due Wed Feb 11
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
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
- Prove that
- From Taylor and Pacelli: 2.7, 2.27, 3.5, 3.28
due Wed Apr 8
Samson and Delilah
|Don't tell secret (T')||Tell secret (T)
||Don't nag Samson (N')||(2,4)||(4,2)
|Nag Samson (N)
Key: ( payoff for Delilah, payoff for Samson ).
Preferences: 4 = best, 3 = next best, 2 = second worst, 1 = worst outcome.
- 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
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).