Lessons from MIT: Game Theory and The Startup Valuation Game

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Lessons from MIT: Game Theory and The Startup Valuation Game

 

As noted elsewhere, I’m working on a graduate degree (M.S. in Management of Technology) at MIT.

 

This term, I’m taking a Game Theory class and we had an example come up that I found interesting.

 

Here’s the game: 

 

Lets say you are Google.  You have the option to buy any number of startup companies (lets say there’s a hundred of them, for discussion purposes).  Each company has a valuation (i.e. what the company is worth) of somewhere between $0 - $1,000,000.  These valuations are evenly distributed across the range -- so a startup is just as likely to have a $0 valuation as it is to have a $1,000,000 valuation (or any value in between).   [Note:  Lets not get into arguments of what actual startups are worth, not relevant to this exercise].

 

You, the head of Google are going to offer to purchase the entire company for some price.

 

Here’s the catch:  The founder of the company knows exactly how much the company/idea is worth (somewhere between $0 - $1,000,000).  You have no clue what its worth.

 

However, given the Google brand, what you do know is that whatever price the founder’s think the company/idea was worth, simply by you buying the company, the value goes up by 50% of what the founders thought it was worth (not what you paid).

 

You have to decide how much you are going to offer each of the 100 possible companies (same offer price for each one, because you have no “information” about any of them).

 

Example:  Lets say your offer is $400,000 to all of the companies.  One of the companies (StellarSoftware) has a founder who knows his company is worth $300,000.  Obviously, he will accept your offer.  Immediately you have made a profit of $50,000 on that transaction (because after you bought it, its now worth $450,000).  Another company, “TerrificTechToys” has a founder who knows his company is worth $600,000.  Since your offer is $400,000, he turns it down – so you make no profit or loss.

 

So, there are 100 such possible companies and you have to make the same offer to all of them.  What would you offer?  (Remember:  A single offering price that each founder will accept or reject).

 

Please send me your responses via email (dshah AT onstartups DOT-COM).  Don’t post them as a comment as that will give away the solution.  I’ll post the names of the winning answers in the next post.

 

Tomorrow, I’ll post the answer (and more importantly, what can be learned from the phenomenon and how it applies to software startups).

 

Stay tuned…

 

 

 

 

 

Posted by on Wed, Mar 15, 2006

COMMENTS

Quick question, or maybe figuring this out is part of the problem, but what's the distribution? Are the values randomly distributed across the million, or normal, grouped around the middle? Or does it matter?

posted on Wednesday, March 15, 2006 at 1:17 PM by Duane


When was this posted??? Would you believe that someone asked me this question 2 weeks ago on a job interview?

The answer is: Google should buy none of them. It's a straightforward calculus problem.

The problem is: This scenario is unrealistic. Change it from "value of company is uniformally distributed" to "normally distributed" or "log-normally distributed", and then you get more realistic result.

Just to clarify: The price of the company being acquired is randomly and uniformly distributed on [0, 1M]. Call this X. The value of the company after acquisition is 1.5*X. A bid less than X is rejected. A bid greater than or equal to X is accepted. So the profit is (1.5X-bid) if bid>=X, zero otherwise. Just do the calculus.

posted on Wednesday, March 15, 2006 at 8:08 PM by fsk


Duane the date of the post was clearly stated and it was also clearly stated NOT to post your answers. You must be an engineer.

posted on Thursday, March 16, 2006 at 8:04 AM by anon


Sorry Duane I copied the wrong posters name it was meant for fsk.

posted on Thursday, March 16, 2006 at 8:09 AM by anon


It would have been a much more interesting post if you had encouraged people to respond with their answers... that way, there could have been some discussion on the problem and perhaps different ways to look at it... is there always just one answer in the world? ok, maybe in school there is...

posted on Saturday, March 18, 2006 at 9:05 AM by anonymous


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