Econ/​Game theory question

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.