Spring 2009

# assignments

due Wed Feb 11

## Assignment 1

From the Dots and Boxes book: 3.4 and 5.3 (Explain your answers).
Consider the Evaluation function for tic-tac-toe we looked at in class. Suppose I can look just one move ahead (instead of the two we did in class). If I go first, can you beat me? If I go second can you beat me?
due Fri Feb 20

## Assignment 2

From Taylor and Pacelli: 7, 8, 23, 24.
Part of the Condorcet Winner Criterion can be phrased as folllows:
• If x appears above y on more than 50% of the lists, then y is not a winner.
The Pareto Condition is:
• If x appears above y on 100% of the lists, then y is not a winner.
Investigate the following condition:
• If x appears above y on more than X% of the lists, then y is not a winner.
Are there values of X higher than 50 that allow us to still prove impossibility? Can you construct a system that satsifies IIA, AAW and this condition for for values of X between 50 and 100? Is it dependent on the number of choices?
due Mon Mar 30

## Assignment 3

• Prove that
• From Taylor and Pacelli: 2.7, 2.27, 3.5, 3.28
due Wed Apr 8

## Assignment 4

Samson and Delilah
Samson
Don't tell secret (T')Tell secret (T)
Delilah Don't nag Samson (N')(2,4)(4,2)
Nag Samson (N) (1,1) (3,3)
Key: ( payoff for Delilah, payoff for Samson ).
Preferences: 4 = best, 3 = next best, 2 = second worst, 1 = worst outcome.
 Game Rules 
• Find the Nonmyopic equilibrium (of Samson and Delilah) assigned to you in class. Please make sure that you include the gaming tree!
• From Taylor and Pacelli: 4.6, 4.10, 4.13, 4.35
due Sat May 9

## Final Project

Either take one of the topics we have studied and go more deeply into it, or select a new topic under the broad heading of game theory and investigate that. There will be a presentation in the last class of the semester and the final product is most easily produced as a series of homework exercises on your topic (though an expository paper is also fine).