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ECON200: Math for Economists

Unit 5: Game Theory   Game theory was first applied to economic problems by the Nobel-Prize-winning economist John Nash.  His discoveries were dramatized in the movie A Beautiful Mind.  In essence, game theory describes and predicts how participants will make decisions based on their expectations of consequences.  In the classic game, the prisoner’s dilemma, two criminals either choose to confess or maintain innocence.  There are four possible outcomes and associated benefits and costs with each.  The choices can be quantified, and a “Nash equilibrium” can be calculated.  Although abstract, this kind of game can describe behavior in oligopolies.

Games can become substantially more complex as additional moves and choices are incorporated into models.  Decision trees can be used to describe sequential move games, and a payoff matrix approximates simultaneous move games like the prisoner’s dilemma.  Algorithms will provide some solutions to Nash equilibriums, while partial derivatives yield answers to other games.  The right tool must be matched to each kind of game.

As a practical example, game theory can be used to describe some kinds of auctions.  This kind of market has gained increasing popularity with the advent of online auctions at eBay.  When calculating a price, the bidder must analyze available data, but some information is held back.  The introduction of uncertainty into the process makes the optimal calculations extremely complex.

Unit 5 Time Advisory
This unit should take you approximately 20.25 hours to complete.

☐    Subunit 5.1: 1.75 hours

☐    Subunit 5.2: 5.5 hours

☐    Subunit 5.3: 3 hours

☐    Subunit 5.4: 2.25 hours

☐    Sub-subunit 5.4.1: 1.25 hours

☐    Sub-subunit 5.4.2: 1.25 hours

☐    Subunit 5.5: 5.25 hours

Unit5 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Develop a toolkit of quantitative methods to solve problems in game theory. - Apply specific quantitative tools (decision trees, Nash equilibria) to solve problems in game theory. - Analyze differences in outcomes of auctions using game theory. - Evaluate the optimal strategy within the broader context of economic theory and practical applications for games. 

5.1 Sequential Move Games   - Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9: Sequential Move Games” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9: Sequential Move Games” (PDF)

 Instructions: Read pages 93–102.  Note this reading covers the
material you need to know for subunits 5.1–5.2.  

 Reading this chaptershould take approximately 30 minutes.  

 Terms of Use: The above reading is licensed under a [Creative
Commons Attribution-NonCommercial 3.0
License](http://creativecommons.org/licenses/by-nc/3.0/).  It is
attributed to Yoram Bauman, and the original version can be found
[here](http://www.smallparty.org/yoram/quantum/).
  • Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “13: Sequential Games: Moral Hazard, Incentives, and Hungry Lions” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “13: Sequential Games: Moral Hazard, Incentives, and Hungry Lions” (YouTube)

    Also Available in:
    Flash, HTML, MP3 or QuickTime
    iTunes U

    Instructions: Watch the entire lecture.

    Watching this lecture should take approximately 1 hour and 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.2 Backward Induction   Note: This subunit is covered by the reading assigned beneath subunit 5.1.  Focus on pages 96–102 to learn more about backward induction.

  • Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “14: Backward Induction: Commitment, Spies, and First-Mover Advantages” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “14: Backward Induction: Commitment, Spies, and First-Mover Advantages” (YouTube)

    Also Available in:
    Flash, HTML, MP3 or QuickTime
    iTunes U

    Instructions: Watch the entire lecture.

    Watching this lecture should take approximately 1 hour and 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 9 Problems” (PDF)

    Instructions: Please go to the webpage and locate the Downloads section.  Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material.  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete problems 9.1–9.12 on pages 98–104 in chapter 9.

    Completing this assessment should take approximately 2 hours.

    Solutions: Answers are in the endnotes beginning on page 236.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10 Problems” (PDF)

    Instructions: Please go to the webpage and locate the Downloads section.  Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material.  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete problems 10.1–10.2 on page 108 in chapter 10.

    Completing this assessment should take approximately 45 minutes.

    Solutions: Answers are in the endnotes beginning on page 238.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: University of California, Davis: Giacomo Bonanno’s Econ 122–Game Theory: “Week 5 Problems” Link: University of California, Davis: Giacomo Bonanno’s Econ 122—Game Theory“Week 5 Problems” (PDF)

    Instructions: Please go to the webpage and locate file “week_ 5.pdf.”  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete questions 1–3.

    Completing this assessment should take approximately 90 minutes.

    Solutions: Answers can be found at file “week5_answ.pdf.”

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.3 Simultaneous Move Games   - Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “05: Nash Equilibrium: Bad Fashion and Bank Runs” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “05: Nash Equilibrium: Bad Fashion and Bank Runs” (YouTube)

 Also Available in:  
 [Flash, HTML, MP3 or
QuickTime](http://oyc.yale.edu/economics/econ-159/lecture-5)  
 [iTunes
U](http://itunes.apple.com/us/itunes-u/game-theory-video/id341651977)  

 Instructions: Watch the entire lecture.  

 Watching this lecture should take approximately 1 hour and 15
minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10: Simultaneous Move Games” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 10: Simultaneous Move Games” (PDF)

    Instructions: Read pages 103–106.

    Reading this chapter should take approximately 15 minutes.

    Terms of Use: The above reading is licensed under a Creative Commons Attribution-NonCommercial 3.0 License.  It is attributed to Yoram Bauman, and the original version can be found here.

  • Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12 Problems” (PDF)

    Instructions: Please go to the webpage and locate the Downloads section.  Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material.  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete problems 12.1–12.10 and C-12.1 and C-12.2 on pages 128–131 in chapter 12.

    Completing this assessment should take approximately 2 hours.

    Solutions: Answers are in the endnotes beginning on page 238.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: University of California, Davis: Giacomo Bonanno’s “Econ 122–Game Theory” Link: University of California, Davis: Giacomo Bonanno’s “Econ 122—Game Theory” (PDF)

    Instructions: Please go to the webpage and locate file “week_ 4.pdf.”  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete questions 2–4.

    Completing this assessment should take approximately 1 hour and 30 minutes.

    Solutions: Answer can be found at file “week4_answ.pdf.”

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.4 Iterated Dominance and Nash Equilibrium   - Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “06: Nash Equilibrium: Dating and Cournot” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “06: Nash Equilibrium: Dating and Cournot” (YouTube)

 Also Available in:  
 [Flash, HTML, MP3 or
QuickTime](http://oyc.yale.edu/economics/econ-159/lecture-6)  
 [iTunes
U](http://itunes.apple.com/us/itunes-u/game-theory-video/id341651977)  

 Instructions: Watch the entire lecture.  

 Watching this lecture should take approximately 1 hour and 15
minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12: Iterated Dominance and Nash Equilibrium” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 12: Iterated Dominance and Nash Equilibrium” (PDF)

    Instructions: Read pages 113–130.  Note that this reading also covers the material you need to know for subunits 5.4.1–5.4.2.

    Reading this chapter should take approximately 1 hour.

    Terms of Use: The above reading is licensed under a Creative Commons Attribution-NonCommercial 3.0 License.  It is attributed to Yoram Bauman, and the original version can be found here.

5.4.1 Infinitely Repeated Games   Note: This subunit is covered by the reading assigned beneath subunit 5.4.  Focus on pages 120–121 to learn more about infinitely repeated games.

  • Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “21: Repeated Games: Cooperation vs. the End Game” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “21: Repeated Games: Cooperation vs. the End Game” (YouTube)

    Also available in:
    Flash, HTML, MP3 or QuickTime
    iTunes U

    Instructions: Watch the entire lecture.

    Watching this lecture should take approximately 1 hour and 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.4.2 Mixed Strategies   Note: This subunit is covered by the reading assigned beneath subunit 5.4.  Focus on pages 122–127 to learn more about mixed strategies.

  • Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “09: Mixed Strategies in Theory and Tennis” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “09: Mixed Strategies in Theory and Tennis” (YouTube)

    Also available in:
    Flash, HTML, MP3 or QuickTime
    iTunes U

    Instructions: Watch the entire lecture.

    Watching this lecture should take approximately 1 hour and 15 minutes.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

5.5 Auctions   - Lecture: YouTube: Yale University, Department of Economics: Ben Polak’s “24: Asymmetric Information: Auctions and the Winner’s Curse” Link: YouTube: Yale University, Department of Economics: Ben Polak’s “24: Asymmetric Information: Auctions and the Winner’s Curse” (YouTube)

 Also available in:  
 [Flash, HTML, MP3 or
QuickTime](http://oyc.yale.edu/economics/econ-159/lecture-24)  
 [iTunes
U](http://itunes.apple.com/us/itunes-u/game-theory-video/id341651977)  

 Instructions: Watch the entire lecture.  

 Watching this lecture should take approximately 1 hour and 15
minutes.  

 Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
  • Reading: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13: Application: Auctions” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13: Application: Auctions” (PDF)

    Instructions: Read pages 131–140.

    Reading this chapter should take approximately 30 minutes.

    Terms of Use: The above reading is licensed under a Creative Commons Attribution-NonCommercial 3.0 License.  It is attributed to Yoram Bauman, and the original version can be found here.

  • Assessment: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13 Problems” Link: Yoram Bauman’s Quantum Microeconomics with Calculus, Version 4.02: “Chapter 13 Problems” (PDF)

    Instructions: Please go to the webpage and locate the Downloads section.  Under “Quantum Microeconomics with calculus,” click on the “entire textbook” link to download the material.  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete problems 13.1–13.5 on pages 140–142 in chapter 13.

    Completing this assessment should take approximately 2 hours.

    Solutions: Answers are in the endnotes beginning on page 242.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: Paul Klemperer’s “Auctions: Theory and Practice” Link: Paul Klemperer’s “Auctions: Theory and Practice” (PDF)

    Instructions: Please go to the webpage and locate the file “Exercises.”  This is an Adobe Acrobat file that requires Adobe Acrobat Reader, which can be downloaded free at Adobe’s website.  Complete question 7.

    Completing this assessment should take approximately 1 hour.

    Solutions: Answers can be found in the “Solutions” PDF.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: The Saylor Foundation’s “Unit 5 Self-Test” Link: The Saylor Foundation’s “Unit 5 Self-Test”
     
    Instructions: Please complete these 10 multiple choice questions by selecting the best possible answer of those provided.  It may be helpful to have pencil and paper available so you can sketch out and solve some of the problems. 
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.