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# choosing_partners - Choosing Partners Ted Bergstrom and Rod...

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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 two-sided 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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choosing_partners - Choosing Partners Ted Bergstrom and Rod...

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