 1 10, 0 Confess 0, 10 5, 5 Costs (negative of payoffs) Example u Calculate PoA and PoS Column player Row player Payoff matrix L U 21, -1 10, 0 D 100, 10 7, 8 R Costs (negative of payoffs) 4
5 PoA vs. PoS u Consider costs u PoA and PoS will be >= 1 u PoA = PoS when all NE have the same cost (e.g., unique NE) u In general, PoA >= PoS u PoA: worst case guarantee in a system of independent agents u PoS: measures benefit of a protocol or proposed outcome Pigou's example u Assume one unit of traffic from s to t u Objective function: average travel time x = amount of traffic on edge u NE: all traffic in lower edge. Avg cost = 1. u Optimal: ½ and ½. Avg cost = ½ * 1 + ½ * ½. u PoA, PoS =? 5
6 Routing Games Model: nonatomic selfish routing u Multicommodity flow network u Directed network with multiple (source, sink) pairs u Each (source, sink) pair is called a commodity u r i amount of traffic for each commodity i u Each edge e has a delay or cost function c e u Every car going through an edge gets same delay u Cost of a path = sum of edge costs u Note: cost doesn't depend on identity of players u Congestion games 6
7 Equilibrium flow u Let f be a feasible flow (combining all commodities) u f is equilibrium flow if u A commodity uses a path P in its flow within f => All detours have higher (or equal) delay equilibrium flow More complex graphs s 1 t 1 s 2 t 2 u What is the traffic flow on an (s,t) path? u Amount of traffic using that path fully (not partially) to go from s à t u What's the cost (or delay) of a path? u Total delay on that path traffic using part of that path also contribute to delay 7
8 Cost of an (s,t) path u Sum of edge costs (or delays) on that path flow on edge e path flow (all the flows, not just on P) cost function of edge e Cost of a flow u Cost (or delay) of a flow = sum of (cost of each path * flow on that path) = sum of (cost of each edge * flow on that edge) flow on edge e flow cost function of edge e 8
9 Example: nonlinear Pigou u Consider large number p; 1 unit of traffic equilibrium flow u Equilibrium: All down. cost = 1. u Optimal: ε up, (1-ε) down u Cost = ε * 1 + (1-ε) * (1-ε) p à 0 PoA à + Example: Braess' paradox u 1 unit of traffic ½ equilibrium flow ½ PoA = 1 Equilibrium cost = ½ * ( ½ + 1) + ½ * (1 + ½) =3/2 9
10 Braess' paradox u New super highway between v and w PoA = 4/3 Equilibrium cost = = 2 Optimal: ½ and ½ (ignore superhighway) Another model: atomic selfish routing u Restricted version of multicommodity flow u r i amount of traffic for each commodity i u Each s à t flow must go through a single path (difference with nonatomic selfish routing) u Each player/commodity chooses the minimum delay path w.r.t. others' choices u Equilibrium flow: No better path for any player 10
11 Drawback of the atomic model u There may not exist any equilibrium flow u 2 players: both s à t u r 1 = 1, r 2 = 2 u Proof: If player 2 goes s à t, then player 1's BR is sàvàwàt, to which player 2's BR is sàwàt. (and so on) Nonatomic model: equilibrium existence u Prove that equilibrium flow exists 11
12 Price of anarchy: nonatomic u Consider linear cost functions only u Pigou's example gives a lower bound of 4/3 x = amount of traffic on edge u NE: all traffic in lower edge. Avg cost = 1. u Optimal: ½ and ½. Avg cost = ½ * 1 + ½ * ½ = 3/4. u PoA = 1 / (3/4) = 4/3 Surprise! u Price of anarchy for any nonatomic routing game with linear costs <= 4/3 12
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
More informationAlgoritmi Distribuiti e Reti Complesse (modulo II) Luciano Gualà
Algoritmi Distribuiti e Reti Complesse (modulo II) Luciano Gualà guala@mat.uniroma2.it www.mat.uniroma2.it/~guala Algorithmic Game Theory Algorithmic Issues in Non-cooperative (i.e., strategic) Distributed
More informationAlgoritmi Distribuiti e Reti Complesse (modulo II) Luciano Gualà
Algoritmi Distribuiti e Reti Complesse (modulo II) Luciano Gualà guala@mat.uniroma2.it www.mat.uniroma2.it/~guala Algorithmic Game Theory Algorithmic Issues in Non-cooperative (i.e., strategic) Distributed
More informationIntro to Algorithmic Economics, Fall 2013 Lecture 1
Intro to Algorithmic Economics, Fall 2013 Lecture 1 Katrina Ligett Caltech September 30 How should we sell my old cell phone? What goals might we have? Katrina Ligett, Caltech Lecture 1 2 How should we
More informationSelfish routing. Ann Nowé. 05/12/12 Herhaling titel van presentatie 1
Selfish routing Ann Nowé 05/12/12 Herhaling titel van presentatie 1 Content Braess Paradox Price of anarchy Slides based on Social and Economic Networks: Models and Applications, lecture 11, by Borodin
More informationTopics in ALGORITHMIC GAME THEORY *
Topics in ALGORITHMIC GAME THEORY * Spring 2012 Prof: Evdokia Nikolova * Based on slides by Prof. Costis Daskalakis Let s play: game theory society sign Let s play: Battle of the Sexes Theater Football
More informationLecture 2: March Introduction. Computational Game Theory Spring Semester, 2011/2012
Computational Game Theory Spring Semester, 2011/2012 Lecture 2: March 14 Lecturer: Amos Fiat Scribe: Hadas Zur & Alon Ardenboim 2.1 Introduction Informally, a set of strategies is a Nash equilibrium if
More informationQuantifying Inefficiency in Games and Mechanisms. Tim Roughgarden (Stanford)
Quantifying Inefficiency in Games and Mechanisms Tim Roughgarden (Stanford) 1 Talk Themes many economic concepts directly relevant for reasoning about applications in computer science Shapley value, correlated
More informationGame Theory and Economics
and Economics Game theory is the study of how people behave in strategic situations. Strategic decisions are those in which each person, in deciding what actions to take, must consider how others might
More informationAnalyze 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
More informationHow bad is selfish routing in practice? Lessons from the National Science Experiment
How bad is selfish routing in practice? Lessons from the National Science Experiment Barnabé Monnot, Francisco Benita, Georgios Piliouras Singapore University of Technology and Design 1 Efficiency and
More informationa study on Robust Mechanisms for Social Coordination
a study on Robust Mechanisms for Social Coordination Philip N. Brown and Jason R. Marden University of California, Santa Barbara CDC Workshop: Distributed Autonomy and Human-Machine Networks December 14,
More information6.896: Topics in Algorithmic Game Theory
6.896: Topics in Algorithmic Game Theory vol. 1: Spring 2010 Constantinos Daskalakis game theory what society we won t sign study in this class I only mean this as a metaphor of what we usually study in
More informationSome network flow problems in urban road networks. Michael Zhang Civil and Environmental Engineering University of California Davis
Some network flow problems in urban road networks Michael Zhang Civil and Environmental Engineering University of California Davis Outline of Lecture Transportation modes, and some basic statistics Characteristics
More informationLecture #2: Introduction to Game Theory. Prof. Dr. Sven Seuken
Lecture #2: Introduction to Game Theory Prof. Dr. Sven Seuken 27.2.2012 Outline 1. Recap of last lecture 2. Go over Game Theory concepts 3. Play some in-class experiments 4. Discussion 5. Questions Quick
More informationROUTING GAMES IN THE WILD: EFFICIENCY, EQUILIBRATION AND REGRET. Hassan Nikaein Amin Sabbaghian
ROUTING GAMES IN THE WILD: EFFICIENCY, EQUILIBRATION AND REGRET Hassan Nikaein Amin Sabbaghian INTRODUCTION We focus on a semantically rich dataset that captures detailed information about the daily behavior
More informationPART THREE Qualifying the Inefficiency of Equilibria
PART THREE Qualifying the Inefficiency of Equilibria CHAPTER 17 Introduction to the Inefficiency of Equilibria Tim Roughgarden and Éva Tardos Abstract This chapter presents motivation and definitions
More informationApproximation in Algorithmic Game Theory
Approximation in Algorithmic Game Theory Robust Approximation Bounds for Equilibria and Auctions Tim Roughgarden Stanford University 1 Motivation Clearly: many modern applications in CS involve autonomous,
More informationWireless Networking with Selfish Agents. Li (Erran) Li Center for Networking Research Bell Labs, Lucent Technologies
Wireless Networking with Selfish Agents Li (Erran) Li Center for Networking Research Bell Labs, Lucent Technologies erranlli@dnrc.bell-labs.com Today s Wireless Internet 802.11 LAN Internet 2G/3G WAN Infrastructure
More informationNetworked Life (CSE 112)
Networked Life (CSE 112) Prof. Michael Kearns Final Examination May 3, 2006 The final exam is closed-book; you should have no materials present other than the exam and a pen or pencil. NAME: PENN ID: Exam
More informationMany of today s engineered systems are tightly. Studies on Robust Social Influence Mechanisms. Incentives for Efficient Network Routing
Studies on Robust Social Influence Mechanisms Incentives for Efficient Network Routing in Uncertain Settings A time-lapse of road traffic on an Atlanta freeway, echoing the model of traffic as a splittable
More informationGatti: A gentle introduction to game theory and crowding games. Outline. Outline. Nicola Gatti
gentle introduction to game theory and crowding games Nicola Gatti Dipartimento di Elettronica e Informazione Politecnico di Milano Italy Outline Examples Game theory groundings Searching for a Nash equilibrium
More informationThe 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,
More informationGames, Auctions, Learning, and the Price of Anarchy. Éva Tardos Cornell University
Games, Auctions, Learning, and the Price of Anarchy Éva Tardos Cornell University Games and Quality of Solutions Rational selfish action can lead to outcome bad for everyone Tragedy of the Commons Model:
More informationCMSC 474, Introduction to Game Theory Analyzing Normal-Form Games
CMSC 474, Introduction to Game Theory Analyzing Normal-Form Games Mohammad T. Hajiaghayi University of Maryland Some Comments about Normal-Form Games Only two kinds of strategies in the normal-form game
More informationNetwork Flows. 7. Multicommodity Flows Problems. Fall 2010 Instructor: Dr. Masoud Yaghini
In the name of God Network Flows 7. Multicommodity Flows Problems 7.1 Introduction Fall 2010 Instructor: Dr. Masoud Yaghini Introduction Introduction In many application contexts, several physical commodities,
More informationOligopoly is a market structure in which Natural or legal barriers prevent the entry of new firms. A small number of firms compete.
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. Oligopoly sell (but more than two) of
More informationECN 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)
More informationECS 253 / MAE 253, Lecture 13 May 10, I. Games on networks II. Diffusion, Cascades and Influence
ECS 253 / MAE 253, Lecture 13 May 10, 2016 I. Games on networks II. Diffusion, Cascades and Influence Summary of spatial flows and games Optimal location of facilities to maximize access for all. Designing
More informationOLIGOPOLY AND DUOPOLY. Asst.. Prof. Dr. Serdar AYAN
OLIGOPOLY AND DUOPOLY Asst.. Prof. Dr. Serdar AYAN WHAT IS OLIGOPOLY? Oligopoly is a market type in which: A small number of firms compete. Natural or legal barriers prevent the entry of new firms.. WHAT
More informationColored Resource Allocation Games
Colored Resource Allocation Games Evangelos Bampas 1, Aris Pagourtzis 1, George Pierrakos, and Vasileios Syrgkanis 1 1 School of Elec. & Comp. Engineering, ational Technical University of Athens {ebamp,pagour}@cs.ntua.gr,
More informationChapter 6. Game Theory One
6.1 Game Theory Introduction Game theory was introduced to better understand oligopoly. Recall the definition of game theory. Game Theory = A framework to study strategic interactions between players,
More informationDo 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
More informationStatic (or Simultaneous- Move) Games of Complete Information
Static (or Simultaneous- Move) Games of Complete Information Dominated Strategies Nash Equilibrium F.Valognes - Game Theory - Chp 2 1 Outline of Static Games of Complete Information Introduction to games
More informationTime-Dependent Network Pricing and Bandwidth Trading
Time-Dependent Network Pricing and Bandwidth Trading Libin Jiang (1), Shyam Parekh (2), Jean Walrand (1) (1) EECS Department, UC Berkeley (2) Alcatel-Lucent Outline Time-dependent Network Access and Pricing
More informationGame Theory - final project
Game Theory - final project The Price of Anarchy in Network Creation Games Is (Mostly) Constant Mat uˇs Mihal ak and Jan Christoph Schlegel Submitter name: Itzik Malkiel ID: 200481273 The Game: When I
More informationGAME THEORY: Analysis of Strategic Thinking Exercises on Repeated and Bargaining Games
GAME THEORY: Analysis of Strategic Thinking Exercises on Repeated and Bargaining Games Pierpaolo Battigalli Università Bocconi A.Y. 2006-2007 Exercise 1. Consider the following Prisoner s Dilemma game.
More informationThe Price of Anarchy in an Exponential Multi-Server
The Price of Anarchy in an Exponential Multi-Server Moshe Haviv Tim Roughgarden Abstract We consider a single multi-server memoryless service station. Servers have heterogeneous service rates. Arrivals
More informationLecture 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
More informationThree New Connections Between Complexity Theory and Algorithmic Game Theory. Tim Roughgarden (Stanford)
Three New Connections Between Complexity Theory and Algorithmic Game Theory Tim Roughgarden (Stanford) Three New Connections Between Complexity Theory and Algorithmic Game Theory (case studies in applied
More informationFOUR MARKET MODELS. Characteristics of Oligopolies:
FOUR MARKET MODELS Perfect Competition Monopolistic Competition Oligopoly Pure Monopoly Characteristics of Oligopolies: A Few Large Producers (Less than 10) Identical or Differentiated Products High Barriers
More informationMiscomputing Ratio: The Social Cost of Selfish Computing
Miscomputing Ratio: The Social Cost of Selfish Computing Kate Larson and Tuomas Sandholm Computer Science Department Carnegie Mellon University 5000 Forbes Ave Pittsburgh, PA 15213 {klarson,sandholm}@cs.cmu.edu
More informationECO 5341 Strategic Behavior Lecture Notes 1
ECO 5341 Strategic Behavior Lecture Notes 1 Saltuk Ozerturk Southern Methodist University Spring 2016 (Southern Methodist University) Introduction to Game Theory Spring 2016 1 / 14 What is game theory?
More informationAlgorithms for Auctions and Games
Algorithms for Auctions and Games Vincenzo Bonifaci and Stefano Leonardi Abstract Economics is one of the diverse aspects of our life in which algorithms play a perhaps subtle role. Whether we are buying
More informationEconomics 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,
More informationLecture 21: Strategic Interaction and Game Theory
Lecture : Strategic Interaction and Game Theory EC DD & EE / Manove Strategic Interaction p EC DD & EE / Manove Clicker Question p Strategic Interaction In perfectly competitive markets (like the market
More informationMicroeconomics LESSON 6 ACTIVITY 41
Microeconomics LESSON 6 ACTIVITY 41 Game Theory Strategic thinking is the art of outdoing an adversary, knowing that the adversary is trying to do the same to you. Dixit and Nalebuff Game theory is used
More informationCalin Dan Morosan (corresponding), INRO Consultants Inc., Canada
Paper Author (s) Michael Florian, INRO Consultants Inc., Canada (mike@inro.ca) Calin Dan Morosan (corresponding), INRO Consultants Inc., Canada (calin@inrosoftware.com) Paper Title & Number On uniqueness
More informationCS 486/686 Lecture 17 2-Player Normal-Form Games 1. Determine dominant-strategy equilibria of a 2-player normal form game.
CS 486/686 Lecture 17 2-Player Normal-Form Games 1 Learning goals: By the end of the lecture, you should be able to Determine dominant-strategy equilibria of a 2-player normal form game. Determine pure-strategy
More informationMICROECONOMICS - CLUTCH CH OLIGOPOLY.
!! www.clutchprep.com CONCEPT: CHARACTERISTICS OF OLIGOPOLY A market is an oligopoly when: Nature of Good: The goods for sale are Setting Price: The sellers are - There are producers - Firms are One firm
More informationSecurity and Game Theory
Security and Game Theory or Out of Eden Jared Saia A hard fact: Not everyone follows instructions Good and Bad A simple moral code for an aspiring deity (or computer scientist) Good: follow instructions
More informationTraffic Paradoxes and Economic Solutions
Journal of Urban Management 2011, Vol. 1, No. 1, pages 63 76 63 Traffic Paradoxes and Economic Solutions Chengri Ding Urban Studies and Planning Program, University of Maryland.; Tel: (301) 405 6626; Email:
More informationEcon 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
More informationGame 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,
More informationOligopoly: 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
More informationCH short answer study questions Answer Section
CH 15-16 short answer study questions Answer Section ESSAY 1. ANS: There are a large number firms; each produces a slightly different product; firms compete on price, quality and marketing; and firms are
More information29/02/2016. 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
More informationStrategic Analysis for Prediction Markets
Strategic Analysis for Prediction Markets Michael P. Wellman University of Michigan Joint work with David Pennock, others Prediction Market Games Agent has Beliefs (about uncertain proposition, other agents)
More informationBertrand competition in networks
Bertrand competition in networks Shuchi Chawla 1, Tim Roughgarden 2 1 Computer Sciences Dept., University of Wisconsin - Madison. shuchi@cs.wisc.edu. 2 Department of Computer Science, Stanford University.
More informationThe Case for Non-cooperative Multihoming of Users to Access Points in IEEE WLANs
The Case for Non-cooperative Multihoming of Users to Access Points in IEEE 802.11 WLANs Srinivas Shakkottai UIUC joint work with Eitan Altman and Anurag Kumar INRIA IISc Institut Eurecom July 28 th 2005
More informationMERITOCRACY AS A MECHANISM IN THE CONTEXT OF VOLUNTARY CONTRIBUTION GAMES
MERITOCRACY AS A MECHANISM IN THE CONTEXT OF VOLUNTARY CONTRIBUTION GAMES HEINRICH H. NAX (HNAX@ETHZ.CH) COSS, ETH ZURICH MAY 26, 2015 BUT BEFORE WE BEGIN Let us clarify some basic ingredients of the course:
More informationTransportation Theory and Applications
Fall 2017 - MTAT.08.043 Transportation Theory and Applications Lecture I: Introduction A. Hadachi Course Syllabus Lecturer: Amnir Hadachi Course website: https://courses.cs.ut.ee/2017/transport/fall Office
More informationPrice 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
More informationCost-Sharing Methods for Scheduling Games under Uncertainty
1 Cost-Sharing Methods for Scheduling Games under Uncertainty GIORGOS CHRISTODOULOU, University of Liverpool VASILIS GKATZELIS, Drexel University ALKMINI SGOURITSA, University of Liverpool We study the
More informationFinal exam and review informa0on
Final exam and review informa0on Monday, May 7th, at 4 PM in Boyden Gym Covers chapters on perfect compe00on, monopoly and monopolis0c compe00on Has 40 mul0ple choice and choice of 1 out of 2 of short
More informationMarkets and Strategy. Topics. Strategic Behavior. Intermediate Microeconomics
Markets and Strategy Intermediate Microeconomics Topics What is strategic behavior? Under what conditions do firms behave strategically? Two examples to introduce game theory as a tool for analyzing strategic
More informationFinance 510 Midterm #2 Practice Questions
Finance 50 Midterm # Practice Questions ) ) Consider the following pricing game between Dell and Gateway. There are two types of demanders in the market, High and Low. High demanders value a computer at
More informationDavid Easley and Jon Kleinberg November 29, 2010
Networks: Spring 2010 Practice Final Exam David Easley and Jon Kleinberg November 29, 2010 The final exam is Friday, December 10, 2:00-4:30 PM in Barton Hall (Central section). It will be a closed-book,
More informationOn the mode of Competition as a Collusive Perspective in Unionized Oligopoly
On the mode of Competition as a Collusive Perspective in Unionized Oligopoly Minas Vlassis * Maria Varvataki Department of Economics, University of Crete, Gallos University Campus, Rethymnon 74100, Greece
More informationWelfare 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
More informationIN THIS PAPER, we consider a congestion pricing approach
992 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 5, MAY 2006 A Scalable Network Resource Allocation Mechanism With Bounded Efficiency Loss Ramesh Johari, Member, IEEE, and John N. Tsitsiklis,
More informationEcon 98 Salazar Final Review Session Problems Part II Fall 04. Name: SID: GAME THEORY EXTERNALITIES INTERNATIONAL TRADE
GAME THEORY EXTERNALITIES INTERNATIONAL TRADE Game Theory What is a prisoner s dilemma? Dominant Strategy Nash Equilibrium Externalities Positive externalities extra marginal benefit to society Negative
More informationMore on public goods 1. For cost of exclusion, the legality of exclusion is irrelevant. We are considering only physical possibility of exclusion -
More on public goods 1. For cost of exclusion, the legality of exclusion is irrelevant. We are considering only physical possibility of exclusion - what is the value of the resources that must be expended
More informationStackelberg Scheduling Strategies. Tim Roughgarden Cornell University
Stackelberg Scheduling Strategies Tim Roughgarden Cornell University 1 The Model m machines 1,2,...,m A quantity r of jobs jobs are small (model in a cts way) For each machine i, a loaddependent latency
More informationStated Preference (Conjoint) Market Research Data
Stated Preference (Conjoint) Market Research Data Data for Estimation of Choice Models Revealed Preferences (RP): observed or reported actual behavior Travel diaries Stated Preferences (SP): Response to
More informationOligopoly Market. PC War Games
Oligopoly Market Ref. Ch 17 PC War Games In some markets there are only two firms. Computer chips are an example. The chips that drive most PCs are made by Intel and Advanced Micro Devices. How does competition
More informationThe social norm of leaving the toilet seat down: A game theoretic analysis
MPRA Munich Personal RePEc Archive The social norm of leaving the toilet seat down: A game theoretic analysis Siddiqi, Hammad UNSPECIFIED 16 November 2006 Online at http://mpra.ub.uni-muenchen.de/856/
More informationUrban Transport Modeling (based on these two sources)
Urban Transport Modeling (based on these two sources) A Transportation Modeling Primer May, 1995 Edward A. Beimborn Center for Urban Transportation Studies University of Wisconsin- Milwaukee http://www.uwm.edu/dept/c
More informationUNIK Multiagent systems Lecture 5. Non-cooperative game theory. Jonas Moen
UNIK4950 - Multiagent systems Lecture 5 Non-cooperative game theory Jonas Moen Highlights lecture 5 Non-cooperative game theory* Classification of game theory Utility of self-interested agents Strategic
More informationOvercoming the Limitations of Utility Design for Multiagent Systems
1402 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 58, NO. 6, JUNE 2013 Overcoming the Limitations of Utility Design for Multiagent Systems Jason R. Marden and Adam Wierman Abstract Cooperative control
More informationThe Traffic Circle of Life
John F. Smith Memorial Professor Department of Operations & Information Management Isenberg School of Management TEDxUMassAmherst, Professor Speaker Showcase November 25, 2013 Special thanks to the organizers
More informationMultiagent Systems: Spring 2006
Multiagent Systems: Spring 2006 Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss (ulle@illc.uva.nl) 1 Combinatorial Auctions In a combinatorial auction, the
More informationH3 Economics: Game Theory and the Economics of Cooperation. theme 2: firms and market failure game theory notes
theme 2: firms and market failure game theory notes introduction dominant strategies, Nash equilibrium and Prisoner s Dilemma repeated games sequential games entry deterrence strategic trade limitations
More informationBilevel Programming and Price Se1ing Problems. Martine Labbé Département d Informatique Université Libre de Bruxelles
Bilevel Programming and Price Se1ing Problems Martine Labbé Département d Informatique Université Libre de Bruxelles Bilevel Program LAAS - CNRS, Toulouse Adequate Framework for Stackelberg Game Leader:
More informationChapter 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
More informationOligopoly 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
More informationWhere are we? Knowledge Engineering Semester 2, Basic Considerations. Decision Theory
H T O F E E U D N I I N V E B R U S R I H G Knowledge Engineering Semester 2, 2004-05 Michael Rovatsos mrovatso@inf.ed.ac.uk Lecture 13 Distributed Rational Decision-Making 25th February 2005 T Y Where
More informationEconomic Analysis Reports: Briefing. Transportation Finance Panel
Economic Analysis Reports: 1. I-84 Viaduct in Hartford 2. I-84/Rt8 Mixmaster in Waterbury 3. New Haven Rail Line Briefing for Transportation Finance Panel Nov 23, 2015 Economic analyses 1 & 2 1. I-84 Viaduct
More informationChapter 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
More informationweather monitoring, forest fire detection, traffic control, emergency search and rescue A.y. 2018/19
UAVs are flying vehicles able to autonomously decide their route (different from drones, that are remotely piloted) Historically, used in the military, mainly deployed in hostile territory to reduce pilot
More information"Solutions" to Non-constant Sum Games
Unit 3 GAME THEORY Lesson 30 Learning Objective: Analyze two person non-zero sum games. Analyze games involving cooperation. Hello students, The well-defined rational policy in neoclassical economics --
More informationLecture 13(i) Announcements. Lecture on Game Theory. Average of HW 1-9 posted at Moodle. Two more to go: HW 10 due Tues, Dec 8 HW 11 due Tues, Dec 15
Lecture 13(i) Announcements Average of HW 1-9 posted at Moodle Two more to go: HW 10 due Tues, Dec 8 HW 11 due Tues, Dec 15 We drop the two lowest homeworks. If you skip HW 10 and HW 11, the current average
More informationIntroduction to Transportation Systems
Introduction to Transportation Systems 1 PART III: TRAVELER TRANSPORTATION 2 Chapter 28: Urban Public Transportation 3 Urban Public Transportation Introduction LOS Services History Costs Temporal Peaking
More informationUNMANNED AERIAL VEHICLES (UAVS)
UNMANNED AERIAL VEHICLES (UAVS) MONITORING BY UAVS I.E. WHAT? (SOME THESES PROPOSALS) UAVs are flying vehicles able to autonomously decide their route (different from drones, that are remotely piloted)
More informationINLAND NAVIGATION ECONOMICS WEBINAR SERIES #8 Elasticity of Demand - Shipper Responsiveness
INLAND NAVIGATION ECONOMICS WEBINAR SERIES #8 Elasticity of Demand - Shipper Responsiveness Michael R. Hilliard, Ph.D. Center for Transportation Analysis Oak Ridge National Laboratory April 10, 2013 US
More informationPARETO-IMPROVING CONGESTION PRICING AND REVENUE REFUNDING WITH ELASTIC DEMAND
PARETO-IMPROVING CONGESTION PRICING AND REVENUE REFUNDING WITH ELASTIC DEMAND Xiaolei Guo, Odette School of Business Cross-Border Transportation Centre University of Windsor Hai Yang, Department of Civil
More informationUniversity Question Paper Two Marks
University Question Paper Two Marks 1. List the application of Operations Research in functional areas of management. Answer: Finance, Budgeting and Investment Marketing Physical distribution Purchasing,
More informationHidden Actions Analysis in p2p Systems
December 6, 2009 1 Introduction 2 Model 3 Analysis 4 Results Currency Based Incentive Peers would earn currency by contributing resources, and spend currency to obtain resources. e.g. MojoNation, Karma
More informationOn the quality and complexity of Pareto equilibria in the Job Scheduling Game
On the quality and complexity of Pareto equilibria in the Job Scheduling Game ABSTRACT Leah Epstein Department of Mathematics University of Haifa 31905 Haifa, Israel lea@math.haifa.ac.il In the well-known
More informationHow do we know the market structure?
Course informa-on Final exam: Tuesday, 12/11 4-6 in Machmer W 15 If you have a conflict, go the the Registrar s office and they will give you a form saying which exam can be changed. Final exam will cover
More information