Are we assuming that the two players have perfect knowledge of each others' prices? Because if so, it seems to me that the price is a simple 500k (minus epsilon). If A has something that B values at that price, and that can't be gotten anywhere else, he will charge what the market will bear; and the market will bear 500k, because that's what the phrase "B values the access at 500k" means. If B is not in fact willing to pay that sum, on the grounds that A's reservation price was much lower, then he did not genuinely value the access at 500k.
If the two parties don't have knowledge of each others' prices, then presumably A makes some offer greater than $5 and B accepts it, or vice-versa. In this case the price is basically random. It gets higher as you increase A's knowledge of B.
If A has something that B values at that price, and that can't be gotten anywhere else, he will charge what the market will bear; and the market will bear 500k.
Try:
If B wants to buy something that A obtained at a certain cost, and that can't be sold anywhere else, he will pay what the market will bear; and the market will bear $6.
If A refuses to pay $500k, B gets nothing. If there were multiple buyers and A had the highest reservation cost, your answer would work and the problem would be boring.
But as the reversal shows, if B offers $6, A would tak...
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.