We study an all-pay contest with multiple identical prizes (“lifeboat seats”). Prizes are partitioned into subsets of prizes (“lifeboats”). Players play a two-stage game. First, each player chooses an element of the partition (“a lifeboat”). Then each player competes for a prize in the subset chosen (“a seat”). We characterize and compare the subgame perfect equilibria in which all players employ pure strategies or all players play identical mixed strategies in the first stage. The partitioning of prizes can lead to coordination failure when players employ nondegenerate mixed strategies. In these equilibria some rents are sheltered and rent dissipation is reduced.
Konrad, Kai A., and Dan Kovenock. "The lifeboat problem." European Economic Review 56.3 (2012): 552-559.