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What is game theory?

Robert J. Aumann, 1985: Brie y put, game and economic theory are concerned with the interactive behavior of Homo rationalis | rational man. . . [An] important function of game theory is the classi cation of interactive decision situations.

Roger B. Myerson, 1991: Game theory can be de ned as the study of mathematical models of con ict and cooperation between

intelligent rational decision-makers. Game theory provides general mathematical techniques for analyzing situations in which two or more individuals make decisions that will in uence one another's welfare. Nobel Prize Citation, 1994: Game theory is a mathematical

method for analysing strategic interaction.

Problem

What is strategic interaction?

(Singapore Management University)

Introduction to Game Theory

Fall 2012

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An Example of a Game | Flat Tire

Two SMU students, Al and Bob, very con dent about their midterm exam performance in ECON 206, decided to attend a party the weekend before the nal exam. The party was so good that they overslept the whole Sunday. Instead of taking the nal unprepared on Monday, they pleaded the professor to give them a make-up exam. Their excuse was a at tire without a spare and any help. The professor, surprisingly, agreed. On Tuesday morning, the professor placed them in separated rooms and handed them the test. The test had just one question:

\Which tire?"......

(Singapore Management University)

Introduction to Game Theory

Fall 2012

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The GPA Rat Race

All of you are now enrolled in ECON 206 that will be graded on a curve. No matter how well you do in absolute terms, only 33.3% of the students will get A's, and only 33.3% of the students will get B's. Therefore, you must work hard, not just in absolute terms, but relative to how hard your classmates work.

All of you are smart enough to recognize this, and after the rst lecture you all hold a secrete meeting where all of you agree not to work too hard.

What will happen in the end?

(Singapore Management University)

Introduction to Game Theory

Fall 2012

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Why Are Professors So \Mean?"

Many professors have rigid rules not to give makeup exams and NEVER to accept late homework assignments. Students might think the professors are so hardhearted to behave in this way.

The truth is....

Most professors are actually very kindhearted (for example....) They are willing to give their students every reasonable break and accept every reasonable excuse

But most professors also know that this is a slippery slope (for example,...) | if they set very exible rules, what may happen?

(Singapore Management University)

Introduction to Game Theory

Fall 2012

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Another Example | Strategic Interactions vs. Individual

Decision Problems

Underlying story: two students (Alice and Bob) are taking a course together. There are three e ort levels for each student: work hard (utility = 5), work sometimes (utility = 2), shirk (utility = 0). Consider the following two grade schemes.

Grade Scheme A: A student's nal grade only depends on her own e ort level | if a student works hard, she will get an A for sure (utility = 10); if she works sometimes, she will get a passing grade (utility = 5); while if the student shirks, she will fail the course for sure (utility = 0).

Individual Decision Problem

E ort Level

Utility Disutility Net

Work Hard

10

5

Work Sometimes

5

2

Shirk

0

0

(Singapore Management University)

Introduction to Game Theory

Payo

5

3

0

Fall 2012

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Another Example | Strategic Interactions vs. Individual

Decision Problems (Cont.)

Grade Scheme B: Each student's nal grade depends on her own

e ort level, as well as on her ranking of the two: whoever gets a higher score receives an A; while if both get the same score, both will fail the course. Alice's payo s are:

E ort Level

Work Hard

Work Sometimes...