Four Game theory questions. 2 are fairly lengthy
5. [f6 Points] DETAILS BERRFINMATH1 8.2.006. For the 2 x 2 game, find the optimal strategy for each player. Be sure to check for saddle points before using the formulas. I" 3 5 5 For row player R: For column player C: Find the value of the game for row player R. Who is the game favorable to? 0 "he game is favorable to the rowI player. 0 "he game is favorable to the column player. 0 "his is a fair game. For the 2 x 2 game, nd the optimal strategy for each player. Be sure to check for saddle pointe before using the formulae. 3" 8 5 I" For row player R: For column player C: Find the value of the game for raw player R. who is the game favorable to? 0 "his game is favorable to the row player. 0 "his game is favorable to the column player. 0 "his is a fair game. ll. [111 Points] BERRFINMATH1 8.2.008. Represent the sltuatlon as a game and nd the optimal stlategy for each player. State your nal answer In the terms of the orrglnal question. Poiio'cal scientists distinguish between two kinds of issues in elections campaigns: "positional" 'ssues (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 posio'onal issues, she trailed the chalienger by 5% if he focused on the same kind of issuesr but she ied him by 5% if he concentrated on valence issues. If she focused on vaiense issues, she nailed him by 15% if he focused on the same kind of issues, but she led him by 25% if he concentted on positional issues Challenger P V ., E. v |:|% Es What does P represent? 0 F' represents valence issues. 0 p represents positional issues. what does V represent? 0 V represents valence issues. 0 It represents pesitiunai issues. For the incumbent: in designing the incumbent's TV ads for the campaign, what proportion shouid locus on positional issues? E \"In 9. [-I15 Points] BERRFINMATHI 8.7.010. MY NOTES I I ASKYOURTEACHER I I PRACTICE ANOTHER Represent the situation as a game and nd the optimal strategy for each player. State youri'lnal answer n the terms of the or al question. In a section of Freshman Composiliun at your college, the English professor gives a daily quiz on either vocabulary or writing, and allows his students to bring either a dictionary ora grammar textbcluk [but not both) to use during the quiz. Joe estimates that iFhe brings a dictionary, he can get a 90 on a vocabulary quiz but only an 50 on a paragraph revision, while with his grammar textbuuk, he can get a so on the reuision but only a 50 on the vocabulary quiz. Quiz on v P What does D represent? 0 D represents dictionary. 0 D represents glamrnar textbook. 0 D represents vocabulary quiz. 0 D represents paragraph revision. What does G represent? 0 G represents vocabulary quiz. 0 G represents paragraph revision. 0 G represents grammar textbook. 0 G represents dictionary. What does If represent? 0 U represents vocabulary qui O V represents grammar textbook. 0 U represents dictionary. 0 Vrepresents paragraph revision. what does P represent? 0 9 represents paragraph revision. 0 n represents vocabulary quiz. 0 n represents dictionary. 0 n represents grammar textbook. How should he decide each day what to bring? 0 He should aiways take the dictionary. 0 He should ask his friend which book to bring. 0 Flip a coin each day; take the dictionary if it is heads and Id'le grammar textbook if it is tails. 0 He should always take the grammar textbook. What grade can he be expected to earn? E
