Choosing Partners
Ted Bergstrom and Rod Garratt
UCSB
October 4, 2010
We describe classroom experiments designed to test and illustrate matching
mechanisms outlined in Gale and Shapley (1962). The first set of experiments
involve a twosided matching problem where
n
differently colored squares must
match with
n
differently colored circles. Each color of square is given a personal
ranking of the
n
colors of circles and each color of circle is given a personal
ranking of the
n
colors of squares.
We define matching payoffs by assigning
points to individuals according to the reverse ranking of their match.
If an
individual matches with their most preferred color then they get
n
points, their
second favorite is worth
n

1 points, etc.
Actual colors and point values used in our experiments are shown in Table
1.
SQUARE
green
purple
blue
orange
lime
grey
red
yellow
pink
green
(4,9)
(9,4)
(5,8)
(7,6)
(3,6)
(1,7)
(8,5)
(6,7)
(2,5)
C
purple
(5,8)
(4,9)
(6,7)
(8,5)
(1,5)
(2,6)
(9,4)
(7,6)
(3,4)
I
blue
(9,4)
(8,5)
(4,9)
(6,7)
(2,7)
(3,8)
(7,6)
(5,8)
(1,6)
R
orange
(7,6)
(6,7)
(8,5)
(4,9)
(3,9)
(1,4)
(5,8)
(9,4)
(2,8)
C
lime
(9,1)
(1,2)
(2,3)
(8,1)
(7,2)
(5,3)
(4,2)
(3,2)
(6,3)
L
grey
(4,2)
(3,3)
(5,1)
(1,2)
(9,1)
(7,1)
(2,1)
(6,3)
(8,1)
E
red
(6,7)
(5,8)
(7,6)
(9,4)
(2,4)
(3,5)
(4,9)
(8,5)
(1,9)
yellow
(8,5)
(7,6)
(9,4)
(5,8)
(1,8)
(2,9)
(6,7)
(4,9)
(3,7)
pink
(1,3)
(7,1)
(9,2)
(3,3)
(4,3)
(5,2)
(8,3)
(2,1)
(6,2)
Table 1: Matching payoffs for
n
= 9: The first number each pair in the matrix
gives the points earned by the circle in the match. The second number of each
pair in the matrix gives the points earned by the square in the match.
1
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The first experiment involves unstructured matching.
Students are given
colored shapes with their ranking written on the back. Cards for the red circle
and red square are shown in Figure 1. Students are asked to move about and
My Values
9 Orange
8 Yellow
7 Blue
6 Dark Green
5 Purple
4 Red
3 Grey
2 Lime
1 Pink
My Values
9 Red
8 Orange
7 Yellow
6 Blue
5 Dark Green
4 Purple
3 Pink
2 Lime
1 Grey
Figure 1: Sample game cards.
find matches. They are told that circles must must with squares and squares
must match with circles. They can string people along while trying to find a
better match, but once they report the match to the instructor it is final. The
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 Fall '08
 Charness,G
 Purple, iterative procedure, stable match

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