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Suppose there are two firms A and B. Firm A owns property P, such as an apartment building. There are two possible mutually exclusive actions that can be taken in the management of P: action X and action Y. Each firm values P a different amount conditional on which action is taken, and it is assumed that firm A (the current owner) has incorrect valuations, and firm B has correct valuations.

I want to consider two scenarios.

In scenario 1, firm A judges incorrectly that the value of P under action X is \$100, and the value of P under action Y is \$90. Firm B judges correctly that the value of P under action X is \$50, and the value of P under action Y is \$150. In this scenario, firm B can profit from its correct valuation by purchasing P from A for \$101. Firm A will agree to this because firm A only expects \$100 income from P. Firm B then takes management action Y, and then receives \$150 income from P, for a net profit to B of $49. I have no question about scenario 1; this is just to provide context for scenario 2.

In scenario 2, firm A again judges incorrectly that the value of P under action X is \$100, and the value of P under action Y is \$90. Firm B judges correctly that the value of P under action X is \$50, and the value of P under action Y is \$80.

Now, how can firm B profit from this knowledge in scenario 2? Firm A is about to take action X which will result in a loss of \$30 compared to action Y, because firm B is correct in its valuation. Firm A is not willing to sell P to firm B at any price firm B is willing to accept. We may suppose that firm A is not willing to pay consulting fees to firm B. Is there any contract that firm B can set up, either with firm A or with some third party, that allows firm B to profit from its correct valuation? Preferably one that does not rely on firm A accurately reporting how much money it got from managing P.

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  • $\begingroup$ Is there any other firm other than B to which A can sell property P? $\endgroup$
    – Dayne
    Commented Feb 28, 2022 at 23:46
  • $\begingroup$ @Dayne Maybe, but only at a price of at least \$101, because firm A thinks P is worth \$100. $\endgroup$
    – causative
    Commented Feb 28, 2022 at 23:50
  • $\begingroup$ Unless that property has an opportunity cost of 100 through some other means, that would be irrational. $\endgroup$
    – Dayne
    Commented Feb 28, 2022 at 23:53
  • $\begingroup$ @Dayne what? Firm A thinks that if it holds P and takes action X, it will receive \$100 in profit from P. It is wrong, but that's what firm A thinks. So firm A is not willing to sell P for any price \$100 or lower. $\endgroup$
    – causative
    Commented Feb 28, 2022 at 23:55
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    $\begingroup$ If so then sooner or later A will realise it's wrong valuation as lower cash starts coming in. If at all anything is possible, B has to act before that. So maybe after a few periods the accumulated losses for A are enough to incentivise B to take property on rent and switch the action to Y and use the generated cash flow to pay rent higher than the perceived loss by A, while keeping something to itself as well $\endgroup$
    – Dayne
    Commented Mar 1, 2022 at 4:44

3 Answers 3

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Assume that there exists a signaling machine - perhaps in the form of an expert council or a consultancy company - that both firm A and firm B trust.

Firm A is convinced about its own evaluation. And since A trusts the signaling machine A also expects the signaling machine to simply confirm its own evaluation. Hence, money spent on getting a signal is wasteful and A has no incentive to pay for the signal.

However, B is also convinced about its own evaluation. And could therefore offer A to pay for the signal. If however, A changes its mind upon receiving the signal, A would have to pay some percentage of the real payoff difference $P(Y) - P(X)$ to firm B. As long as this percentage is higher than the cost of the signal both companies should be willing to make the contract.

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  • $\begingroup$ How would you know the "real" payoff difference if you can only take one of the actions and not the other? If you take action Y then you get the payoff from Y, and don't know or get the payoff from X. Anyway, if you are willing to trust A to report the actual payoff, then there's a simpler solution without needing a third-party signaling machine. B just makes a bet with A that the payoff after action X will be <$80. A takes action X and loses the bet. The problem is that A could use "Hollywood accounting" to inflate the apparent payoff and "win" the bet. $\endgroup$
    – causative
    Commented Mar 1, 2022 at 15:43
  • $\begingroup$ Gives me an idea though. Say that B offers A a contract where A pays B \$28 in the event that A chooses action Y, and B pays A \$1 in the event that A chooses action X. A accepts the contract because A expects to take action X and thinks the contract would pay out a free \$1. $\endgroup$
    – causative
    Commented Mar 1, 2022 at 15:53
  • $\begingroup$ Then B persuades A that the value from action Y is at least \$30 greater than the value from action X (because it is). Then A knows that if A takes action Y it gets \$30 in added value but has to pay B \$28, for a net gain of \$2 compared to action X, so A would take action Y and B would gain the \$28. It does rely on A being able to understand and be persuaded by B, and it relies on A accurately reporting the action taken. (Also if action Y is complicated&subjective, like adopting a certain "corporate culture," then A might not even be capable of accurately reporting which action was taken.) $\endgroup$
    – causative
    Commented Mar 1, 2022 at 15:55
  • $\begingroup$ In your example, you state that A judges incorrectly and B correctly so the real payoffs are those held by B. I am assuming that there is a mechanism that you can pay to get information about the true payoffs. If B knows A's belief, B must think that A will incorrectly choose X. Once they receive the signal with the true payoffs (those B believe) A will do Y getting and get 80 instead of 50 having earned 30 compared to the payoff if A had acted without the signal. If the signal only costs 10$ B can profit by offering to pay for the signal in return for 50% of the payoff difference. $\endgroup$
    – Jesper Hybel
    Commented Mar 1, 2022 at 16:18
  • $\begingroup$ The idea is very much like the contract you suggest except of course that I am explicit about the fact that there has to exist some kind of signal mechanism both find credible. B has to find the signal mechanism credible because otherwise, B would not expect the signal that the payoffs actually are what B knows to be true and A has to find it credible to be willing to alter he or hers beliefs. $\endgroup$
    – Jesper Hybel
    Commented Mar 1, 2022 at 16:25
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Adding some more valuations to your construct (based on your comments):

Let the property value without any investment X or Y be normalized to 0.

Further value of investments X = Y = 60 (if this had been less than 50, it would have been profitable for A to continue business even with the wrong assumptions).

So to formalize your set up say B knows exact returns: 50 under X and 80 under Y. While A has uncertain idea but thinks that X will give return of 100 with probability 0.999 and Y will give 90 with probability 0.999

After first period, it incurs a profit of -10. The only effect is that the probability decreases marginally to 0.998. So decides to again keep on.

In the meanwhile B starts to calculate that if he buys the property from A at some price Z and changes the investment to Y (with switching cost of say S) then his total expenditure is Z+Y+S. As long as Z+Y+S<80, it is profitable for him. So Z+S<20

For A this deal is profitable if, Z > Accumulated profit+ ~90

Approximately 90 because his previous losses will weigh on him to change is perceived probability.

Since accumulated profit is negative (-10) after some period, Z=20-S will be higher than accumulated profit + 90, allowing him to agree to this deal.

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  • $\begingroup$ Same as in the comments - useful sometimes, but depends on the choice of X or Y being repeatable, and on A eventually understanding the true value from X. It also depends on A not also understanding the true value from Y, because if A does that then firm B would lose their only advantage. $\endgroup$
    – causative
    Commented Mar 1, 2022 at 14:46
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I'm not learned in economics, so I don't know about the viability of any of these options. But here are the ones I thought of:

1.

Firm A helps B sell the property to firm C for $101, before action X or Y has been taken, and firm A stays hidden. X is presented as increasing the value up to \$100. Firm A may do this through hiring some other firm, whose business is doing these kinds of things. This way, firm A stays more hidden and their motives are less clear.

Then, after firm C has bought it, and before they have done action X, firm A proves to them action X will result in the valuation $50. At the same time, they tell them action Y will result in an even lower valuation. Now, maybe firm C will sell it to them for this price, as they're scared of losing more money by keeping the property. Firm A sold it for a reason, and they were incompetent enough to give a valuation that was off by 50%. As such, firm B, bring their knowledge to the table, can convince firm C that they should just sell now and minimize their total losses. Then, firm B buys P, does action Y, and nets \$40, minus any costs introduced if firm B chose to use another firm for their aid in firm A's selling.

Firm B here has an advantage in that they're actually correct, meaning if firm C is competent enough to see the truth when presented (even though they were incompetent enough to not see firm A's incorrectness). The only problem is that firm B will be lying too, as they'll be incorrectly stating the value of action Y. However, firm C were incompetent enough to believe firm A, so they should be able to believe firm B in their lies about Y. However, they're likely more wary this time, as they've just been told they bought something for $51 more than what it was worth.

This issue leads to an alternative version of this specific option: firm B can instruct firm A to not disclose action Y. If firm B is using this proxy firm for their interactions with firm A, that firm may bring some ethos to the table, convincing firm A that the non-disclosure of Y is beneficial. This means that the issue of lying about the valuation of Y disappears, unless firm C finds out about that action on their own.

2.

Sell the information itself. Go to the potential buyers of the property, and let them know you have essential information about the real value. If they aren't convinced, you may show them parts of that information, to convince them you do actually possess relevant and important info. Scare them with the possibility of them making a bad purchase.

3.

Seek out the potential buyers of the property, and tell them the same thing you'd tell firm C in option 1., that is, the true value of X combined with the lie about Y. This will in-turn cause low offers to firm A, which you can bid above, knowing that you can make a profit off of option Y.

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    $\begingroup$ A solution that relies on a third party being gullible isn't really about firm B's correct valuation. There are practical problems with selling the information - like selling "hot stock tips," it's very hard for the buyer to be certain he's getting good information. $\endgroup$
    – causative
    Commented Mar 1, 2022 at 5:35
  • $\begingroup$ Your title asks about obtaining value from knowing the correct info, not about necessarily stating the correct info. The fact that firm B has the correct valuation is essential to 1. and 3., and very helpful to 2., so it is very much is "about firm B's correct valuation". $\endgroup$
    – user110391
    Commented Mar 1, 2022 at 5:42

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