Tie-breaking and efficiency in the laboratory school choice

In school choice problems with weak priorities, the deferred acceptance (DA) mechanism may produce inefficient stable matchings due to tie-breaking. The stable-improvement-cycles (SIC) and choice-augmented deferred acceptance (CADA) mechanisms were proposed to remedy inefficiencies but they are manipulable. In a simple environment, we theoretically and experimentally analyze students' strategic behavior when DA, SIC, and CADA are implemented. We show that obtaining the efficiency gain relative to DA crucially depends on whether students report their preferences truthfully in SIC and whether they play a particular equilibrium strategy in CADA. Our laboratory experiment reveals that (i) non-negligible degrees of untruthful reporting are observed but they are not a major drawback for practical efficiency improvements of the mechanisms we consider; (ii) SIC achieves gains from trade whenever they exist, both on and off the equilibrium paths; and (iii) the additional layer of equilibrium coordination required by CADA makes it harder for CADA to fully produce the promised welfare advantage relative to DA. These findings are robust to various environments.