DP12348 The Third Place Game

Author(s): Aner Sela
Publication Date: October 2017
Keyword(s):
JEL(s):
Programme Areas: Industrial Organization
Link to this Page: www.cepr.org/active/publications/discussion_papers/dp.php?dpno=12348

We study an elimination tournament with four contestants, each of whom has either a high value of winning (a strong player) or a low value of winning (a weak player) and these values are common-knowledge. Each pair-wise match is modelled as an all-pay auction. The winners of the first stage (semifinal) compete in the second stage (final) for the first prize, while the losers of the first stage compete for the third prize. We examine whether or not the game for the third prize is profitable for the designer who wishes to maximize the total effort of the players. We demonstrate that if there are at least two strong players, there is always a seeding of the players such that the third place game is not profitable. On the other hand, if there are at least two weak players, then there is always a seeding of the players such that the third place game becomes profitable.