Fall 2002

**Math 486, Game Theory**

MFW 8-8:50 am, 322 Sacket

office hours: MWF 9:05-11:00 am. 205 MB

outlines & grading

integrity |

textbook: Introduction to Game Theory by P.Morris, Springer Verlag

100% = 298 pts on Dec. 13.

Grades: F, D, D, C, B-, B-, B+, A, A, A, A, A, A. 13 students.

Homework due Friday September 6, 8:00 am.

Solve Nim with intitial position 10, 100 and last move loosing. 25 pts.

*Hint*: Consider smaller initial positions.

To solve this game means finding a winning strategy for the first or second player.

So it should be clearly indicated which player wins and how.

Homework, 30 pts. due W, Sept.11.

A correction to Roulette solution: If you guess a number, your payoff is $35, not $36.

So the value of game is (1/38)$35+(37/38)(-$1)=-$1/19. For Roulette without 00,

the value is (1/37)$35+(36/37)(-$1)=-$1/37.

Betting total of $1 on any combination of numbers gives the same value.

**Sept 25.** W. midterm. min = 14, average = 30, max = 42.

midterm 2 pictures.

midterm 3 November 20. pictures. |

homework, 20 pts, due F November 15.

Find the Shapley values for the game given by the characteristic function v :

coalition A B C D AB AC AD BC BD CD

v 1 2 3 4 5 6 7 8 9 10

---------------------------------------------------

coalition ABC ACD ABD BCD ABCD

v 21 22 23 24 40

**Dec 2**. poker .

**Dec 4**. hnwrk 20 pts, due Dec 6: compute the probabilities of a pair and 4 of a kind in poker.

See poker for solution. Several students included two pairs (but not 3 of a kind) in their answers

for probability of a pair.

Repeated Prisoner's Dilemma graded.

Dec 9. We discussed, among other things, hex. See the link to

Playing the Numbers: An Introduction to Game Theory by Ben Davis

for a proof that the first player wins:, his webpage .