Interim payment identity
= Interim payment identity
{title2=$m(\theta)=\theta G(\theta)-\int_0^\theta G(t)dt-u(0)$}
For a risk-neutral single-parameter bidder with incentive-compatible type reports, interim utility satisfies $u'(\theta)=G(\theta)$ wherever the winning probability is continuous. Consequently expected payment is determined by allocation probabilities and the utility of the lowest type. The common normalization $u(0)=0$ must be justified, not obtained from allocation alone.