Simultaneous Search: Beyond Independent Successes

When applying to schools and colleges, a key decision commonly faced by students is how to optimally choose their portfolio of schools. In many settings, large numbers of schools are available, but due to costs or constraints students apply only to a few, often without perfect information about how the school will respond to their application. Determining which subset of programs to apply to-balancing the desire to attend sought-after programs with the need to hedge-forms a critical part of the decision problem, with these decisions deeply affecting the final outcomes in the market. To achieve this balance, students are often advised to apply to a combination of "reach," "match," and "safety" schools [2]. In practice, it is also seen that when reductions in application costs permit students to apply to more schools, they expand the range of schools to which they apply both upwards and downwards, including safer and more selective schools [1, 7].