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Vladimir_Nesov comments on Econ/Game theory question - Less Wrong Discussion
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Comments (56)
This is essentially an ultimatum game (if we focus on the interesting bits). There is no theory that reliably helps with the process of picking a fair price, and the fair price depends on many factors which you didn't specify, including the details of how players' minds work, and what each player believes about the other. This makes intuition the only method that can take into account all the varieties of potentially relevant information, although there might be some explicit algorithms that show better performance in practice, especially if the other player doesn't know what algorithm you use.
There are some ideas from game theory that suggest certain algorithms for picking fair price, but their outcomes are mostly the product of privileging those algorithms as Schelling points for reaching agreement and not of clear a priori considerations for which price should be chosen. If players' brains are completely rotten by CDT thinking, they will additionally insist that A should accept whatever B is demanding, and conversely, depending on who gets the last say.
This is using "rationality" is a wrong sense. The word should refer to whatever it is they should do.
How is this an ultimatum game? There is no limitation in the problem of how long A and B can take to negotiate over the matter or what form that negotiation may take. Adding such limitations is not focussing on the interesting bits, it is focussing on a different problem.
Nesov is right, this is just the ultimatum game.
Consider B granting the easement and charging A $10. B gets $0, A gets $499,990.
Consider B granting the easement and charging A $500,000 dollars. B gets $499,990, A gets $0.
Consider B not granting the easement. A and B get $0 each.
So they are playing a reversible ultimatum game for $499,990. Either A or B may make or reject offers. Any negotiation would immediately reduce to the ultimatum game - if A and B have a common Schelling point (say at 50/50) then they aren't homo economus, they are homo sapiens.
Strictly as formulated, this is not an ultimatum game, for ultimatum game specifies a particular protocol: one player proposes a price, the other has one chance of accepting or rejecting. The post assumes no such restriction, the players could for example go through 100 bargaining iterations of any nature, such as usually proposed in various bargaining protocols.
But as long as the payment itself is not iterated (ie there is still only one easement) then at any point during the bargaining both players can make more money for themselves by pushing for more money.
I think it doesn't matter how long they have to decide, if we are resolved to ignore intuitive hunches for Schelling points and causal updating (which are important in practice, but not in principle). You can see any problem as one-step by deciding a whole (possibly infinite) strategy instead of just the next action. The questions governing the way this strategy should be chosen are similar (for the purposes of my comment) to what happens with simple ultimatum game.
The original problem is symmetrical: there is a potential trade which will benefit both A and B, and they need to strike a price. The Ultimatum game is asymmetrical: one player goes first. This seems to me a conclusive proof that this problem cannot be modelled as an Ultimatum game.
I don't think this works in the large unless P=NP (or something of the sort). In the small, e.g. analysing chess, it reduces the problem to no steps at all: both players exhaustively analyse the game and know the outcome without playing a single move. (I'm using "small" and "large" in the sense of the dispute between small-world and large-world Bayesians.) If that worked for the bargaining problem, A and B would independently come up with the same price and no bargaining process would be necessary. No-one has posted a method of doing so.
You are correct. Vladimir is discussing an entirely different problem.
I agree with this post.
Also an important idea implicit in the above post that I think deserves to get spelled out is that the mere act of thinking about a Schelling point can move its location.
An additional point worth spelling out is that Homo Economicus has by definition already thought everything through so no such movement is possible here.