Quantum strategies.

http://arxiv.org/pdf/quant-ph/9804010 

Classic strategies:

-  Deterministic: TFT - if last move C do C otherwise D)
-  Probabilistic: 75% D and 25% C

Quantum strategies:

-  Take opponent into account when picking your move OR working with the superposed game state

Take that quantum strategies!

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V8S-4SYCPM2-2&_user=520880&_coverDate=12/31/2008&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_searchStrId=1660849561&_rerunOrigin=google&_acct=C000023460&_version=1&_urlVersion=0&_userid=520880&md5=dd79ad0697318746c79dc8eb34464050&searchtype=a

Quantum PQ penny flip (P and Q don't know each others moves):
- Penny is placed heads up in a box by a refree
- P makes a move to place the penny in a superposed state
- Q can not modify the superposed state
- P can now make a move to win the game with probability 1 ... using Hadamard matrix (http://en.wikipedia.org/wiki/Hadamard_matrix)

No! Only works in a quantum environment where the penny is a qubit, not a real penny. Even so, if you can successfully place the penny in a superposed state how can you know how to extract the correct results from it?

Simple, by cheating ... the Hadamard matrix assumes to know the state of the penny, thus the action isn't taken until P has actually looked at the state of the penny before making his move. 

All in all it seems that quantum and real world aren't playing the same game. Quantum gets to take a peek at your move before deciding what to do. Going to question some quantum people on this tomorrow.... 

Athugasemdir

[Björn Leví Gunnarsson, 1.3.2011 kl. 22:42]

More than that: http://en.wikipedia.org/wiki/Nash_equilibrium

This stuff completely breaks the Nash equilibrium ... saying that you can do better by adopting a quantum strategy. Yet before you did you knew every strategy of every player.

Essentially you are not "peeking" at the penny before flipping it, you are actually just turning it to your winning state no matter what your opponent does.

[Björn Leví Gunnarsson, 1.3.2011 kl. 23:16]

Ok, a note on that Hadamard matrix stuff. Essentially P is playing both flip/not flip ... he's playing the superposed quantum move. Because of this no matter what Q does P just plays the quantum move again later and picks the "winner".

Such is the quantum. This still means that there are two different games being played here.