MATH 210, PROBLEM SET 1
DUE IN LECTURE ON FRIDAY, JAN. 18
1. Frankfurts theory of lying and bullshit.
Read Frankfurts book On Bullshit. In particular, see the description of the distinction
he makes between lying and bullshit on pages 50 through 62.
1. Di
LINEAR PROGRAMMING PROBLEMS HAVE SOLUTIONS
1. Statement of the Result
Suppose n, m 1 are integers, B = (bi,j )1in,1j m is an n m matrix of positive numbers, and b = (b1 , . . . , bm ) and c = (c1 , . . . , cn ) are vectors of positive numbers. The linear
ROW RANKS AND VERTICES
MATH 212 NOTES
1. Some linear algebra
The object of these notes is to simplify the problem of nding the vertices in a linear
programming problem when the matrix dening the problem has enough linear dependencies among its rows. To st
LINEAR PROGRAMMING PROBLEMS AND VERTICES
1. Statement of the Result
Suppose n, m 1 are integers, B = (bi,j )1in,1j m is an n m matrix of positive numbers, and b = (b1 , . . . , bm ) and c = (c1 , . . . , cn ) are vectors of positive numbers. The linear
pr
MATH 212, PROBLEM SET 6
DUE FRIDAY, APRIL 5
1. Partial conflict games
In these problems, players I and II each have the option of either competing or cooperating with the other player. There are thus four possible combinations of option choices
the two co
MATH 212, PROBLEM SET 5
DUE MONDAY, MARCH 25
In these problems we consider the linear programming problem of nding the vectors
s = (s1 , . . . , sn ) (0, . . . , 0) for which sB (1, . . . , 1) and f (s) = s1 + + sn is minimal,
where B = (bi,j ) is an n m
MATH 212, PROBLEM SET 4
DUE FRIDAY, MARCH 1
Please give mathematical justications for your answers to these problems.
1. Closed sets and bounded sets
1. Let M be the subset of R2 which is the graph of the function h(x) = 1/x for x > 0.
Thus
M = cfw_(x, 1/
MATH 212, PROBLEM SET 3
DUE IN JONATHAN KARIVS MAILBOX IN THE MATH OFFICE BY 5 P.M. ON WEDNESDAY, FEB. 13.
A multi-option two-person game.
The object of this set of exercises is to nd the optimal strategy in a two-person zero sum
game in which the rst pla
MATH 212, PROBLEM SET 2
DUE IN LECTURE ON MONDAY, FEBRUARY 4.
A three option two person zero sum game.
The rock-paper-scissors game has two players who simultaneously choose between three
options; rock, paper or scissors. If they choose the same option, t
The Effectiveness of Tit-for-Tat
Miguel Dvila
Josh Jackson
Sung-Ho Park
Introduction
The Prisoners Dilemma, a simple game in which two players have the choice
between either cooperating or defecting, has long been used in game theory and many
of its appli