# Game Theory – The Beautiful Mind

By John Nash

“I received the Economics Nobel Prize for that work (in Game Theory). It is not a prize in Mathematics although my work was mathematical. It used a very central theorem in topology, the Brouwer Fixed Point Theorem. That’s a theorem that has a particular topological or geometrical character. It has to do with space but the space could be of various dimensions.”

The Nash Equilibrium of the Game Theory is demonstrated below using the Oligopoly of Hamburgers between McDonald’s and Burger King:

Watch this touching video of John Nash: there is a silverlining between genius and madness.

– Extract: “Mathematicians – an outer view of the inner world”

# Rock- Scissors- Paper Game

‘Rock- Scissors- Paper’ Game Theory

Let r, s, p be the Probability of the resp. occurrence.

1. Any state of the game can be represented by a point X (r, s, p) inside an equilateral triangular RPS with r+s+p=1.
2. r is perpendicular distance (normal) from the point X to side SP; similarly, s to side RP; p to side RS

Scientists have discovered that some lizards use R-S-P Game Theory for survival strategy.

# De Moivre

De Moivre (1722)

$(Cos A+iSin B)^n = Cos nA + i.Sin \:nA$
– French Protestant, jailed by the Catholic King Louis XIV (14th), exiled to UK.
– Gave Tuition in the Duke home where he met Newton with the newly published book “Principia” and the “New Math” Calculus, he self-paced study to become expert in Calculus.
– He never got a Professor job despite Newton and Leibniz’s help.
– He observed gambling in coffee shops, invented the Game Theory.
– He liked to sleep. One day he declared he would sleep 20 mins more per day. On 73rd day when he accumulated 24 hrs more, he died at 87 yrs old !