| Abstract: |
We examine the fairness and intensity of sequential round-robin tournaments
with multiple prizes. With three symmetric players and two prizes, the
tournament is completely fair if and only if the second prize is valued half
of the first prize, regardless of whether matches are organized as Tullock
contests or as allpay auctions. For second prizes different from half of the
first prize, three-player tournaments with matches organized as Tullock
contests are usually fairer than tournaments with matches organized as all-pay
auctions. However, unless the second prize is very small, they are less
intense in the sense that players exert less ex-ante expected aggregate effort
per unit of prize money. Moreover, we specify how the relative size of the
second prize influences the extent and the direction of discrimination as well
as the intensity of three-player tournaments. Finally, we show that there is
no prize structure for which sequential round-robin tournaments with four
symmetric players are completely fair in general. |