1. Name: Trương Hoài Anh
Facebook: Quasar Hoaianh
Website: qm-for-business-class-of-mr-Huy8.webnode.vn
Class
Pass: qmiu

2. Chapter 1: Introduction to Quantitative Analysis
Describe the quantitative analysis approach
Understand the application of quantitative analysis in a real situation
Describe the use of modeling in quantitative analysis
Use computers and spreadsheet models to perform quantitative analysis
Discuss possible problems in using quantitative analysis
Perform a break-even analysis

3. Chapter 2: Probability
Basic Definitions: Events, Sample Space, and Probabilities
Basic Rules for Probability
Conditional Probability
Independence of Events
Combinatorial Concepts
The Law of Total Probability and Bayes’ Theorem
Random variables

4. Module 1: Game theory
Two-person means there are two competing players in the game.
Zero-sum means the gain (or loss) for one player is equal to the corresponding loss (or gain) for the other player.
The gain and loss balance out so that there is a zero-sum for the game.
What one player wins, the other player loses.

5. Module 1: Game theory Payoff table 4 steps
Row minimum
Maximin
Column maximum
Minimax
Pure vs Mixed vs Dominated strategies
Expected value (EV)/saddle point

6. Example 1 Player II Player I b1 b2 a1 19 20 a2 5 -4 Row minimum 19 -4
Best Strategy
For Player II
Player II
Player I b1 b2 a1 19 20 a2 5 -4
Row minimum 19 -4
Column maximum 19 20
Maximin
Payoff
Best Strategy
For Player I
Minimax
Payoff

7. Example 2
Player I holds a black Ace and a red 8. Player II holds a red 2 and a black 7. The players simultaneously choose a card to play. If the chosen cards are of the same color, Player I wins. Player II wins if the cards are of different colors. The amount won is a number of dollars equal to the number on the winner’s card (Ace counts as 1.)
Establish the payoff table
Find the value of the game and the optimal mixed strategies of the players

8. Player II Player I Red 2 Black 7 Row minimum b1 b2 Black Ace a1 Red 8
Column maximum -2 -2 1 -7 8 -7 8 1

9. Expected value Player I EV for q: -2q+8(1-q)=q-7(1-q) => q=15/18
Red 2
Black 7 EV
Player I
b1 (p)
b2 (1-p)
Black Ace
a1 (q)
Red 8
a2 (1-q) -2 1 8 -7
-2p + (1-p)
8p -7(1-p)
-2q + 8(1-q)
q -7(1-q)
EV for q: -2q+8(1-q)=q-7(1-q) => q=15/18
EV for p: -2p+(1-p)=8p-7(1-p) => p=4/9
EV: -2(4/9)+(1-4/9)= -1/3

10. Dominated strategy 2 players, zero-sum
At least one player has more than 2 options
Solution
Payoff
4 steps
Pure strategy or mixed strategy
Pure => EV
Mixed => elimination => EV

11. Example 3 Row minimum Y1 Y2 X1 13 X2 6 8 X3 12 14 6 12 Column maximumX2 6 8 X3 12 14 6 12
Column maximum 13 14

12. Example 3 Row minimum Y1 Y2 X1 13 X2 6 8 X3 12 14 12 Column maximum 13X2 6 8 X3 12 14 12
Column maximum 13 14

13. M4.15
ST Co. and FF Co. are both vying for more share of the market. If ST does no advertising, it will not lose any share of market if FF does nothing. It will lose 2% of market if FF invests $10,000, and it will lose 5% if FF invests $20,000 in advertising. On the other hand, if ST invests $15,000 it will gain 3% if FF does nothing; gain 1% if FF invests $10,000; and lose 1% if FF invests $20,000 in advertising.
Develop a payoff table
Find the value of the game

14. M4.15 (sol.) ST Co. Do nothing $10,000 $20,000 Row minimum b1 b2 b3 a1-2 -5
$15,000 a2 3 1 -1
Column maximum -1