Mechanism design with two alternatives in quasi-linear environments

We study mechanism design in quasi-linear private values environments when there are two alternatives. We show that under a mild range condition, every implementable allocation rule is a generalized utility function maximizer. In unbounded domains, if we replace our range condition by an independence condition, then every implementable allocation rule is an affine maximizer. Our results extend Roberts’ affine maximizer theorem (Roberts, 1979) to the case of two alternatives.