In this situation, I would say that whatever you currently believe is the minimum, is the actual minimum. If you manage to convince yourself that a higher minimum is required, you have simply updated the variable.
This is a good point. I’ve clarified the example a bit to address this.
Furthermore, updating your minimum is the right thing to do in this thought experiment. Just reason: “If my minimum is x, then the chance that I’ll get an acceptable offer is y and the expected profit of those accepted (given that other agents can guess x) is z. Select x to maximize y*z.” No self-deception involved.
My opinion is that if you convincingly told yourself a lie about something like this it stops being a lie. As best as I can tell, this is the same thing you are saying but with different words.