Experimental Design
Participants complete a two-stage online experiment. In Stage 1, they take a 12-question logic quiz of randomly assigned difficulty and report an incentivized belief about how their performance on six shared questions compares to a reference pool of 100 earlier participants. In Stage 2, over two rounds, one of two managers generates 50 paid tokens per round. One manager pays a green token when the participant beats a randomly drawn member of the reference pool; the other pays green at a fixed rate that is disclosed to participants as a numerical probability. By design this rate equals the participant's own performance rate, so the two managers produce statistically identical token streams. After each round, participants report incentivized beliefs about their own performance and about which manager they face. A manager is randomly assigned before round 1. After round 1, all participants state whether they want to stay or switch; for half, randomly assigned, this choice is implemented (active-choice treatment), and for the other half the round-2 manager is randomly assigned (control). Further details are provided in the pre-analysis plan.