SPOILERS

Both 1 and 2 are self-evident and pretty much true. True enough for them to work. (Not for argument as a whole to work though.)

see, this is the problem: you're using hard mathematical induction when your premises are just "true enough". you can't do that: induction requires axiomatic truth. the thing must always be true, with no caveats or exceptions. Premise 1 can be replaced with "you can sell your house far enough under market value that someone will buy it" in order to work around potential legal issues that may arise from a $0 sale, but Premise 2 just doesn't hold in the face of scrutiny. there are too many circumstances where that just isn't true, so you can't use induction.

note that the end result of this is roughly comparable to your conclusion: convincing someone to go up is different from them initially being willing to pay that price. the reason this breaks your system, though, is not because mathematical induction fails from your premises (it doesn't) but because your premises are flawed. the equivalence of the two states is baked into Premise 2. so you have the right conclusion, but you've misidentified the point of failure.