Econ/Game theory question

Stuart_Armstrong has written several top-level postings on this standard topic in game theory recently.

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

It introduces the ability for either party to make precommitments (page 130)

So it applies to perfectly rational agents.

and a four stage negotiation process.

A bit later he gives an alternate derivation.

Well, of course. But assuming B is a rational agent, and assuming the expected damages awarded in court per trespass are additive, she's going to wait until A has finished building his house, then take him to court for all counts of trespassing, rather than fight each one individually, since that'll save her a great deal on time and legal fees.

B could do all of these things to keep the problem in the box you're trying to define, but if he does, it's clear that friendly relations have already broken down between A and B, and by acting in this way, B is reducing the value of the land to A. Does A still want to live next door to a neighbour who is going to be so obnoxious about trifling property disputes?

I understand that you're asking the question: how can prices be rationally decided in a bilateral monopoly? But the response that bilateral monopolies don't happen can't be brushed aside. Rational agents in this hypothetical situation will always be looking for alternatives, and the more is at stake the more creative they will get about it.

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.

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.

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.

You are correct. Vladimir is discussing an entirely different problem.

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.

No, our decision theories don't have any new insights for solving bargaining games. But such games are widely studied elsewhere, so maybe you can find a model that solves your problem if you feed it some more detail. Sorry for the disappointing response :-(

The problem is that if A is perfectly rational, in a sense, he can't make a credible take it or leave it offer

Of course he can - he signs an enforceable contract to pay C $500,001 in the case that he is ever seen to be offering B more than $8191 for the land, and has done with it.

The problem is that if A is perfectly rational, in a sense, he can't make a credible take it or leave it offer.

I think James meant adding a new limitation to the situation such that there is only one chance to make the deal and one person goes first. ie. Turn it into an ultimatum game.

Do any of the elaborate decision theories popular around these parts solve this problem?

No. At least not if there isn't also a solution specified in Causal Decision Theory. The same problem exists in both. In fact using Timeless Decision Theory makes the problem apply even in the ultimatum game variant. Because even if I was perfectly rational if A offered me $11,000 I would tell him or her to go @#$@#$ @#$@#$.

I think assuming away the secondary variables in a negotiation problem is less interesting/useful than assuming away friction and air resistance in a physics problem, for tworeasons.

First, air resistance usually explains only a small fraction of the variance in outcomes -- my numbers won't be quite right, but the distribution of physics parameters across all back-of-the-envelope physics calculations will probably be something like: log(air pressure in atms) = 0 +- 0.2, log(density in g/ml) = 0 +- 0.3, and log(initial velocity in m/s) = 1 +- 1. If you vary the air pressure by one standard deviation, you get maybe a 3% change in the distance traveled. If you vary the initial velocity by one standard deviation, you get maybe a 200% change in the distance traveled. So it's relatively safe to leave out air resistance. By contrast, bargaining power, precommitment, BATNA, transactional costs, etc. often explain as much or more of the variance in the agreed-upon price as does the deal's utility to each person. It's not at all safe to leave those factors out -- if you do leave those factors out, it's unlikely that you'll get even 4 full bits of Bayesian evidence about the final price as compared to a prior that allows any price between $0 and $10 million.

Second, air resistance is much harder to measure than initial velocity, and, even if you figure out what the level of air resistance is, introducing that variable makes the math considerably harder -- you might have to upgrade from algebra to calculus. Each additional variable superlinearly increases the risk of calculation error, because physics reasons from explicit mathematical equations whose counterintuitive results should be trusted, assuming the math and the inputs are correct. By contrast, it's often just as hard if not harder to measure the utility a person gets from a deal as it is to measure, e.g., their BATNA. Adding new variables to the calculation doesn't necessarily add much to the difficulty of the calculation, because there is no unified, complex mathematical equation -- just Bayesian updating on what each piece of data has to say about the overall likelihood of any particular deal. In other words, if the deal is worth a lot of money to you, that suggests that you're relatively more likely to agree to a higher price; if your BATNA is quite good; that suggests that you're relatively less likely to agree to a higher price. Total up all the evidence pro and con, and you'll get a sense of where the price is most likely to be. There's no need to factor complex mathematical expressions; at worst, the complexity of the calculation increases at a linear rate as new variables are added.

You mean [$5,$10), no?

I do actually mean ($5, $10] but I can understand if you would prefer the other variation. My reasoning is that 'between' sounds to me to be non-inclusive ("between Fred and Joe" for example) while making the trade at $10 would just be pointless. The $10 in particular could be seen as ambiguous and if there was a symbol that meant "')' or ']', whatever" then I would use that instead.

Ok, as a point of game theory you've convinced me. As a matter of human psychology, I think A has B over a barrel, although possibly not a half-million-dollar barrel. Although A gets nothing if B refuses to buy, A is not the one who wants a specific, very valuable change in the starting situation. B is the one who wants the status quo changed in a specific way; he has, so to speak, the burden of proof.

Although both parties have an opportunity cost from not making a deal, it seems to me that the opportunity cost "I don't get to do these specific things I had planned on" will weigh more heavily in a human mind than "I don't get some amount of free money, which may be small".

no special privilege for the resource that happens to be the service

I don't understand why this should be the case. Presumably A has other sources of money, but B has no other sources of access; unless you are specifying otherwise, there is an obvious asymmetry. If the situation is intended to be symmetric, the example is a bad one; it is cross-grained to well-established intuition about how money works.