Game Theory Problem

[scotty34]

Here was a game theory question posed today in my economics class. Can anyone figure it out?

There are two companies, Company A and Company B. Company A wishes to acquire Company B. Company B is about to undertake an oil exploration project.

-If the exploration is a complete success, Company B's shares will be worth $100 each
-If the exploration is a complete failure, Company B's shares will be worth $0 each
-Any value in between these is also possible, and no outcome is any more likely than any of the others
-Under Company A's management, Company B's shares will be worth 50% more

Here are the rules of the acquisition:

Company A must make a proposal for how much money they will pay for each share of Company B
Company A must make this proposal before the exploration project begins
Company B will decide whether or not to accept Company A's proposal after they have learned the results of the exploration project
Company B will only accept an offer greater than the value of its share price

Assume Company A wants to maximize profits, how much should they offer per share?

[bigredlemon]

Sounds pretty straight forward and a few minutes worth of logic and basic math... whats the problem?

[xadrez]

Colonel Mustard in the study with the pistol?

Pretty easy. Do u c y?

[kipin]

Try this (http://forumserver.twoplustwo.com/postlist.php?Cat=&Board=scimathphil) forum.

[kipin]

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Colonel Mustard in the study with the pistol?

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Candle stick.

[jdl22]

good old winners' curse.

[scotty34]

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Sounds pretty straight forward and a few minutes worth of logic and basic math... whats the problem?

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Not sure, our prof said it seems simple but it's not as easy as you think. Then again, it's only a second year course, and is basically a revisit of intro to microeconomics, so maybe he figures we aren't really that smart.

[applejuicekid]

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Assume Company A wants to maximize profits, how much should they offer per share?

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I think the answer is 0.

[scotty34]

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Assume Company A wants to maximize profits, how much should they offer per share?

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I think the answer is 0.

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That is what I came up with too, but that seems like it would make it a kind of pointless question. Maybe it is though.

[lgas]

My guess (in white): <font color="white">$50.01</font>

[DrSavage]

Looks like a zero to me as well. Unless I'm messing up something major here (and I am pretty tired), company A's profit is an integral from 0 to X of (1.5Y-X) dY , where X is company A's offer. This integral calculates to -0.25 X^2, which has a maximum value of 0 and never really becomes positive anyway. Unless company A can offer a complex number as a share price they can't make any profit here.

[Jdanz]

EDIT: Nevermind read it wrong pay no attention



Company B's EV is $50 per share if it's worth the spectrum of 0-100 if no price is more likely then any other.

Company A's EV after take over is $75 per share with the spectrum of 0-150.

B will accept A's offer if it's more then their current price.

Therefore A will offer the smallest amount over 50 they can and wind up with a profit of slightly under $25/share.

I have no idea how people got 0, as i assume we're talking about expected not guarenteed profit. If there is some risk aversion in either company that will effect the outcome, but i don't see that in the problem.

[dtbog]

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Therefore A will offer the smallest amount over 50 they can and wind up with a profit of slightly under $25/share.

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I'm not so sure about this.

If A offers $50.01 (just assume cents are discrete for now) -- then for all we are concerned, the only relevant values of the straight cash $EV of B are between 1 and 50, because A is not going to get to buy B unless its price is below $50. Obviously then the $EV of B to B is $25, and then the $EV of B to A is ($25)(1.5) after the acquisition.

Therefore A is paying $50 for ($25 * 1.5) = $37.50 of EV, so they are making a decision that has an EV of -$12.50...

... i think. i'm rushing out, might have missed something dumb

[dtbog]

... so basically i think 0 is the answer as well

[SmileyEH]

Just intuitively 0 is the right answer. Say you offer $50. You make a profit only when the value of the company is $33.3. But you lose whenever it is less. So you lose twice as often as you gain. I don't think that analysis is perfect, but if you say drop the price to $25 same thing happens. Is that what the winner's curse is called?

-SmileyEH

[Cry Me A River]

A strange game. The only winning move is not to play. How about a nice game of chess?

[jdl22]

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Assume Company A wants to maximize profits, how much should they offer per share?

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I think the answer is 0.

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That is what I came up with too, but that seems like it would make it a kind of pointless question. Maybe it is though.

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This is a very famous problem. As I said above it's known as the winner's curse.

The problem is that in a common value auction (where you've bidding on the value of something to the public not to you personally, basically like you're buying stuff for business reasons) bidders often don't take into account that if they win the auction they must have estimated the value of the good to be higher than others thought. This leads to a "curse" because that probably means that the winner overbid and will lose money on the transaction. This often happens in actual auctions for oil fields and that kind of thing.

So the basic principle at work here is that you need to consider what your offer being accepted means. In this case it's only bad news for you.

The problem seems (and should be) easy for people here because we're accustomed to making EV decisions often and taking the greater picture into account. Just wait until class, you'll see that most people [censored] it up and would lose money.