Download Formal Theory Exam 2008

Formal Theory Minor Field Examination
Department of Political Science
The Ohio State University
September 22, 2008
Instructions: You have four hours to complete this examination. Answer all
three questions. You may type and print the answers or write them by hand,
whichever you prefer. This is a closed book, closed note exam.
1.
Consider a stylized model of an election between an Incumbent and a Challenger,
in which the two players simultaneously choose whether to compete in the
election or stay out
a.
The following normal form represents the game for the case of a strong
challenger. What are the Nash equilibria to this game?
b.
The following normal form represents the game for the case of a weak
challenger. What are the Nash equilibria to this game?
c.
Consider a somewhat more complex game in which, prior to the
simultaneous choice, Nature chooses whether the challenger is strong
(with probability p) or weak (with probability 1  p ). This information is
revealed only to the challenger.
i.
ii.
Draw the extensive form of this game.
Draw the normal form of this game.
d.
Find all pure strategy Bayesian perfect equilibria to the game in part (c)
for all ranges of p.
e.
Based on this analysis, if an incumbent knows that one-third of all
potential challengers are strong, should she seek to remain in office or
should she retire? Why?
2.
Suppose that a group of n individuals is engaged in a collective choice problem
over the provision level of some public good (e.g., school financing), where the
decision will be made by simple majority rule. Let [0, x ]  R  denote the set of
possible levels with common element x. Individual preferences are defined over
two parameters, the level of the public good x and money income y, where the
latter will reflect the payments an individual has to make towards the financing of
the public good. Suppose individual i’s preference over x and y can be
represented by a utility function of the form
ui ( x, y)  vi ( x)  y,
where the function vi(x) is strictly concave. The cost associated with the level of
the public good x is equal to c(x) where c() is increasing and convex. The project
is financed by a uniform tax, so that if the level x is selected, each of the n
individuals pays c(x)/n. Given this financing scheme, what is the equilibrium
level of public good? Justify your answer.
3.
For an important question in political science that is relevant to your research,
discuss the contributions of formal theory toward answering that question. A
complete answer should include: background on the question you are addressing,
a history of the formal theoretical models that have been advanced to address the
question (with sufficient derivations to make the work clear to formal modelers
who have not worked in the particular substantive area), and a discussion of the
extent to which the predictions of those formal models have been tested (and with
what findings).