6/17/2017 Unit 8 Homework Assignment (8.2) armstrong Olivier MAT230, section MAT230.30 MOD5 2017, Summer 1 2017 Instructor: James Segala WebAssign Unit 8 Homework Assignment (8.2) (Homework) Current Score : - / 48 Due : Sunday, June 25 2017 11:59 PM EDT 1. -/1 pointsBerrFinMath1 8.2.001. For the game and mixed strategies, find the expected value. 3 4 1 1 Let G = , r = and c = 4 1 2 2 1 2 1 2 Show My Work (Optional) 2. -/1 pointsBerrFinMath1 8.2.002. For the game and mixed strategies, find the expected value. 3 2 2 3 Let G = , r = and c = 4 1 5 5 4 5 1 5 Show My Work (Optional) 3. -/1 pointsBerrFinMath1 8.2.003. For the game and mixed strategies, find the expected value. 1 3 4 1 3 1 1 1 Let G = , r = and c = 8 7 6 2 2 3 1 3 Show My Work (Optional) 4. -/1 pointsBerrFinMath1 8.2.004. For the game and mixed strategies, find the expected value. 9 3 1 1 Let G = 5 9 , r = 0 and c = 2 2 5 6 3 5 2 5 Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 1/6 6/17/2017 Unit 8 Homework Assignment (8.2) 5. -/6 pointsBerrFinMath1 8.2.005. For the 2 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 7 3 2 7 For row player R: r1 = r2 = For column player C: c1 = c2 = Find the value v of the game for row player R. v = Who is the game favorable to? The game is favorable to the row player. The game is favorable to the column player. This is a fair game. Show My Work (Optional) 6. -/6 pointsBerrFinMath1 8.2.006. For the 2 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 3 1 1 2 For row player R: r1 = r2 = For column player C: c1 = c2 = Find the value of the game for row player R. v = Who is the game favorable to? The game is favorable to the row player. The game is favorable to the column player. This is a fair game. Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 2/6 6/17/2017 Unit 8 Homework Assignment (8.2) 7. -/6 pointsBerrFinMath1 8.2.007. For the 2 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. 5 7 3 5 For row player R: r1 = r2 = For column player C: c1 = c2 = Find the value of the game for row player R. v = Who is the game favorable to? This game is favorable to the row player. This game is favorable to the column player. This is a fair game. Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 3/6 6/17/2017 Unit 8 Homework Assignment (8.2) 8. -/11 pointsBerrFinMath1 8.2.008. Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question. Political scientists distinguish between two kinds of issues in elections campaigns: "positional" issues (voters have sharply divided and incompatible views) and "valence" issues (voters agree on goals but are divided on the best ways to achieve them). In a race between the incumbent and the challenger for state governor, a marketing survey found that if the incumbent focused on positional issues, she trailed the challenger by 15% if he focused on the same kind of issues, but she led him by 15% if he concentrated on valence issues. If she focused on valence issues, she trailed him by 20% if he focused on the same kind of issues, but she led him by 25% if he concentrated on positional issues. Challenger P V Incumbent P V % % % % What does P represent? P represents positional issues. P represents valence issues. What does V represent? V represents valence issues. V represents positional issues. For the incumbent: r1 = r2 = For the challenger: c1 = c2 = In designing the incumbent's TV ads for the campaign, what proportion should focus on positional issues? % Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 4/6 6/17/2017 Unit 8 Homework Assignment (8.2) 9. -/15 pointsBerrFinMath1 8.2.010. Represent the situation as a game and find the optimal strategy for each player. State your final answer in the terms of the original question. In a section of Freshman Composition at your college, the English professor gives a daily quiz on either vocabulary or writing, and allows his students to bring either a dictionary or a grammar textbook (but not both) to use during the quiz. Joe estimates that if he brings a dictionary, he can get a 80 on a vocabulary quiz but only an 60 on a paragraph revision, while with his grammar textbook, he can get a 70 on the revision but only a 50 on the vocabulary quiz. Quiz on V P Joe brings D G What does D represent? D represents paragraph revision. D represents grammar textbook. D represents vocabulary quiz. D represents dictionary. What does G represent? G represents vocabulary quiz. G represents grammar textbook. G represents dictionary. G represents paragraph revision. What does V represent? V represents grammar textbook. V represents paragraph revision. V represents vocabulary quiz. V represents dictionary. What does P represent? P represents grammar textbook. P represents dictionary. P represents vocabulary quiz. P represents paragraph revision. r1 = r2 = c1 = c2 = v = How should he decide each day what to bring? Flip a coin each day take the dictionary if it is heads and the grammar textbook if it is tails. He should always take the dictionary. He should ask his friend which book to bring. He should always take the grammar textbook. https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 5/6 6/17/2017 Unit 8 Homework Assignment (8.2) What grade can he be expected to earn? Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106778 6/6 6) r1 = 3/5 r2 = 2/5 c1 = 1/5 c2 = 4/5 v = 7/5 The game is favourable to the row player. 7) r1 = 2/5 r2 = 3/5 c1 = 3/5 c2 = 2/5 v = 1/5 The game is favourable to the row player. 8) P V P 15 -15 V -25 20 P represents positional issues. V represents valence issues. r1 = 3/5 r2 = 2/5 c1 = 7/15 c2 = 8/15 1% 9) D V P 80 60 G 50 70 D represents dictionary. G represents grammar textbook. V represents vocabulary quiz. P represents paragraph revision. r1 = 1/2 r2 = 1/2 c1 = 1/4 c2 = 3/4 v = 65 He should always take the dictionary. He is expected to earn 75