The expectation of the maximum of RVs is greater or equal to the maximum of the expectations

For any sequence of RVs X1,...,Xn the following holds: E[max{X1, ..., Xn}] >= max{E[X1], ..., E[Xn]}    (*) Proof. We have that max{X1, ..., Xn} >= Xi for all i. Thus, this holds in expectation as well, i.e. E[max{X1, ..., Xn}] >= E[Xi] for all i. Since this holds for all i, it holds for … Continue reading The expectation of the maximum of RVs is greater or equal to the maximum of the expectations

Research tournaments are Tullock contests and hence WTA is optimal

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 … Continue reading Research tournaments are Tullock contests and hence WTA is optimal