Matching in the Large: An Experimental Study

Market size has been predicted to play an influential role in a broad class of environments. We study performance of the Boston and the Deferred Acceptance (DA) mechanism in a laboratory where we increase the market size. Our results show that increasing the market size from 4 to 40 students per match increases participant truth-telling under the DA but decreases it under the Boston mechanism, leading to a decrease in efficiency for both mechanisms but no change in the large stability advantage of the DA over the Boston mechanism. We then further increase the market size to 4,000 by introducing robots. When humans play truthful robots (without strategic uncertainty), we find that scale has no effect on best response behavior. However, when humans play empirical robots (with strategic uncertainty), scale increases best responses under both mechanisms, which is likely due to the increase in the precision of subjects' beliefs about others' strategies.