Competition May Increase Social Utility in Bipartite Matching Problem

Figure 4

The average ‘energy’ of different popularity groups; the horizontal axis shows the different values of popularity. ; the result is averaged over 100 realizations. (a) The average ‘energy’ of men at and ; (b) the average ‘energy’ of women at and ; (c) the average ‘energy’ of three representative popularity groups of men, bottom(0,0.1), middle(0.45,0.55), and top(0.9,1), versus ; (d) the average ‘energy’ of three representative popularity groups of women, bottom(0,0.1), middle(0.45,0.55), and top(0.9,1), versus . Note that when (triangles) the average ‘energy’ of men or women stays the same as the value shown in Figure 2(a); the small deviations are the random fluctuations which are irrelevant to the popularity.

(a)

(b)

(c)

(d)