In much of the existing literature on rent-seeking games, the outcome of th
e contest is either infinitely sensitive or relatively insensitive to conte
stants' efforts. The current paper presents a family of contest games that
permit characterization of equilibrium for all levels of sensitivity of the
outcome to contestants' efforts. Specifically, the outcome of the contest
depends on the difference between efforts, which encompass the lottery and
the all-pay auction as polar cases. The equilibrium converges to that of th
e all-pay auction as the probability of winning the prize grows infinitely
sensitive to one's effort, and the main qualitative features of equilibrium
persist over a large parameter region. Journal of Economic Literature Clas
sification Numbers: D44, D72. (C) 2000 Academic Press.