Examining the Effects of Outside Options on Matching Outcomes in the DA Mechanism: An Experimental Approach

Participants in the experiment will be assigned to groups of 24 individuals. Each group will compete for one of three prize types:

1) Prize A: 600 rubles (approximately $6.50 at current exchange rate)
2) Prize B: 400 rubles ($4.33)
3) Prize C: 200 rubles ($2.17)

In each group, a total of 6 prizes of each type will be awarded. Consequently, no more than 18 participants per group will receive a prize in the baseline version with no outside option available. The language used is neutral and not tied to the university admissions context.

Whether a participant receives one of the prizes depends on their own decisions, the decisions made by the other group members, and a random component. The prizes will be distributed according to the following process:
1. Each participant in the experiment submits a rank-ordered list of the prizes, with their most preferred prize listed first and their least preferred prize listed last.
2. Participants in the experiment are randomly assigned numbers from 1 to 24. A lower participant number indicates higher priority eligibility for the prizes.
3. The prizes are distributed according to the deferred acceptance algorithm.

The goal of the study is to analyze how participants' decisions on what ROLs to submit depend on their access to an outside option, and for those without access, how their decisions depend on knowing that other participants have access to an attractive outside option. Therefore, in the treatment groups, some participants will have access to an outside option of 500 rubles ($5.41).

Another goal is to investigate how integrating the outside option into the centralized prize distribution system affects participants' decision-making, in comparison to the control group and the treatment group with the non-integrated outside option.

In groups where the outside option is not integrated into the centralized prize distribution system, participants with an outside option (call it prize O) will receive 500 rubles if they do not win Prize A at the conclusion of the algorithm. Prizes B and C that are vacated will be redistributed to other participants without outside options, based on their submitted ROLs and priority numbers assigned in the second stage.

In groups where the outside option is integrated into the centralized prize distribution system, participants with access to the outside option Prize O will need to include it in their ROLs in order to be considered for that option.

2024-09-30

2025-05-31

Unconstrained and constrained ROLs:
1) Proportion of participants who truthfully/optimally reported their preferences in all 12 of their submitted ROLs
2) Average share of truthful/optimal ROLs submitted by participants
3) Average share of ROLs with the top prize type A as first priority (out of 12)
Constrained ROLs only:
4) Average share of ROLs with top prize type A (out of 12): lack of A in ROL indicates more cautious strategy

The primary outcomes are used to test the following hypotheses.
Note that participants are required to submit 12 separate ROLs, and their payoffs are randomly determined based on one of the 12 ROLs submitted.

Unconstrained ROLs:
Hypothesis 1: The fraction of ROLs in which participants report their true preferences over prizes, listing all prizes, is 1 for all participants, and this does not depend on whether the participant or their competitors have access to the outside options, regardless of whether the outside option is integrated into the centralized system.
Hypothesis 2: Participants without access to the outside option prize should employ the same strategies across all unconstrained ROLs versions of the model, as they are expected to submit truthful ROLs of three prize types in each version. Similarly, participants with access to the outside option prize should not exhibit any differences in strategies across the unconstrained ROLs versions, as they should rank all the prizes available to them in the system truthfully and completely in every version.
Hypothesis 3: The resulting matchings are stable.

Constrained ROLs:
Hypothesis 4: The fraction of ROLs in which participants report preferences that are theoretically optimal of the maximum allowed length is 1 for all participants, regardless of whether they or their competitors have access to the outside option, and regardless of whether the outside option is integrated into the centralized prize distribution system.
In experimental groups where the outside option is integrated into the centralized system, participants who are highly likely to have access to the outside option will optimally list it in all their submitted ROLs.

Hypothesis 5: Participants with access to the outside option are more likely to list the top prize A as first priority on their ROLs compared to participants without access to the outside option.

Hypothesis 6.1: In versions II.2) and II.4), where one-third of participants have access to the outside option prize, participants without the outside option are expected to submit a lower proportion of ROLs that include the top prize type A, compared to participants in the baseline model without the outside option.
Explanation: The participants without access to the outside option should recognize that the competition for programs less attractive than the outside option is relatively lower, as those with access to the outside option will not be competing for them.

Hypothesis 6.2: Integrating the outside option prize into the centralized system does not affect the mixing probabilities of various types of partial ROLs for participants without the outside option. That is, there are no expected differences in the share of ROLs that include the top prize type A for the participants without access to the outside option in versions II.2) and II.4).

Hypothesis 7: The percentage of stable matchings is less than 100%. Unlike the participants without the outside option, those with the outside option are never undermatched.

The experiment is conducted in a total of seven versions:
I. Unconstrained ROLs:
I.1) Control condition: no outside option for any participants;
I.2) Treatment: outside option is integrated (embedded) into the centralized system, available for 1/3 of participants;
I.3) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.
II. Constrained ROLs, participants can list only two out of the three available prize types:
II.1) Control condition: no outside option for any participants;
II.2) Treatment: outside option is integrated into the centralized system, available for 1/3 of participants;
II.3) Treatment: outside option is integrated into the centralized system, available for 2/3 of participants;
II.4) Treatment: outside option is available for 1/3 of participants, but not integrated into the centralized system.

The experiment is conducted on paper. The majority of participants take part in two versions of the experiment. For each version, participants are required to submit 12 separate ROLs. The final winnings are randomly determined based on one of the 12 submitted lists.

All participants receive detailed instructions on the rules of the prize draw and an example of the DA algorithm. Following the instructions, the participants take a quiz on the structure of the experiment and the DA algorithm, and quiz performance earns points exchanged for monetary compensation (up to 400 rubles or approximately $4.33).

Following the main experiment, participants also complete a bomb risk elicitation task designed to assess their risk preferences. This additional task is included because the degree of risk aversion can influence the optimal strategies of the participants in the main experiment. The bomb risk elicitation task is accompanied by financial incentives, with an expected average payout of 250 rubles ($2.71) per participant.

By computer.

Participants are recruited from first-year Bachelor's degree students at the International College of Economics and Finance and the Faculty of Economics (NRU HSE, Moscow). They are also recruited from first-year Bachelor's degree students from Saratov State University, Faculty of Mathematics and Mechanics and Institute of Physics.

First-year BSc students are organized into academic groups of 25-30 for their studies, and the experimental sessions are conducted separately for each academic group. Randomization of students into the different versions of the experiment occurs at the individual and academic group level.

However, since there are more academic groups than versions of the experiment, and most participating students take part in two versions of the experiment, each group of 24 participants for each version is composed of randomly drawn (by computer) participants from all academic groups participating in the same version of the experiment. Participants are informed that they are not necessarily competing for prizes with the people in the same room, but potentially with any other 23 out of all participating students.

Yes

400 individuals

400*2 = 800 individual-version observations. Most of the 400 participants take part in 2 versions of the experiment.

On average, there are 33 participants per treatment group per type. As each individual will take part in two different versions of the experiment, this should result in an average of 66 individuals per treatment.