The way I was trained to think about this type of problem was to consider each party’s best available alternative (BATNA). Even without trying to deal with psychological considerations, A could probably sell his property, buy a new property elsewhere, and build his dream house there. That might cost him $300,000 in transaction costs and in the decreased value of the second-best dream house site, but it would still provide an upper limit on how much he was willing to pay to escape a holdup.
Similarly, even if ultimate legal victory is certain, B’s alternative to negotiation involves going to court to enforce a holdup—the inconvenience is probably worth at least on the order of $400.
So you can narrow the likely range of settlement from [$5 $500,000] to something like [$400; $300,000]. Within that space I agree with the other commenters that the answer is more a matter of psychology than economics—although economics might have something to say based on relative bargaining power if we add more details about, e.g., each party’s timeline for construction or suit, each party’s access to credit, and so on.
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.
The way I was trained to think about this type of problem was to consider each party’s best available alternative (BATNA). Even without trying to deal with psychological considerations, A could probably sell his property, buy a new property elsewhere, and build his dream house there. That might cost him $300,000 in transaction costs and in the decreased value of the second-best dream house site, but it would still provide an upper limit on how much he was willing to pay to escape a holdup.
Similarly, even if ultimate legal victory is certain, B’s alternative to negotiation involves going to court to enforce a holdup—the inconvenience is probably worth at least on the order of $400.
So you can narrow the likely range of settlement from [$5 $500,000] to something like [$400; $300,000]. Within that space I agree with the other commenters that the answer is more a matter of psychology than economics—although economics might have something to say based on relative bargaining power if we add more details about, e.g., each party’s timeline for construction or suit, each party’s access to credit, and so on.
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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.