# 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.

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.

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.

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.

• 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)

Completing this assessment should take approximately 2 hours.

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

• 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)

Completing this assessment should take approximately 45 minutes.

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

• 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)

Completing this assessment should take approximately 90 minutes.

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

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.

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)

Reading this chapter should take approximately 15 minutes.

• 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)

Completing this assessment should take approximately 2 hours.

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

• 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)

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

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

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.

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.

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.

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.

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.

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)

Reading this chapter should take approximately 30 minutes.

• 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)

Completing this assessment should take approximately 2 hours.

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

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