MATH 125 - Reading Assignment 7 - Section 9.4 - Spring 2008
Give it up for !
1. A for a player with options 1 to nis a set of nonnegative
numbers p1; p2; :::; /pnsumming to 1. The player using selects option iwith probability
pi:
2. A is a special case where one of the probabilities is 1 and
the others are 0.
3. The expected value of a set of values x1; x2; :::; xnthat occur with probabilities p1; p2; :::; /pn
summing to 1 is:
4. What are the two steps in computing expected payo¤ to a player when using the
options described in question #1 are used by both players?
5. The implies that there is a value vin a game in which
players select di¤erent options with di¤erent probabilities at which the expected value
of the Row Player is v; and expected value of the Column Player is v; and neither
player can do better by unilaterally changing strategies.
6. Suppose the reduced payo¤ matrix of a game is
Column Player
C1 C2
Row Player R1 a b
R2 c d
The probability the Row Player opts for R1 is given by
The probability the Column Player opts for C1 is given by
The value of the game for the Row Player is