You are right, it's not the same thing. I had an English teacher who tossed out her vocabulary lesson one day and instead went off on a very energetic rant about critical thinking, ultimatums, game theory, dilemma, paradox and so on. I've always wanted to recreate her lesson but never get it right.
I do think my final line still applies for this scenario. There's always another way. I think War Games does the same idea I was trying to convey but I've never seen it, I've only seen enough references to it, to vagely know what it's about..