Fall 2007
G
AME
T
HEORY IN THE
S
OCIAL
S
CIENCES
Problem Set 2
(Due in Lecture Tuesday, October 2)
1.
In lecture we studied how political parties or candidates choose their positons when all they
care about is winning.
This question explores what happens when political candidates care
not only about winning but also about the policies they espouse.
The U.S. Congress is up for grabs in the election this November.
Bipartisanship
has again broken down, and the parties are very polarized.
The more liberal faction of the
Democratic Party now dominates that party and a more conservation faction dominates the
Republican Pary.
As the election appoaches, these parties are trying to stake out positions
that reflect their own policy preferences and will attract enough voters to win.
To simplify
matters, suppose the parties have to choose a position along a left-right spectrum and can
adopt one of
the following positions: Liberal (L), Liberal leaning centrist (LC), Middle of
the Road (M), Conservative Centrist, (CC), Conservative (C).
These positions are
represented on the line below where the distance between any two neighboring positions is
the same.
L
LC
M
CC
C
Since the voter’s ideal points are evenly distributed along the political spectrum,
the party whose position is closer to the middle of the road (M) wins.
If, for example, the
Republicans,
R
, choose a position of CC and the Democrates,
D
, announces, L, then
R
would win because CC is closer to M.
If the parties run on platforms that are equally
distant from M, each party is equally likely to win.
Finally, each party chooses its
platform secretly.
As noted above,
R
and
D
care about policies as well as winning.
D
’s von
Neumann-Morgenstern payoffs are: 5 for winning with L; 4 for winning with LC; 3 for
winning with M; 2 for winning with CC; 1 for winning with C; -1 for losing with L; -2
for losing with LC; -3 for losing with M; -4 for losing with CC; and –5 for losing with C.
R
’s von Neuman-Morgenstern payoffs are the opposite: 5 for winning with C; 4
for winning with CC; 3 for winning with M; 2 for winning with LC; 1 for winning with
L; -1 for losing with C; -2 for losing with CC; -3 for losing with M; -4 for losing with
LC; and –5 for losing with L.

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