We consider a rent-seeking contest of the kind introduced by Tullock (
1980) in which two players compete for a monopoly rent. We extend the
contest by requiring that if a player puts forward an effort, his expe
nditures must be larger than or equal to some minimum level. We show t
hat, depending on the model parameters, the number of Nash equilibria
of the extended model can be zero, one, two or four. Furthermore, it t
urns out that the extent of rent dissipation in a Nash equilibrium of
the extended model can be larger than, equal to, or smaller than the e
xtent of rent dissipation in the unique Nash equilibrium of the origin
al model.