Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic Bipartite Matching Market with Arrivals and Departures   In this paper, we study a matching market model on a bipartite network where
agents on each side arrive and depart stochastically by a Poisson process. For
such a dynamic model, we design a mechanism that decides not only which agents
to match, but also when to match them, to minimize the expected number of
unmatched agents. The main contribution of this paper is to achieve theoretical
bounds on the performance of local mechanisms with different timing properties.
We show that an algorithm that waits to thicken the market, called the
$\textit{Patient}$ algorithm, is exponentially better than the
$\textit{Greedy}$ algorithm, i.e., an algorithm that matches agents greedily.
This means that waiting has substantial benefits on maximizing a matching over
a bipartite network. We remark that the Patient algorithm requires the planner
to identify agents who are about to leave the market, and, under the
requirement, the Patient algorithm is shown to be an optimal algorithm. We also
show that, without the requirement, the Greedy algorithm is almost optimal. In
addition, we consider the $\textit{1-sided algorithms}$ where only an agent on
one side can attempt to match. This models a practical matching market such as
a freight exchange market and a labor market where only agents on one side can
make a decision. For this setting, we prove that the Greedy and Patient
algorithms admit the same performance, that is, waiting to thicken the market
is not valuable. This conclusion is in contrast to the case where agents on
both sides can make a decision and the non-bipartite case by [Akbarpour et
al.,$~\textit{Journal of Political Economy}$, 2020].

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The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org