It's a tough problem from a game theory point of view. The company wants to hire someone who wants the job, is paid within (below?) budget, and so on. They'll

It's a tough problem from a game theory point of view. The company wants to hire someone who wants the job, is paid within (below?) budget, and so on. They'll also try to pay you less if they can. If they publish the salary range, there goes the chance to pay you less. If the salary is low, you cut out people who might like the job but won't even consider it. The company might like them enough to pay more, too. Employees don't want to waste time on jobs where they wouldn't take the pay. I suspect not publishing salaries is a Nash equilibrium. Might not be great but you converge to it anyway.