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Material Type: Assignment; Class: IDEAS IN MATHEMATICS; Subject: Mathematics; University: University of Pennsylvania; Term: Fall 2004;
Typology: Assignments
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C N C 2 - N 0 1
(a) If Row knew that Column would pick C with a probability of 100%, what should Row’s optimal strategy be? What utility would Row expect from this strategy? (b) If Row knew that Column would pick C with a probability of 25%, what should Row’s optimal strategy be? What utility would Row expect from this strategy?
(a) Do either of the sides have a dominant strategy? If so, what? (b) Are there any Nash equilibria? If so, what? (c) If Yanukovych doesn’t know anything about Yushchenko’s prefer- ences, what should his optimal strategy be? (d) If Yanukovych knows Yushchenko’s preferences, what should his optimal strategy be? (e) If Yushchenko doesn’t know anything about Yanukovych’s prefer- ences, what should his optimal strategy be? (f) If Yushchenko knows Yanukovych’s preferences, what should his optimal strategy be?
C N C (2,3) (3,1) N (4,2) (1,4)
(a) Write the matrix of a 2×2 ordinal game reprsenting this situation. Determine the Nash equilibrium. (b) Starting from the Nash equilibrium, with Rwanda moving first, use the Theory of Moves to determine whether the two sides will move away from the Nash equilibrium. (c) Do the same thing with Congo moving first.