A classic paper of “research tournaments” by Fullerton and McAfee (1999) assumes a single prize (by design). Hoppe-Wewetzer and Wagener (2019) show that a Fullerton–McAfee “research tournament” with multiple prizes is strategically equivalent to a (nested) multi-prize Tullock contest. Given that it is known that Tullock contests are strategically equivalent to “effort+noise” contests with Gumbel noise, the result of this paper implies that a single reward (winner-takes-all) is optimal for the Fullerton and McAfee (1999) model.
Hoppe-Wewetzer and Wagener, Multiple prizes in research tournaments, Economics Letters, 175:118-120, 2019.
Fullerton and McAfee, Auctioning Entry into Tournaments, Journal of Political Economy, 107(573):581-82, 1999.
See also the related work:
Baye, M.R. and Hoppe, H.C. The strategic equivalence of rent-seeking, innovation, and patent-race games. Games and economic behavior, 44(2), pp.217-226, 2003.