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

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Chapter 1: Introduction to Quantitative Analysis 1.Describe the quantitative analysis approach 2.Understand the application of quantitative analysis in a real situation 3.Describe the use of modeling in quantitative analysis 4.Use computers and spreadsheet models to perform quantitative analysis 5.Discuss possible problems in using quantitative analysis 6.Perform a break-even analysis

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

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

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

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Example 1 Player I b1b1 b2b2 a1a a2a2 5-4 Player II Best Strategy For Player I MaximinPayoff Best Strategy For Player II MinimaxPayoff Row minimum Column maximum

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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

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Red 2Black 7Row minimum Player I b1b1 b2b2 Black Acea1a1 Red 8a2a2 Column maximum Player II

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Expected value 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 Red 2Black 7 EV Player I b 1 (p)b 2 (1-p) Black Acea 1 (q) Red 8a 2 (1-q) EV p + (1-p) 8p -7(1-p) -2q + 8(1-q)q -7(1-q)

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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

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Example 3 Y1Y2 X1130 X268 X31214 Row minimum Column maximum

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Example 3 Y1Y2 X1130 X268 X31214 Row minimum Column maximum

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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

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M4.15 (sol.) Do nothing $10,000$20,000Row minimum ST Co. b1b1 b2b2 b3b3 Do nothing a1a $15,000a2a2 31 Column maximum 31 -1

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