Wednesday, March 31, 2010

Chope!, or The Problem of Seat Reservation

If I were to have lunch at noon at the campus canteen, the following would invariably occur: I would walk down the stairs leading to the canteen and observe that many tables are unoccupied, and think to myself, "Oh, lucky!". A few moments later, on a closer approach, I would realize that the seats at the "unoccupied" tables are occupied with bags or items - Yes, these tables have been 'Choped', or reserved by the owners of the items. It is a culture prevalent in Singapore.

It is not that I have a problem with items being used to reserve tables. My objection would be equally great if someone (of presumably a party greater than 2 members in size) was left behind to take watch over the tables. The issue is seat reservation. It does not require extensive thought to realize that seat reservation reduces the useful seating capacity of the canteen (or hawker center); simply consider the amount of time that a table is not put to useful work (ie, being used by people in the act of eating). A table is not being actively used when the reserver is out ordering her food. If we were to parametrize the amount of time spent eating as E and the amount of time when the table is reserved as R, then the useful capacity of the canteen has been reduced to a fraction E/(E+R).

The problem can also be considered from the perspective of game theory. The choices available are to not reserve, hence exposing yourself to the risk of having no table to eat at but marginally improving everyone's chance of obtaining a seat, or to reserve, ensuring that you have a seat when you have purchased your food but decreasing everyone's chances of finding a table. In such a situation, given that largely non-observable and minor benefits of not reserving a seat as compared to the considerable benefit of reserving a seat, the outcome is understandable.

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