Why does this matter? Consider what happens if more HIV testing is funded. If you're behind the veil and don't know about your status or your partner's, prudence dictates some caution. If you're tested, you know your status but don't necessarily know your partner's. If you're tested and wind up being negative, then the returns to prudence are higher, as you know with certainty that you aren't already infected so you can make things worse, but you might also think that the risks you've taken so far are safer than you'd thought. And how much weight people put on the risk they impose on partners is hard to tell: if you find out you're positive, you either reduce caution if partners' utility doesn't weigh heavily, or increase caution if others' utility counts.
And so what people do on getting a test result is an empirical question.
Enter Erick Gong. He finds that ..., well, scratch that. I'll just quote from his introduction as it's rare to see this kind of clarity in academic writing. Bottom line: if you're going to fund free testing, couple it with funding for anti-retro virals so that when people find out they're positive, they do less harm to others.
The other particularly interesting bit: surprise negatives yield reductions in risk-taking.
I'd missed this when it came out in 2015. I thank Ole Rogeberg for the pointer.