The Ponds Dilemma

Is it better to be a big fish in a small pond or a small fish in a big pond? To find out, we study self-selection into contests among a large population of heterogeneous agents. Our simple and highly tractable model generates many testable and sometimes surprising predictions. For example: 1) Entry into the big pond–in terms of show-up fees, number or value of prizes–is non-monotonic in ability; 2) Entry into the more meritocratic (i.e., discriminatory) pond is likewise non-monotonic, exhibiting two interior extrema and disproportionately attracting contestants of very low ability; 3) Changes in reward structures can produce unexpected selection effects. For instance, offering higher show-up fees may lower entry, while raising the value of prizes or making a contest more meritocratic may lower the average ability of entrants.