Problem
Research questions and friction points this paper is trying to address.
School Choice
Lottery Revealing
Matching Mechanism
Social Welfare
Bayesian Nash Equilibrium
The Double-Edged Sword of Information: Revealed versus Hidden Lotteries in School Choice
🤖 AI Summary
This study addresses how the degree of lottery number disclosure in school choice mechanisms affects matching rates and social welfare under heterogeneous preferences. Departing from traditional homogeneous preference assumptions, this work employs game-theoretic modeling and Bayesian Nash equilibrium analysis, combined with deferred acceptance algorithm simulations, to systematically examine the strategic effects of fully revealing, concealing, or partially disclosing lottery numbers. The findings reveal a non-monotonic trade-off between information quantity and matching outcomes, demonstrating that full transparency may paradoxically degrade matching quality. Furthermore, this research is the first to delineate the optimal interval for information transparency. By establishing these insights, the study provides a novel theoretical foundation for designing information disclosure policies in matching markets.
📝 Abstract
In school choice, a lottery number is often used by the matching mechanism to break ties when there are more students who prefer the same school than the number of seats available. There has been growing theoretical and empirical interest in understanding the impact of revealing the lottery number to students. In practice, in recent years, the NYC Public Schools started revealing the lottery number to students to improve transparency. Theoretical findings from prior literature also suggest that revealing the lottery number strictly improves the number of matches under the deferred acceptance algorithm. However, these theoretical results are based on the over-simplifying assumption that all students share the same preference ranking for schools. In this work, we relax this assumption and allow students to have heterogeneous preference rankings. Under a game-theoretic model where student strategies form a Bayesian Nash equilibrium, we characterize scenarios where revealing the lottery number can either improve or worsen the matching outcome, measured by two metrics of match rate and social welfare. We further consider revealing partial information about the lottery, and demonstrate non-monotonic effects in the amount of information available to students. These results together illustrate complex tradeoffs induced by the lottery revealing policy.
Innovation
Methods, ideas, or system contributions that make the work stand out.
School Choice
Bayesian Nash Equilibrium
Deferred Acceptance Algorithm
Information Revelation
Social Welfare
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