Nonlinear Dynamics in College Admissions

Even under the fairly restrictive market restrictions given in my previous post, we can generate instances of school-choice markets that exhibit chaotic dynamics. Here is an example. I let tâtonnement process run for 8000 iterations and plotted the final 7000 cutoffs. The blue and red points indicate even and odd iterations; the behavior is bounded and quasiperiodic but has no obvious symmetry. Here is the code.