"Strategic" Behavior in a Strategy-proof Environment.

A mechanism is said to be strategy-proof if no agent has an incentive to misrepresent her true preferences. This property is considered highly desirable for mechanisms that are used in real-life markets. And indeed, many of the great success stories of market design employ strategy-proof mechanisms, such as the second-price sealed-bid auction [Vickrey 1961], or Deferred Acceptance (DA, [Dubins and Freedman 1981; Gale and Shapley 1962; Roth 1982]. Specifically, in school-choice settings, the appeal of strategy-proof mechanisms is one of the main reasons many school districts choose the applicant-proposing version of DA over pre-existing mechanisms. At the core of the attractiveness of these mechanisms is the assumption that agents report their preferences truthfully in strategy-proof environments. We present direct field evidence of preference misrepresentation by applicant's under the applicant-proposing DA. Our study is based on the recently redesigned admission process in Israel for graduate studies in psychology (MA or direct PhD track), where several participating institutions offer positions in the same study track, but under different terms. In particular, in some cases only some of the positions are funded. Until recently, this market employed a matching process that left much room for strategic behavior and was quite complex and demanding [Hassidim et al. 2016]. In response to concerns with the performance of this process, in 2014 a centralized matching mechanism, based on a variant of the applicant-proposing version of DA, was introduced. With the goal of achieving strategy-proofness and stability in a matching-with-contracts environment [Hatfield and Milgrom 2005], the mechanism was designed to be expressive enough to accommodate the potentially crucial role of funding in some applicants? preferences. Similar to [Sönmez 2013] and [Sönmez and Switzer 2013], applicants were asked to rank program-terms pairs. Thus, applicants could rank a funded position in program A over a position in program B over a non-funded position in program A. The fact that the mechanism was strategy-proof for applicants was emphasized and communicated in numerous ways, and applicants had a long period of time to familiarize themselves with the rules and with the simple user interface. The unique features of the Israeli Psychology Master's Match imply that for the common case where terms correspond to funding, applicants are asked to report their preferences between naturally ranked alternatives. For programs with both funded and non-funded positions, it is unlikely that applicants truly prefer the latter, as, beyond the monetary benefit, funding is also prestigious and comes with no strings attached. This feature allows us a rare opportunity to directly assess the degree of truth-telling in the field. We find that a significant fraction of the applicants submitted Rank-Ordered Lists (ROLs) in which a non-funded position was ranked higher than its funded counterpart. We term this behavior obvious misrepresentation. Obvious misrepresentation can be detected only in applicant ROLs that include a nonfunded position in a program that offers both funded and non-funded positions. Out of 704 relevant ROLs that were submitted during the 2014 and 2015 matches, 137 (19.5%) contained an obvious misrepresentation. The large proportion of untruthful agents is particularly striking given that our pool of participants was composed of well-educated individuals who faced a high-stakes decision and who were provided with all the necessary information about the dominant strategy. The number of untruthful agents may be much higher as applicants may have misrepresented their preferences in ways that we cannot detect, such as ranking a program other than their favorite first. We provide survey evidence supporting this hypothesis. In addition, comparing reports of obvious misrepresentation with observed behavior, we find that survey-based estimates of misrepresentation are biased downwards. We evaluate the correlation between misrepresentation and ability (desirability) in several ways. First, we note that applicants who were not acceptable to any program under any circumstances are twice as likely to submit an obvious misrepresentation. Second, we provide a lower and an upper bound for the number of applicants who lost a funded position as a result of their obvious misrepresentation. Third, we augment the administrative data with data from a survey we conducted following the 2015 match and find a negative correlation between obvious misrepresentation and ability as measured by the self-reported standardized admission test score. Altogether, these approaches all suggest that obvious misrepresentation is more prevalent in the weaker segment of the market. [ABSTRACT FROM AUTHOR]