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 6/17/2017 Unit 7 Homework Assignment (8.1) armstrong Olivier MAT230, section MAT230.30 MOD5 2017, Summer 1 2017 Instructor: James Segala WebAssign Unit 7 Homework Assignment (8.1) (Homework) Current Score : 2 / 48 Due : Sunday, June 25 2017 11:59 PM EDT 1. 2/6 points | Previous AnswersBerrFinMath1 8.1.001. For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. In an attempt to gain more viewers, Channel 86 and Channel 7 are each trying to decide whether to schedule a quiz show or a reality series in their 8:00 prime time slot. Market research indicates that if Channel 86 chooses a quiz show, it will gain 3% of the market if Channel 7 runs a quiz show and lose 5% if Channel 7 runs a reality series, while if Channel 86 chooses a reality series, it will gain 7% if Channel 7 runs a quiz show and lose 7% if Channel 7 runs a reality series. [Hint: Use Q and R for quiz show and reality series.] Channel 7 Q R Channel 86 Q 2 R 9 % 4 % % 9 % What does Q represent? Q represents a quiz show. Q represents a reality show. What does R represent? R represents a quiz show. R represents a reality show. Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106777 1/4 6/17/2017 Unit 7 Homework Assignment (8.1) 2. -/12 pointsBerrFinMath1 8.1.002. For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict. Andersonville has two gas stations, Ralph's QwikServ and Charlie's GasnGo. Both Ralph and Charlie are considering raising prices by 1, staying with their current prices, or lowering prices by 1. If they both make the same choice, there will be no change in their market shares, but if they make different choices, the one with the lower price will gain 4% of the market for each penny difference in their prices. Charlie R S L R Ralph S L % % % % % % % % % What does R represent? R represents raising the price by 1. R represents lowering the price by 1. R represents keeping the price the same. What does S represent? S represents lowering the price by 1. S represents raising the price by 1. S represents keeping the price the same. What does L represent? L represents lowering the price by 1. L represents raising the price by 1. L represents keeping the price the same. Show My Work (Optional) 3. -/5 pointsBerrFinMath1 8.1.003. For the game, identify the saddle point and determine the corresponding optimal strategy for each player. 6 8 2 7 The saddle point is the in row and column The optimal strategy is for R to always choose row . and for C to always choose column . Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106777 2/4 6/17/2017 Unit 7 Homework Assignment (8.1) 4. -/5 pointsBerrFinMath1 8.1.004. For the game, identify the saddle point and determine the corresponding optimal strategy for each player. 4 2 3 5 1 3 The saddle point is the in row and column The optimal strategy is for R to always choose row . and for C to always choose column . Show My Work (Optional) 5. -/5 pointsBerrFinMath1 8.1.005. For the game, identify the saddle point and determine the corresponding optimal strategy for each player. 2 1 4 6 4 6 3 1 2 The saddle point is the in row and column The optimal strategy is for R to always choose row . and for C to always choose column . Show My Work (Optional) 6. -/5 pointsBerrFinMath1 8.1.006. For the game, identify the saddle point and determine the corresponding optimal strategy for each player. 24 7 5 1 16 12 13 27 9 11 14 8 The saddle point is the in row and column The optimal strategy is for R to always choose row . and for C to always choose column . Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106777 3/4 6/17/2017 Unit 7 Homework Assignment (8.1) 7. -/10 pointsBerrFinMath1 8.1.007. Determine the optimal strategy for the situation by representing it as a game and finding the saddle point. State your final answer in the terms of the original question. In an ongoing price war between Burger Haven (locally owned) and MacArches (a chain), both restaurant managers plan to change the price of a hamburger by 10. If they both raise their prices, there will be no change in their market shares, but if they both lower their prices, the chain's national advertising will ensure that MacArches gains 3% of the market. Again because of advertising, if Burger Haven lowers their price and MacArches raises their price, Burger Haven will gain only 2% of the market, but if Burger Haven raises their price and MacArches lowers their price, MacArches will gain 8% of the market. Use this information to decide what the managers should do. MacArches L R L Burger Haven R % % % % What does L represent? L represents lowering the price by 10. L represents raising the price by 10. What does R represent? R represents lowering the price by 10. R represents raising the price by 10. The saddle point is the in row and column . What should the managers do? Both restaurants should raise the price. Burger Haven should lower its prices, while MacArches raises its prices. Both restaurants should lower the price. MacArches should lower its prices, while Burger Haven raises its prices. Show My Work (Optional) https://www.webassign.net/web/Student/Assignment-Responses/last?dep=16106777 4/4