This is basically correct. It is a two-person cooperative game and the 'classical' solution is the Nash Bargaining Solution - introduced in the 1950 paper that you cite. Stuart_Armstrong has written several top-level postings on this standard topic in game theory recently. So it is shocking to me that so many people failed to identify the problem and even more shocking that so many of them incorrectly think that it is the ultimatum game.
I have one minor quibble with your solution, and one improvement. The quibble is that it is not necessarily the case that the marginal utility of money is the same for the two players. The Nash bargaining solution is based on maximizing the product of the utility gains - not the money gains.
The improvement follows Rubinstein. If the two parties do not reach agreement today, then they can still reach agreement tomorrow. (This is why it is different from an ultimatum game.) So the threat that each party holds over the other is to delay the (ultimately inevitable) agreement. But although the delay applies to each party (one has a delay in building the house, the other has a delay in receiving and then investing the cash), it may be that the two have different discount factors. The opportunity to build now is worth $500,000 to the one guy, but perhaps he is in such a hurry that the ability to build next year is worth only $400,000. But the other guy may figure that $500,000 next year is worth about $475,000 now. His discount factor is is only about a quarter of that of the eager home-builder. This puts him at a significant advantage in the bargaining - so much so that the solution of the Rubinstein bargaining model is close to $400,000 to be paid for the easement.
Stuart_Armstrong has written several top-level postings on this standard topic in game theory recently.
Actually, I think that's how I heard of this solution. Links for the interested.
This puzzled me. I'm pretty sure it's one of those unsolvable questions, but I'd want to know if it's not.
Two members of the species Homo Economus, A and B, live next to each other. A wants to buy an easement (a right to cross B's property, without which he cannot bring anything onto his lot) from B so that he can develop his property. B, under the law, has an absolute right to exclude A, meaning that nothing happens unless B agrees to it. The cost to B of granting this easement is $10 - it's over a fairly remote part of his land and he's not using it for anything else. A values the easement at $500,000, because he's got a sweet spot to build his dream house, if only he could construction equipment and whatnot to it. A and B know each others costs and values. They are "rational" and purely self-interested and bargaining costs zero. What's the outcome? I'm guessing it's "Between $5 and $500k," or "There is no deal unless one can credibly commit to being irrational." But I'm really not sure.
This could be asked as "In a bilateral monopoly situation where the seller's reservation price is $5 and the buyer's is $500,000, what is the predicted outcome?" But I figured the concrete example might make it more concrete.
Now that I've written this, I'm tempted to develop a "True price fallacy" and its implications for utilitarian measurement. But that's a separate matter entirely.