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Beach Rentals as a Market

The market I have chosen to describe here is the market of rental beach chairs and umbrellas on public beaches, particularly in Hilton Head Island, South Carolina, where I worked last summer. One set is defined as two chairs and an umbrella. I have attached pictures of Shore Beach Service’s sets below.

https://www.hospitalityonline.com/hilton-head-island-resort/jobs

http://www.shorebeach.com/index.php/rentals

What is being exchanged or allocated here is beach chairs and umbrellas in exchange for money. The market may include just a few sets, or a large amount of sets (up to ~120) depending on the area of beach. Each set must be set up the same distance apart from each other, and must be in a straight line parallel with the shore line. Each set of chairs and umbrellas costs a certain amount of money, however, there is also an option to tip the beach patrol who is renting the chairs and umbrellas. In this case, the renter is not only purchasing a chair and an umbrella, but they may also be purchasing comfort, shade, cooler temperature and perhaps a decreased risk of passing out due to the heat. In addition, the option to tip means that the customer can also attempt to exchange additional money for increased customer service and even the chance at a temporary friendship with the beach patrol, who is more likely to check in on and chat with customers who tip.

The feature of this market design is that all customers have the opportunity to choose their favorite set of umbrellas and chairs, out of all the available sets in the row. For example, imagine there are 10 sets of two chairs and one umbrella. They are set up in a straight line along the beach. Customers who arrive first will get their top choice of set; perhaps the one of the sets on the end, as that is always popular. Customers who arrive later will get their first choice out of the remaining available sets. While renters could be “assigned” sets, this is not ideal, as they are less willing to be happy with the beach patrol and less willing to tip. There does exist a  priority order f over a where f(1) = a1 is the first agent to arrive, and f(10) = a10 is the last agent. This is essentially a matching market, however, the matching is not pareto-efficient and not a serial dictatorship because customers can have weak preferences. To illustrate, a1 arrives first and can choose whatever set out of the 10 that they wish, however, they may prefer both end sets equally, in which case they will  be assigned one of those two sets randomly. Then a2 arrives an hour later and settles for the other open set on the end of the line, even though a1’s set S1 is a2’s first choice. The problem here is that the weak preferences allow for random assignment that could create two different potential matchings M and M’, where M’(a2) > M(a2) and M’(1) is equally as happy as M’(1), meaning that the matching is not pareto-efficient.

The matchings are not always in the core, either. Some customers may arrive and realize that they want to be placed in a set (s2) next to their friends set (s1), but there is already a renter sitting in that set. The matching mechanism, i.e. the beach patron, cannot force renters out of their set in favor of another renter, but the two agents may talk to each other after being assigned sets and decide to swap their initial endowments (sets). The fact that these renters can form a coalition of agents and create a different matching M’ where M’(a) ≥ M(a) and M’(b) > M(b) shows that the matching of beach rentals is not in the core.

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