But that soon changed, thanks in part to a graduate student - now an MIT professor - named Parag Pathak. Just a decade ago, it seemed like an intractable problem. And a frustrating one: At least 20 percent of Boston students, by some estimates, were making strategic errors in New York, a third of students were shut out of the system without receiving any school assignments.

Picking a school wasn’t just a matter of figuring out which schools were good: Because students had to think strategically and anticipate which choices others would make, it was a real-world exercise in game theory. That made school selection a stressful quandary for many students and their families: Should they put highly rated but popular schools on their lists, despite the low odds of acceptance? Or should they list less desirable schools, to increase their chances of getting in? In Boston, for instance, many students would list their three top school choices - but were not guaranteed acceptance at any of them.

For students in New York and Boston, who have a range of options beyond their neighborhood school, choosing a high school used to be a maddeningly complicated guessing game.

Real life examples of game thery