The search for a work space and it’s application in matching markets
In the article on “Finding a good place to study”, mentions common sense individuality in preference in work spaces and I saw these individual values in the spaces, especially in a college setting, applicable in some ways to matching markets.
Some students, including me, like working in spaces where there are few to none students are around. For those living in doubles, this can even exclude their own dorms/rooms, and even for those living in singles, they may prefer not working their due to a work-home complex so we will exclude these rooms as possible work spaces for this model. This can be due to various reasons (avoiding background conversations, better focus, lack of interruption because no friends are nearby, etc.). As such, locations such as the library (especially the bigger rooms) or atriums aren’t an optimal location but small, discrete spots where not too many people go to, including study rooms, lounges, conference rooms and even lecture rooms when not in use. We can model these desired spaces with a matching market, each room with its own specifications and the buyers being students, wishing to work in these spaces. In a matching market, if many of these rooms are available but there is no cost then a clearing market may not occur where everyone gets their most preferred choice accounting for the cost. With this model and variations to account for this case, we can see several solutions that lead to a clearing market where every student has a space.
For now, let’s make the market identical to in-class examples where there is only 1 item (i.e. room) in stock for each of the possible options, which fits our case if every student wishes to be isolated in their room. From our class we learn some solutions including the trivial solution which is the matching market is already clearing. This can be done by having all of the students have distinct highest preferred room excluding the cost. This is possible when the buyer population has dwindled down, examples include holiday breaks where way less students are present on campus, and have less reason to go to academic halls because there are no classes then. We can also clear the market by increasing the cost. Unlike a monetary item there are various factors that can play in the role of how the student sees the cost of the item (such as distance away, how noisy it is, the current time and how much longer will that space be accessible for the student until it closes, etc.). We can model the cost where we make each student individually weigh these obstacles creating various values of the rooms across the students, this however will make it incredibly difficult to adjust the cost to achieve market clearing since incrementing one of the cost factors (decreasing the times the room is available) will not decrease everyone’s value of the room by the same amount (Student X which values long availability will decrease its value way more than Student Y who doesn’t weigh that value as much). We could also attain the model used in class and give a single value to each room for each person and a single cost, so we can uniformly decrease the value of a room for all the students if the cost increases. However it is now the model’s job to account for how such costs translate into real life obstacles as mentioned above or vice versa, which practically doesn’t affect everyone as uniformly. Despite the flaws in our two options for modeling the cost/obstacles of each of these rooms, they can still give us an idea of how we can clear the market for the students by redistributing the cost of each of the rooms.
Now to remove the 1 stock restraint mentioned, many students don’t mind sharing these rooms with a varying amount of people, some intentionally wish to work with a certain group to help each other on preparing for that next exam or collaborating on a problem set. We can model the latter, as 1 buyer since they wish to share the room together, as long as the room is big enough they will still consider all the same possible rooms.To model the former, we need to duplicate the same rooms to the quantity of available spaces, assuming no students lose value in the space as more students enter it. [If we did have to account for this this, we could account for this in the cost of these spaces, increasing as the room becomes populated (better with individual weighting), but let’s ignore this.] We can continue to treat this market like the model in class (if there is no individual weighting), and continue to adjust the price until there is no longer a constricted set of students.
Lastly, I’ll talk about the flaws that fundamentally come with modeling this situation as a market. Each student has various information/access to each of the possible spaces, so we cannot have a large scale model be accurately portrayed since Student X may not know about Space A, but every other student does, even if Student X would have chosen that as the most preferred choice, he would not be matched to it in this application because he doesn’t know about it and can’t prefer a room he doesn’t know exist. Even if all the students knew about each of the rooms, Student X might be a part of Club E and in exchange have access to room E but none of the other students in the model don’t have access to it, so no students could match to a room they can’t access. Another flaw is that we are implicitly assuming all of the rooms (or the rooms slots) are empty at this moment. Any of the possible spaces may be occupied for a program or taken up by another student. We could attempt the model by filtering out any rooms that are taken from being considered but in practice, no student knows which rooms are taken or not (unless we’re talking about the reserved spaces like the library where you can book the room ahead of time). Despite these issues, within a small enough scale, we can still see market effects for several spaces where each student develops a preference based on the cost of finding these spaces.
https://www.educationcorner.com/study-location.html