Cards and Finance

Quantum Theory is one of the most bizzare yet fascinating theories. You can read volumes about it and yet still be in the dark about it. It is truly weird and amazing and applicability to practical life seems unfathomable.

On the other hand Game Theory which was once an economic theory has now been expanded and is being used in all aspects of our lives. From bidding in auctions to deciding geo-political balances of power.

Q) So what do we get when we add these 2 ingredients in a recipe for Science ?
Ans.) The death of Game Theory ( in practice at least).

Let me propound this grave statement by talking about a cat. Schroedinger's Cat.
Let us find a small kitten and put him in a box. And put the lid on. Add in the box a tiny capsule of cyanide gas, which breaks when the cat steps on it and kills the cat. Now close the lid of the box.

After the lid has been shut we have no way of knowing whether the cat is alive or dead as we can't see the cat. So quantum theory states that the cat is both alive and dead in a weird superposition of states. The moment we close the box , the cat moves into 2 parallel states of universe ; One in which it is dead and one in which it is alive. Opening the box superposes the 2 universes back together and the cat appears as dead or alive.

Now what is the implication for game theory. Game theory tries to pre-empt the actions of opposing parties by finding out what will logically due to happen. But in games where one does not know for sure what the opposing action will be and there is a play of probability ( eg Say Company A , decides to launch a product. Now Company B , may or may not decide to play a price war on it. Company A can never know this and must assume probabilities) .

We see that whenever there is a probability component because we cannot see the state of a system ( as in the cat) there are multiple possibilities and they all exist at the same time. Hence game theory cannot predict the action as all actions are equally likely and hence there can be no best strategy for player A, based on decisions for player B.

BUT, this is not seen to be true, Why ? Because the theory implies that the state of the system is not visible to the observer. But in Reality, in all cases the observer has an idea of the system state at all times and hence Quantum States is not true and Game Theory still is Alive and Kicking !!!