Referrals, Cooperation, and Competition

Participants are invited to apply for the Academic Excellence Award through one of three channels:
- Faculty Referral: Recommended by university faculty.
- Peer Referral: Recommended by another student applicant.
- Direct Invitation: Invited directly by the university without referral.

The third stage of the application process consists of:
1. Belief Elicitation: Participants estimate participation and average performance by referral group.
2. Real-Effort Tasks:
- Part B: Individual task (1 min), earns 1 point per correct answer.
- Part C: Competition task (1 min); participants probabilistically assign chances to be paired with a competitor from each referral group.
Winner earns 2 points per correct answer; loser earns 0.5.
- Part D: Cooperation task (1 min); participants assign chances to be paired with a teammate from each referral group. Team score is
average number of correct answers × 1.5.
- The order of competition and cooperation is randomized across participants.

2025-04-21

2025-05-16

- Partner/Competitor Selection
- Beliefs

- Partner/Competitor Selection: Distribution of assigned probabilities to each referral group.
- Beliefs: Accuracy and distribution of elicited beliefs about performance and participation by referral group.

- Task Performance
- Consistency between Beliefs and Choices
- Quality of Justification

- Task Performance: Number of correctly solved matrices across individual, cooperative, and competitive tasks.
- Consistency between Beliefs and Choices: Correlation between beliefs and probabilistic partner/competitor assignment.
- Quality of Justification: Qualitative coding of open-ended rationales for probabilistic assignments.

The expected number of participants to reach this stage of the application process and thus participate in the experiment is about 1020. The number from each group is expected to be:

- Faculty referred: ~127
- Peer referred: ~ 173
- Directly invited: ~ 720

Participants are randomly assigned (stratified by referral source) to one of two task sequences:

- Sequence 1: Cooperation → Competition
- Sequence 2: Competition → Cooperation

This design controls for order effects and enables estimation of how referral identity affects preference in collaborative versus competitive settings.

The primary outcomes focus on partner/competitor selection and belief accuracy. I will test the following hypotheses:

Hypothesis 1 (Competition): Participants are more likely to allocate probabilities to compete against applicants directly invited or referred by peers rather than those referred by faculty.

H1 reflects expectations about lower ability of peer/direct-invite groups compared to faculty referrals.

Hypothesis 2 (Cooperation): Participants are more likely to allocate probabilities to cooperate with applicants referred by faculty rather than peers or direct invites.

H2 reflects expectations about higher ability or greater trustworthiness among faculty referrals.

Hypothesis 3 (Referral homophily): Participants are more likely to assign higher probabilities to partners/competitors who share the same referral source as themselves (faculty referred select faculty, peer referred select peer, etc.).

H3 tests if homophiily is a heuristic driving selection and whether it is stronger than following the reported beliefs.

Hypothesis 4 (Belief-driven choice): Participants’ selections (probability allocations) will be positively correlated with their stated beliefs about the performance of each group.

Hypothesis 5 (Null order effects): The order in which competition and cooperation tasks are completed will not significantly affect partner/competitor selection patterns.

Randomization into task sequences (cooperation-first or competition-first) is done inside the online experiment in Qualtrics, stratified by referral source.

Individual

No

n/a

Expected participants: 1020 = 127 (Faculty referred) + 173 (Peer referred) + 720 (Directly invited)

n/a

Assuming a significance level of 0.05, statistical power of 0.80, and a binary outcome based on selection preference (baseline probability of 33.3%), the minimum detectable effect size (MDE) between the smallest referral group (faculty, N=127) and any other group is approximately 11.6 percentage points. This reflects the smallest difference in selection probability that can be detected with adequate power in pairwise group comparisons. Calculations assume independent observations and no clustering.