Show notes
Have you seen the movie a beautiful mind? Have you ever been facing jail time if you cooperate against an accomplice?
Well, let’s focus on the movie first – there’s a scene where five guys, one of those guys being John Nash, and they are at a bar when a group of women walk in …
In the movie, the focus of the men is on the blonde – one of the women.
They then go on to quote Adam Smith – “In competition, individual action serves the common good” – we will return to that in a second. Here’s a bit about Adam Smith from Adamsmith.org if you have never heard of him – ‘Adam Smith (1723-1790) was a Scottish philosopher and economist who is best known as the author of An Inquiry into the Nature and Causes of the Wealth Of Nations (1776)…’
In the movie, John Nash claims that Adam Smith needs revision. He says it’s what’s best for the individual and the group. He then lays out that if they all went for the blonde, they’d all get rejected and having a chance with her friends would then be impossible since no one wants to be second choice.
So, is the movie trying to depict the Nash equilibrium and if so does it do correctly?
Okay, that’s not fair – read the definition from Wikipedia, ‘In game theory, the Nash equilibrium, named after the late mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.’
What does that mean to you?
Okay, let’s see if this helps. The prisoner’s dilemma –
There are two people convicted of a crime – let’s say Antonio and Jordy. You’ll normally see this example in a table format so imagine this in your head.
Jordy has two choices and Antonio has two choices. Keep quiet or betray their partner. The person that confesses against their partner gets out Scott free. If they both confess, they both get five years. In one confesses and the other doesn’t then one gets 10 years and the other gets nothing.
So, what do you do?
Nash showed for the first time in his dissertation, Non-cooperative games (1950), that Nash equilibria must exist for all finite games with any number of players. Only 27 pages!!!
I like to think of it as the point when all players have played their best strategy knowing what other players can do.
Graduate Alumni Records – https://findingaids.princeton.edu/collections/AC105/c3
Let’s return back to a beautiful mind then ….
Adam Smith does write ‘It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.’ – Wealth of Nations
https://hbr.org/2002/04/wealth-happens
Cooperative vs. non cooperative games – in cooperative games there is some sort of binding agreement.
So, let’s return to the Beautiful Mind movie. What scenario would be a Nash Equilibrium?
#gametheory #gametheory
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