## Game Theory in School Selection

Game theory, in the real world: http://news.mit.edu/2012/profile-pathak-0501

The above article is about how an MIT professor redesigned the Boston school matching system. In Boston, and other cities like Chicago and New York, students don’t always go to the school associated with the school district they reside in. Instead, they give their preferences and they are matched with a school with capacity. The article details how an MIT professor improved this matching system. My personal favorite line was that the system was the fruits of “trying to think of economics as an engineering discipline”

As it relates to Networks, such a system gives rise to a plethora of game theoretic considerations on the part of parents and students. For instance, is it better for a student to only list really good schools at an increased risk of not getting selected to any because every other student wants to attend those schools? Or is it better to select schools you would be content with but that aren’t top tier, in an attempt to increase your chances of getting in at a decent school. Such considerations cause undue stress on the parents and students. The article above describes how an MIT professor attempted to make this system “strategy proof.” He essentially changed the system into an iterative process, where at each round, students put down their top choice, and then are matched as best as possible. The remaining students then select their next preference and the matching continues until every student is matched with a school. This new system makes the dominant strategy of students to put their first choice in each round so that parents and students don’t have to fret about what the best strategy is. This topic draws on concept from both game theory and perfect matchings as discussed in class. For instance, instead of having a probabilistic mixed strategy, parents and students all share the same dominant strategy, mitigating the need for them hedge their bets. Additionally, this topic is at heart a perfect matching problem. Every student needs to go to school, and there is only so much space at school. Therefore, the problem is to find the perfect matching with greatest social utility, which in this case is measured by how good a match is for a student with regard to their preference list.