Notes on Introduction to Game Theory
Introduction to Game Theory
Fall 2012
1 / 18
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
2 / 18
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
3 / 18
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
Fall 2012
1 / 18
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
2 / 18
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
3 / 18
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