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.
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.
Actually, I think that’s how I heard of this solution. Links for the interested.