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. Our simple model predicts that: (i) entry into the big pond – in terms of show-up fees, number or value of prizes – is non-monotonic in ability; (ii) entry into the more meritocratic pond is likewise non-monotonic, exhibiting two interior extrema and disproportionately attracting very low ability types; and (iii) changes in rewards can produce unexpected effects, e.g. higher show-up fees may lower entry, while higher prizes or more meritocracy may lower the average ability of entrants.