1 research outputs found
Which Random Matching Markets Exhibit a Stark Effect of Competition?
We revisit the popular random matching market model introduced by Knuth
(1976) and Pittel (1989), and shown by Ashlagi, Kanoria and Leshno (2013) to
exhibit a "stark effect of competition", i.e., with any difference in the
number of agents on the two sides, the short side agents obtain substantially
better outcomes. We generalize the model to allow "partially connected" markets
with each agent having an average degree in a random (undirected) graph.
Each agent has a (uniformly random) preference ranking over only their
neighbors in the graph. We characterize stable matchings in large markets and
find that the short side enjoys a significant advantage only for exceeding
where is the number of agents on one side: For moderately
connected markets with , we find that there is no stark effect
of competition, with agents on both sides getting a -ranked partner
on average. Notably, this regime extends far beyond the connectivity threshold
of . In contrast, for densely connected markets with , we find that the short side agents get -ranked
partner on average, while the long side agents get a partner of (much larger)
rank on average. Numerical simulations of our model confirm and
sharpen our theoretical predictions. Since preference list lengths in most
real-world matching markets are much below , our findings may help
explain why available datasets do not exhibit a strong effect of competition