Mathematics

### Homework Assignments

#### Assigned Jan. 12

"For All Practical Purposes," pp. 537 - 538, exercises 2a, 4, 5. (In MA 103Q coursepack.)

#### Assigned Jan. 14

"For All Practical Purposes," pp. 538 - 540, exercises 7, 8, 28. (In MA 103Q coursepack.)

#### Assigned Jan. 16

"For All Practical Purposes," p. 540, exercises 25, 27. (In MA 103Q coursepack.)
Additional problem: A university has four colleges with enrollments of 1450, 1440, 1650, and 5450. The student senate has 100 seats. Apportion the seats using Jefferson's method. Is the quota rule violated?

#### Assigned Jan. 21

"For All Practical Purposes," p. 538, exercises 14, 15. (In MA 103Q coursepack.)

#### Assigned Jan. 23

"For All Practical Purposes," pp. 539 - 540, exercises 19, 21, 22, 24, 26. (In MA 103Q coursepack.)

#### Assigned Feb. 2

"For All Practical Purposes," pp. 430 - 431, skills check 2, 3, 4; pp. 432 - 433, exercises 7abc, 9abc, 11abc. (In MA 103Q coursepack.)

#### Assigned Feb. 4

"For All Practical Purposes," p. 431, skills check 5; pp. 432 - 433, exercises 5, 7d, 9d, 11d.
Turn in on Friday Feb. 6: p. 433 exercise 14a.
(In MA 103Q coursepack.)

#### Assigned Feb. 6

"For All Practical Purposes," pp. 433 - 435, exercises 12, 13, 14b, 15, 16, 20, 21.
Turn in on Wednesday Feb. 11: p. 433 exercise 12 a and b.
(In MA 103Q coursepack.)

#### Assigned Feb. 23

"Game Theory and Strategy," pp. 11 - 12, exercises 1, 2, 3. On exercise 3, omit the "movement diagrams." Answers are on p. 225.

#### Assigned Mar. 1

"Game Theory and Strategy," p. 43, exercise 5a.
Also: Write down a 2 by 2 game with a saddle point. Investigate what happens when you try to find optimal mixed strategies, both algebraically and graphically.

#### Assigned Mar. 3

"Game Theory and Strategy," pp. 42 - 43, exercises 3, 5bc.
Also: Complete the table we began in class.

#### Assigned Mar. 5

In "Game Theory and Strategy," read the bottom of p. 39 and the top of p. 40. List the strategies for both players, then compare your answer to the answer at the bottom of p. 40.
"Game Theory and Strategy," p. 43, exercises 5de. On problem 5e, "solve the matrix" means do what you did for p. 11 problem 2: Successively eliminate dominated strategies, then use the minimax/maximin idea to look for a Nash equilibrium. (This is a zero-sum game.)
"Game Theory and Strategy," p. 72, exercises 2a and 2b: (1) list any dominant strategies, (2) find any Nash equilibria (just check the boxes in the table to see if they are Nash equilibria), (3) check whether the Nash equilibria are Pareto optimal.
Same as last problem, but first row is (2,4), (4,3); second row is (1,2), (3.1).

#### Assigned Mar. 15

"Game Theory and Strategy," p, 80, exercises 5 and 6. For exercise 6, think of two situations other than those mentioned in the text or in class.

#### Assigned Mar. 17

"Game Theory and Strategy," p. 80, exercise 6 again. This time, don't worry about whether the situations you think of are exactly prisoner's dilemmas or not. Just make a matrix for your situation and look for dominant strategies and Nash equilibria, then check whether the Nash equilibria are Pareto optimal.

#### Assigned Mar. 26

1. "Game Theory and Strategy," p. 132, exercise 2bc. For 2b, instead of the movement diagram, just find the Nash equilibria using our circling method.
2. "Game Theory and Strategy," p. 133, exercise 3. Ignore the questions in the book.
1. Find the Nash equilibria using our circling method.
2. Notice that when we circled Rose's best outcome in each column, we always circled the outcome corresponding to Rose A. Does this mean Rose A dominates Rose B?
3. Notice that when we circled Colin's best outcome in each row, we always circled the outcome corresponding to Colin A. Does this mean Colin A dominates Colin B?
4. Notice that when we circled Larry's best outcome in each stack, we always circled the outcome corresponding to Larry A. Does this mean Larry A dominates Larry B?
3. Three companies, Sunglass Arcade, Sunglass Booth, and Sunglass Counter, are considering opening kiosks in two shopping malls, Triangle Towne Centre and Olde Triangle Malle. Each company will pick one mall for its kiosk. Each company's payoff is 3 if it is the only sunglass company in its mall, 2 if there is one other sunglass company in its mall, and 1 if all three companies are in its mall. Draw tables of outcomes and payoffs and find Nash equilibria. (You will need two 2 by 2 tables.)

#### Assigned April 13

"Game Theory and Strategy," pp. 143-144, exercises 2, 3, 4cd.

#### Assigned April 14

"For All Practical Purposes," p. 467, skills check 1, 2, 3, 4; pp. 468 - 469, exercises 3, 4, 5, 6, 7. (In MA 103Q coursepack.)

#### Assigned April 16

"For All Practical Purposes," p. 469, exercises 9, 11cde. Ignore "extra votes," just find the Banzhaf power index. (In MA 103Q coursepack.)

#### Assigned April 19

"For All Practical Purposes," pp. 469 - 472, exercises 10abcd, 18ab, 33a. (In MA 103Q coursepack.)

#### Assigned April 21

"For All Practical Purposes," pp. 469 - 470, exercises 13, 15cd. (In MA 103Q coursepack.)

#### Assigned April 23

"For All Practical Purposes," pp. 470 - 472, exercises 17, 24, 25, 33bc, 35b. (In MA 103Q coursepack.)