On asymmetric equilibria in rent-seeking contests with strictly increasing returns

This paper revisits the n -player rent-seeking contest with homogeneous valuations and increasing returns. Our main result says that, for any m∈ \2,… ,n-1\ m ∈ { 2 , … , n - 1 } , there are threshold values 1<R_*(m)<R^*(m)≤ 2 1 < R ∗ ( m ) < R ∗ ( m ) ≤ 2 for the Tullock parameter R such that a pure strategy equilibrium with m active players exists if and only if R∈ [R_*(m),\,R^*(m)] R ∈ [ R ∗ ( m ) , R ∗ ( m ) ] . Among other things, this observation leads to a simple characterization of the values of R for which the n -player contest has a unique pure strategy equilibrium.