Econ Papers Daily / 期刊论文
关于随机市场中波士顿机制策略脆弱性的一个注记
A note on the strategic vulnerability of the Boston mechanism in random markets
摘要
We provide the first asymptotic analysis of the Boston Mechanism under equilibrium play in random markets. We provide two results. First, while 63% of students receive their first preference under truthful reporting–outperforming any other known mechanism in the literature–this rate converges to zero in any Nash equilibrium of the corresponding preference revelation game as the market size grows. Second, we show there exists a Nash equilibrium where the average student receives a dramatically inferior assignment: in markets with 1,000 students, the average placement shifts from the 7th choice (under truthfulness) to the 145th choice, representing a change from logarithmic to nearly linear average rank.
中文摘要
我们首次对随机市场中均衡行为下的波士顿机制进行了渐近分析。我们提供了两项结果。第一，尽管在真实报告下，63%的学生能获得其首选偏好——这一比例超越了文献中任何其他已知机制——但在相应的偏好揭示博弈中，随着市场规模扩大，这一比例在任何纳什均衡下都趋近于零。第二，我们证明存在一个纳什均衡，其中平均学生获得的分配结果显著恶化：在拥有1000名学生的市场中，平均分配位置从第7选择（在真实报告下）移至第145选择，这标志着平均排名从对数级转变为近乎线性级。