The actual solution to this in the real world, 99 times out of 100, is that B just says OK, or A insists on giving him $100 to cover the damages, or something generally amiable. The reason I asked this question is because I'm thinking about the efficiencies of injunctions (which result in bargaining) versus damage awards (which generally don't). So the only characters I care about are the ones who aren't neighborly.
Indeed, having confirmed my suspicions that this problem is insoluble, it favors a damage award in this context. B's actions are almost pure holdup. If all he were entitled to were damages and not injunctive relief, he wouldn't have nearly the same capacity for holdup, and the outcome looks more like the neighborly one (except with more bad will, perhaps).
In other words, I'm assuming that the agents are selfish and somewhat inhuman - irrational in a big picture sense - because occasionally these disputes do happen. There's a MAJOR case where a landlord sued over having to install a 1 cubic foot cable-box that increased their property value, and there's a case of a guy suing to stop someone from using an easement to get to a contiguous property (i.e. he had a right to cross A to get to B, but he was crossing A to get to B and then continuing on to C, and that was impermissible and went to court).
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.