  We prove a uniqueness theorem for the obstacle problem for linear equations
involving the fractional Laplacian with zero Dirichlet exterior condition. The
problem under consideration arises as the limit of some logistic-type
equations. Our result extends (and slightly strengthens) the known
corresponding results for the classical Laplace operator with zero boundary
condition. Our proof, as compared with the known proof for the classical
Laplace operator, is entirely new, and is based on the probabilistic potential
theory. Its advantage is that it may be applied to a wide class of
integro-differential operators.
