The skipping-down strategy and stability in school choice problems with affirmative action: theory and experiment. (English) Zbl 1390.91244
Summary: This paper presents a theoretical and experimental study of affirmative action policies in school choice problems focusing on the minority reserve mechanism, or DA-Reserve, proposed by I. E. Hafalir et al. [“Effective affirmative action in school choice”, Theor. Econ. 8, No. 2, 325–363 (2013; doi:10.3982/TE1135)] and the majority quota mechanism, or DA-Quota, proposed by A. Abdulkadiroglu and T. Sönmez [“School choice: a mechanism design approach”, Am. Econ. Rev. 98, No. 3, 729–747 (2003; doi:10.1257/000282803322157061)], F. Kojima [Games Econ. Behav. 75, No. 2, 685–693 (2012; Zbl 1239.91039)] and T. Matsubae [“Do minority students benefit from affirmative action policy in school choice markets?: reconsidered”, Preprint, doi:10.2139/ssrn.2701111]. An evaluation of the performance of these mechanisms showed that, (1) while truth-telling is a dominant strategy in both mechanisms, the rate of its occurrence was less than 60%; (2) the average payoff was significantly higher with DA-Reserve than with DA-Quota, as theoretically predicted; (3) surprisingly, the proportion of students exhibiting justified envy was higher with DA-Reserve than with DA-Quota; and (4) a systematic pattern of deviation from the dominant strategy (referred to as skipping-down) was observed, and it was theoretically proven that this constituted Nash equilibrium with DA-Quota in some environments but not with DA-Reserve. More generally, the set of stable matchings was found to be larger with DA-Quota than with DA-Reserve, which explains the matching instability observed with the latter.
Citations:
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