Exams are an oft-used example in economics. (Or at least they were in my monetary theory course). Especially with regard to the game-theoretic aspects of monetary policy.
Suppose we have a policymaker running a university. Suppose further their objective function is to maximize the knowledge recieved by students. This does not seem ridiculous.
The first attempt would be to simply devote all classes to teaching - exams are a waste of time, since spending a class writing down what you know does not actually increase your level of knowledge. Plus, there's a loss involving the time spent in correction.
However, this is likely to fail since there is now little incentive for a student to go home and study, if they're going to pass just by attending class. (And as Steven Levitt likes to say, economics is all about incentives.)
So the policymaker imposes an exam. This will probably result in people doing a lot more work, and thus learning more. But our policymaker in question is quite crafty: Just when our students show up for the exam, they find out it's been cancelled.
This is obviously the optimal strategy: All the benefit of the studying, but none of the waste involved in writing the actual exam.
We refer to this sort of situation as a dynamic time inconsistency: The optimal strategy changes, despite the fact that no new information has surfaced in our game.
Of course, eventually, successive vintages of students will catch on to this madness, and not study, producing an inferior outcome. The implication is that shamelessly believing the lies ad infinitum would be the Pareto superior outcome.
We have similar implications for monetary theory. If the central bank could repeatedly lie to the public and have that dissemblance accepted, we could theoretically observe a superior economic outcome.
I'll concede the chances are nil. Though I do think it's worth remarking on how rationality is actually producing a detrimental outcome.