(Interim) Bayesian efficiency implies two-agent Bayesian implementation

We study the relationship between two-agent implementation problems and the notion
of interim efficiency due to Holmström and Myerson (1983) in Bayesian environments
with private values and independent types. We present a general property, Bayesian
efficiency, and show that it is sufficient for implementation of social choice functions.
We also show that this condition is sufficient for implementation of social choice sets
under a weak domain restriction - in particular, no economic condition is required. As
an application, we show that the generalized two-person Nash bargaining solution, due
to Myerson (1984), is Bayesian efficient.