A multiple scattering theory of competition effects in diffusion-controlled reactions are presented. We consider a random array of stationary sinks which react with a density field of another reactant. Using the radiation boundary condition to describe the reaction at the surfaces of the sinks, we treat the modification of the density field due to reaction with sinks exactly. By keeping only the most divergent terms in a given order of scattering and summing them, we obtain the rate constant as a function of the sink concentration in the steady state. We also calculate the concentration-dependent diffusion constant of the density field. Both the rate and diffusion constants have nonanalytic behavior in the sink concentration.