Game Theory on Measurement Problem in QM

[sardar]

Hi All,

I was thinking if we can use the concepts of Von Neumann;s games specially the zero-sum two person games and pay of matrix with related dominant strategies and Nash equilirbria as a mathematical and a conceptual tool to understand Measurement Problem as a "game" between Nature(one player) and Scientist or Observer(as another player) where Nature tries to hide its information and she is clever but malicious she is not while Observer tries to get as much information possible as it can from the Nature and so the resulting dynamics gives rise to measurement of the system and related pay offs and probably equilibrium condition which we most often see in physics as stable global equilibrium. So it would be really very fascinating and interesting to apply a yet unrelated field of Game Theory to QM in general and measurement problem in particular.

Join in for your views in numbers.

Sardar.

 

[Karlisbad]

Hi.. Sardar, i find your observations very interesting... it would be nice, if we could consider "Nature vs. observer" as a 2 people's game to get some results, however i think it wouldn't work since (i believe) "Game theory" is not applyable whenever there is some "randomness" involved on it.

 

[Manchot]

Well, I don't know anything about game theory, but your idea is pretty far out there. Having said that, some of the best ideas have been out there, so there's a small chance that there's something to it. The only way to know for sure is to formulate your ideas more rigorously, crunch through the math, and see if you can make any useful predictions.

 

[sardar]

Well, I don't know anything about game theory, but your idea is pretty far out there. Having said that, some of the best ideas have been out there, so there's a small chance that there's something to it. The only way to know for sure is to formulate your ideas more rigorously, crunch through the math, and see if you can make any useful predictions.

I take your view and am in the process of understanding the mathematics of Game theory in more detail before venturing into the problem which is not only related with Measurement problem, but in general any physical experiment can be visualised as game between nature and observer with relevant goals and strategies.

 

[sardar]

Well, I don't know anything about game theory, but your idea is pretty far out there. Having said that, some of the best ideas have been out there, so there's a small chance that there's something to it. The only way to know for sure is to formulate your ideas more rigorously, crunch through the math, and see if you can make any useful predictions.

I am sure we can involve games with an element of randomness, as Nash himself applied it to economic theory which is obviiously not a predicatable settiing and thus we have to see how the quantum mechanics superposition be carried over in this case.

 

[selfAdjoint]

I am sure we can involve games with an element of randomness, as Nash himself applied it to economic theory which is obviiously not a predicatable settiing and thus we have to see how the quantum mechanics superposition be carried over in this case.

The trouble with this is that quantum randomness doesn't follow the same rules as macroscopic randomness as used in economics and so on. This is because the things combined are not probabilities but "amplitudes" defined by complex vectors (or worse!). Probabilities are only produced in the last step. Not to say that people probably haven't worked to make a version of stochastic game theory that works with the quantum assumptions.

 

[sardar]

The trouble with this is that quantum randomness doesn't follow the same rules as macroscopic randomness as used in economics and so on. This is because the things combined are not probabilities but "amplitudes" defined by complex vectors (or worse!). Probabilities are only produced in the last step. Not to say that people probably haven't worked to make a version of stochastic game theory that works with the quantum assumptions.

I would be interested in your last sentence of weather there is any work done on extending stochastic game theory with quantum assumptions, I would love to see the pay-off matrix of a quantum game and the prisonner;s dilemma and Nash equilibria applied to it.

 

[vanesch]

Not to say that people probably haven't worked to make a version of stochastic game theory that works with the quantum assumptions.

Well, David Deutsch has a highly discussed paper on it, where he "derives" the Born rule from game-theoretical principles and unitary quantum theory.

If you look for David Deutsch on the arxiv, you'll find his paper (and a cleaned-up version of his proof by Wallace) on the arxiv, and also in the Proceedings of the Royal Society. It was around the year 2000.

Ah, I have it:
quant-ph/9906015
quant-ph/0211104