Nash was a brilliant mathematician and strategist. His demise is a great loss to all, but nevertheless he has left us with a beautiful theorem we all could benefit from
John Nash, the Noble Prize-winning mathematician who invented the Nash Equilibrium, which led to the popularity of game theory, died in a car accident recently. In popular culture, John Nash was the character played by Russell Crowe in the acclaimed movie A Beautiful Mind, but to many of us — students of math, economics and strategies — Nash was perhaps one of the greatest heroes of our time that many admire deeply. It was disheartening to learn about his passing. As I pondered on how Nash’s theory has changed our world, I thought perhaps it would be beneficial to illustrate the concept of Nash Equilibrium in a startup-funding scenario to revisit Nash’s brilliant creation.
Imagine there are two startups of the same size that are providing exactly the same online service: we name them Startup A and Startup B. Both startups are pitching to a world-famous VC firm on getting series A funding. Both startups have no intention of cooperating with each other.
There are four scenarios:
Scenario 1: Both startups ask for a low valuation, the VC firm sees value in both deals and could be putting in $3 million in each, to bet on both.
Scenario 2: Startup A asks for a high valuation, Startup B asks for a low valuation. VC firm invests $3 million in Startup B, and Startup A gets nothing.
Scenario 3: Startup A asks for a low valuation, Startup B asks for a high valuation. VC firm invests $3 million in Startup A, Startup B gets nothing.
Scenario 4: Both startups ask for high valuation, VC is not entirely happy with either deal but has no choice but to put $3 million in each company in order not to pass over the opportunity.
Now in a competitive environment, Startup A will attempt to anticipate Startup B’s move and evaluates its own position to stop its competitor from getting funding. If Startup B opts for a high valuation, Startup A would be better off with a low valuation, so that it can win over the VC to get funding and ensure Startup B will not get any funding.
If Startup B opts for a low valuation, Startup A thinks it would be better off to pick a low valuation so that it won’t lose out on the funding. Startup A eventually comes to the conclusion that whichever Startup B’s choice will be, it will always be best to opt for a lower valuation.
Startup B will see it exactly the same opposite symmetrical scenario as Startup A and hence will always opt for a lower valuation.
Both startups picking a low valuation stance is the Nash Equilibrium in this scenario although both could have opted for high valuation and still raise the same amount of money (assuming less dilution is beneficial).
Ignoring the blonde
In another application of Nash’s theory, we could borrow the ‘Ignoring the Blonde’ scene from the movie A Beautiful Mind. Imagine, in a startup event, there is a world-famous VC and four other less famous local VCs. There are four startups canvasing for funding. If all the startups clamor over the world-famous VC, the world-famous VC will be overwhelmed and may not invest in any of them.
After being rejected by the world-famous VC, the startups will congregate on the local VCs. The local VCs feel like they are the undesired second choice and reject all the startups.
It would have been better for all the startups to ignore the world-famous VC from the outset and focus on the local VCs; they would have a high chance of all getting funded (not Nash Equilibrium).
Nash was a brilliant mathematician and strategist. His demise is a great loss to all, but nevertheless he has left us with a beautiful theorem we all could benefit from.
Here’s the ‘Ignoring the Blonde’ scene from the award winning A Beautiful Mind.
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