Assigned Monday 8/6 and due 8/8:

Read the handout about the Prisoner's Dilemma game. On Wednesday we will be analyzing strategies for this game by playing it. Come to class on Wednesday with a strategy to use. It could be a pure strategy, a mixed strategy (six sided dice will be provided if you'd like to use them to randomize your strategy), a strategy that depends on the previous moves of your opponent, or something else entirely - be creative.

Complete the following problems:

3.2: 27

9.1: 12

9.2: 6

Supplementary exercises p.451: First do problem 6. Then do (b) - Add a constant to each entry in the payoff matrix and compute the expected value. Confirm the effect mentioned in class and in Example 4 on pg 438. Also do (c) - Multiply each entry in the payoff matrix by a constant and compute the expected value. Confirm the effect mentioned in class and in Example 4 on pg 439.

Essay question due 8/13:

Note that some are writing whole books to address the questions below. Please don't feel the need to go into that much detail - responses should fall between two and four pages. Please type your responses to these questions. And as usual cite all references (including web pages) that you use.

(A) Explain the method that the U.S. uses to choose a presidential candidate. In particular explain how the electoral college is used to represent the votes of the people.

(B) What was the voting paradox that occured in last fall's presidential election? What were the particular numbers that led to this result?

(C) How would you run presidential elections? How would your method improve on the current one? Also consider the logistics of your method - judging from last years 'hanging chad' controversies it is clear that the process of gathering votes needs to be as simple as possible.

Assigned Wednesday 8/8 and due 8/10:

Read the second Prisoner's Dilemma handout. We'll talk about the results of our tournament, and that of Dr. Axelrod's, at the beginning of Friday's class.

Read the handout about social choice. In particular read the introduction and the section about plurality voting.

Complete the following problems:

Remember, before doing all of the math to find an optimal mixed strategy look for an optimal pure one first!

9.3: 2, 3 (look at EXA 4 on p.446 if you have trouble with this one), 4

Answer this question in a paragraph: Consider the strategy that you used to play the Prisoner's Dilemma game in class. What were the flaws in the strategy? How could it be improved? If your strategy was flawless explain why. (Note: there is no clear solution to this game.)

(Zac and Emily - write about the strategy you would have played.)

Assigned Friday 8/10 and due 8/13:

In the handout about social choice please read the sections entitled, "Sequential Voting," "Condorcet Winners," and "Everyone wins." Note that the preference schedules in the handout don't use upward pointing arrows - but they contain the same information.

Complete the following problems:

9.3: 11 see below

Social Choice handout: 1abc, 5

For #11 in 9.3 please make sure the following are clearly presented in your write-up. Use lots of paper, write big!

(i). payoff matrix
(ii). adjusted payoff matrix, and number you adjust by (only if necessary)
(iii). linear programming problem setup (including the objective function, constraints and graph of constraints and vertices)
(iv). test points (vertices) and the objective function's value at those points
(v). solution to linear programming problem
(vi). finding the optimal strategy and the value of the game from the solution to the linear programming problem

Test 2 Review Information

There are many practice problems at the ends of Chapters 9 and 12. In addition I will post some practice problems here, and write up their solutions later this week.

Logic:

For logic I recommed the 'Review of Fundamental Concepts' at the end of Chapter 12. Skip numbers 12 and 15-18. Know the Rules of Inference and Logical Equivalences on the handout, as well as the equivalences related to implication (ie. which of the implication, the contrapositive, the converse and the negation are logically equivalent to each other)

As usual review the logic problems that were assigned for homework.

Game Theory:

The 'Review of Fundamental Concepts' at the end of chapter 9 is a good place to test your knowledge of game theory. It may also be useful to review linear programming from Chapter 3.

As usual review the game theory problems that were assigned for homework.

NOTE: The blue box on pg. 443 and the blue box on pgs. 444-5 will be provided during the exam. They'll be on the last page of the exam.

Voting Theory:

Be able to use the voting methods described in the handout in the sections 'Everyone Wins' and 'Approval Voting.' (That is plurality, plurality with runoff, eliminate the loser, Borda count and approval voting.) Also be familiar with what a Condorcet winner is, what strategic voting is, and what sort of undesirable outcomes certain voting methods can lead to.

As usual review the voting theory problems that were assigned for homework.