Game-Theoretic Analysis of Decentralized College Admissions in the Kingdom of Saudi Arabia

We study the decentralized college admissions in the Kingdom of Saudi Arabia (KSA), where students submit their applications to each college separately, and colleges use a ranking based on weighted centralized test scores. Unlike the other decentralized college admissions, a student is not allowed to keep two offers on hand at the same time for more than two days. Colleges give their acceptance decisions at different times and may finalize their admissions before the others. Moreover, offers are usually expiring offers. Motivated by these features, we formalize the college admissions in KSA as a game where colleges may give acceptance decisions simultaneously or sequentially. When there are two colleges, we show that the equilibrium outcomes of both simultaneous and sequential moves are fair. We propose a methodology to compare games by their wastefulness, and we show that the sequential move game outperforms the simultaneous move game in terms of eliminating waste. We find that allowing colleges to determine the number of students to accept strategically will result in fair and non-wasteful equilibrium outcomes under both simultaneous and sequential move games.