Can quantum mechanics be combined with game theory?

[Spathi]

I suppose, anybody here knows about the Elitzur–Vaidman bomb tester and the counterfactual definiteness:

https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

https://en.wikipedia.org/wiki/Counterfactual_definiteness

I have a question: can this experiment be performed at the level of countries for avoiding a nuclear war? I mean, if a dictator threatens the humanity a nuclear extermination, the states will have a difficult choice: according to all international laws, using nukes against the country of this dictator can be done only in response of his use. However, maybe a superposition can be created of two Earths (two universes) – in the first, the nuclear war has not started, and in the second, this dictator had pushed the button. Like in the Elitzur–Vaidman bomb experiment, the information that the dictator has pressed the button will be accessible in the first universe so the states will have the right to nuke the country of this dictator.

I remember that this forum does not like politics and philosophy, but my question relates physics only and is sufficiently specific and clear. We can discuss it without politics. Besides that, I have a question, what applications of the game theory are mostly useful. My idea is a suggestion of a new science, which combines the quantum mechanics and the game theory; the game theory has important use with the strategy of nuclear wars, and if the nuclear wars are not a good subject for this forum, I can think about combining quantum mechanics with other applications of the game theory.

 

[Frabjous]

Where are you using game theory?

 

[Spathi]

Where are you using game theory?

The game theory is broadly used in planning a strategy for a nuclear war. Two pics from Web googled:

 

[Frabjous]

Your scenario is just game theory using an information source that happens to be quantum. I would’t say that they are combined.

 

[Spathi]

The Game of Chicken illustrates cases where people can win through "rational irrationality":

https://en.wikipedia.org/wiki/Chicken_(game)

This is an explanation of the politics of Kim Jong Un and Putin, and my idea is that in the quantum reality the civilized world can find solutions against this. If it is not allowed to discuss the nuclear war at this forum, I will try to find other applications of the game theory which can be similar.
I suppose my idea does not look crazy, because the EV bomb experiment is "crazy" already and the physicists must know that.

 

[Spathi]

An example of a situation which can be studied by the game theory is the Truel:


https://en.wikipedia.org/wiki/Truel


One example of this game was described in a book of Martin Gardner. The shooters A, B, C have chosen a truel. A never misses, B hits 80% of the time, C hits 50% of the time. In such a game, C has the best chance of winning because he can shoot into the air first while A and B are shooting at each other.

My question is: is it possible to suggest some versions of this truel in which players have access to the Mach–Zehnder interferometerwith bombs, and this can change the probabilities of the outcomes. I mean something like this: player C does not shoot either A or B, but creates a superposition of these two states, and in one of the states also sends a message to B - if you don’t want me to shoot at you next time, do as I ask. I hope my idea can be understood.

 

[pines-demon]

if a dictator threatens the humanity a nuclear extermination, the states will have a difficult choice: according to all international laws, using nukes against the country of this dictator can be done only in response of his use. However, maybe a superposition can be created of two Earths (two universes) – in the first, the nuclear war has not started, and in the second, this dictator had pushed the button. Like in the Elitzur–Vaidman bomb experiment, the information that the dictator has pressed the button will be accessible in the first universe so the states will have the right to nuke the country of this dictator.

Be clearer with the analogy. How the dictators, action of pushing a botton and response of the other countries maps to the Elitzur–Vaidman (EV) experiment?

Does the action of pushing the botton correspond to the EV bomb?

My idea is a suggestion of a new science, which combines the quantum mechanics and the game theory;

This is not new. Quantum game theory exists. Here are some links:

• CHSH game
• Quantum pseudo-telepathy
• Quantum game theory

 

[Spathi]

This is not new. Quantum game theory exists. Here are some links:

• CHSH game
• Quantum pseudo-telepathy
• Quantum game theory

The refs are nice, I'll study all this later, but for now I would like to formulate my idea (in my opinion it is quite simple).
Imagine that it is 2200 year now. A cobalt bomb has been developed that can destroy the entire Earth if used anywhere (i.e., the user will also die). Many countries have this bomb. In the country of Eritrea, dictator A is in power and is threatened by revolution; to keep his power, he decides to attack a neighboring country that has many natural resources.
The humanity is collectively governed by the UN, under the leadership of the Secretary. The Dictator announces to the Secretary that if the UN intervenes in the war, the Dictator will activate the bomb. The dictator expects that the Secretary, choosing between concessions and complete destruction, will choose the first. He has calculated that the probability of activating the Bomb is 1%, and the probability for him to win is 60%; if he does not start a war, with a 50% probability he will be overthrown and judged.
The Secretary can preventively nuke Eritrea, and then the Bomb will not be activated; but moral standards prohibit doing this.
The Dictator has programmed the Bomb so that it would work as he promised; there is also a small chance of the Bomb going off due to random errors and accidents.
It is known that a Bomb can be either true or nude. If the Bomb is true, this gives the Secretary the right to perform a preventive nuclear strike. Now it turns out that the Secretary can create a superposition of two universes: in the first he starts a conventional war and the Dictator activates the Bomb, in the second nothing happens. Is my further logic clear?

 

[Frabjous]

creates a superposition of these two states

it turns out that the Secretary can create a superposition of two universes:

What makes you think this is possible?

 

[Spathi]

What makes you think this is possible?

I suppose, the concept that in the Wigner's friend experiment a superposition of two universes is created, is mainstream in the scientific community? Since the superposition of the Schrödinger's cat occurs due to the superposition of a radioactive decay device or a beamsplitter, the Secretary can use a beamsplitter too for choosing his actions.

Perhaps one more assumption must be added - Dictator A is obliged to use quantum entanglement when interacting with the Secretary. Let's say that Eritrea have signed a pact on the use of quantum entanglement to avoid nuclear criseses, and the Dictator promised to comply with these conditions (if he broke his promises, the Secretary General would have the right to destroy Eritrea).

 

[Frabjous]

I suppose, the concept that in the Wigner's friend experiment a superposition of two universes is created, is mainstream in the scientific community? Since the superposition of the Schrödinger's cat occurs due to the superposition of a radioactive decay device or a beamsplitter, the Secretary can use a beamsplitter too for choosing his actions.

Perhaps one more assumption must be added - Dictator A is obliged to use quantum entanglement when interacting with the Secretary. Let's say that Eritrea have signed a pact on the use of quantum entanglement to avoid nuclear criseses, and the Dictator promised to comply with these conditions (if he broke his promises, the Secretary General would have the right to destroy Eritrea).

Superposition is a not a magic spell. You cannot apply it willy nilly to whatever you want. Look at the bomb tester. It is convertible to a quantum-only problem. Your scenarios are not.

Regardless, game theory is there to help us think through complex situations. I do not see how your scenarios are of interest.

 

[Spathi]

I try to uderstand the article about quantum pseudotelepathy:

Game rules[edit]​

This is a cooperative game featuring two players, Alice and Bob, and a referee. The referee asks Alice to fill in one row, and Bob one column, of a 3×3 table with plus and minus signs. Their answers must respect the following constraints: Alice's row must contain an even number of minus signs, Bob's column must contain an odd number of minus signs, and they both must assign the same sign to the cell where the row and column intersects. If they manage they win, otherwise they lose.

Alice and Bob are allowed to elaborate a strategy together, but crucially are not allowed to communicate after they know which row and column they will need to fill in (as otherwise the game would be trivial).

Classical strategy[edit]​

It is easy to see that if Alice and Bob can come up with a classical strategy where they always win, they can represent it as a 3×3 table encoding their answers. But this is not possible, as the number of minus signs in this hypothetical table would need to be even and odd at the same time: every row must contain an even number of minus signs, making the total number of minus signs even, and every column must contain an odd number of minus signs, making the total number of minus signs odd.

With a bit further analysis one can see that the best possible classical strategy can be represented by a table where each cell now contains both Alice and Bob's answers, that may differ. It is possible to make their answers equal in 8 out of 9 cells, while respecting the parity of Alice's rows and Bob's columns. This implies that if the referee asks for a row and column whose intersection is one of the cells where their answers match they win, and otherwise they lose. Under the usual assumption that the referee asks for them uniformly at random, the best classical winning probability is 8/9.

Currently I don't understand the point. If their task is to simply name three bits each, why can’t they, if the judge tells them the third row and the third column, name the option not based on this picture, but so that everything matches? For example -1,+1,-1 in the third row and +1, +1, -1 in the third column?

 

[jbriggs444]

Currently I don't understand the point. If their task is to simply name three bits each, why can’t they, if the judge tells them the third row and the third column, name the option not based on this picture, but so that everything matches? For example -1,+1,-1 in the third row and +1, +1, -1 in the third column?

It is not clearly specified, but I believe that Alice is only told which row she is to fill in and Bob is only told which column he will fill in.

Alice reads from the agreed-upon 3 x 3 table by looking at the selected row and making the set of three choices listed in that row.

Bob reads from the agreed upon 3 x 3 table by looking at the selected column and making the set of three choices listed in that column.

If the strategy is successful, the resulting configuration (for the selected row and column) must match Alice and Bob's agreed upon table.

But since any column could have been selected, every column must have an odd number of minus signs. The total number of columns is odd, so the total number of minus signs in the agreed-upon table must therefore be odd.

Similarly, since any row could have been selected, every row must have an even number of minus signs. The total number of minus signs in the agreed-upon table must therefore be even.

 

[Spathi]

Now I try to understand the second example from the article, firstly the classical version too.

The players win if �⊕�⊕�=�∨�∨�

, where ∨

indicates OR condition and ⊕

indicates summation of answers modulo 2. In other words, the sum of three answers has to be even if �=�=�=0

. Otherwise, the sum of answers has to be odd.

I can't paste correct symbols here. What means modulo 2 - the remainer of the devision by 2 (0 mod 2 =0, 1 mod 2 =1, 2 mod 2=0, etc)? Then it is unclear for me, why in the tables the strings 0 mod 2, 1 mod 2 are written instead of simply 0 and 1.

 

[nuuskur]

Are you trying to shoehorn the use of game theoretical techniques in the argument? That never goes well. Better formulate your problem in game theoretical terms, the technique follows naturally.

 

[jbriggs444]

Now I try to understand the second example from the article, firstly the classical version too.


I can't paste correct symbols here. What means modulo 2 - the remainer of the devision by 2 (0 mod 2 =0, 1 mod 2 =1, 2 mod 2=0, etc)? Then it is unclear for me, why in the tables the strings 0 mod 2, 1 mod 2 are written instead of simply 0 and 1.

Computer people and mathematical people tend to think about modulus differently.

For computer folks, we think about modulus arithmetic as a function. You put a dividend and a divisor in. You get a remainder out. So "3 mod 2" is a number: The remainder of three upon division by two. Just as you say.

Computer folks tend to have conventions for what happens when the divisor is negative or if the dividend is not an integer. One can find those conventions mentioned in the documentation.


Mathematicians, on the other hand, tend to think about modulus arithmetic in terms of an equivalence. Two numbers are "equivalent" if they have the same remainder when divided by the modulus. A mathematician would write: $$3 \equiv 1 \ (\text{mod 2})$$and might think about the equivalence relation as partitioning the original set, establishing a quotient algebra on the equivalence classes.

 

[Spathi]

This is not new. Quantum game theory exists. Here are some links:

• CHSH game
• Quantum pseudo-telepathy
• Quantum game theory

These refs are really great. And if the quantum mechanics can be united with the game theory, this means that our views in the field of philosophy must be reconsidered.
I mean, that the game theory now together with ethology gives the answers to the questions about the nature of Good and Evil. Here are these answers in brief:

1) The Good is altruism, Evil is selfishness. More exactly, the Evil is a behavior that is beneficial for the one who commits it, and disadvantageous for others;
2) For each person it is beneficial to behave selfishly, but when everybody in the population behaves selfishly, this population suffers from that;
3) The altruism is unstable; this means, that if some people in the population behave selfishly, they live better than others and correspondingly they spread their genes or memes more efficiently, and their number increases;
4) The altruism can be supported by group selection and the Simpson's paradox, but this requires certain conditions;
5) A more common way of suppressing the selfishness is the social contract ("Leviathan"); however this way has its own faults, in particular a new type of Evil can occur with it - authoritarian state.

How should these principles be reconsidered for the world where quantum effects play a big role?

 

[Hornbein]

I suppose, anybody here knows about the Elitzur–Vaidman bomb tester and the counterfactual definiteness:

https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester

https://en.wikipedia.org/wiki/Counterfactual_definiteness

I have a question: can this experiment be performed at the level of countries for avoiding a nuclear war? I mean, if a dictator threatens the humanity a nuclear extermination, the states will have a difficult choice: according to all international laws, using nukes against the country of this dictator can be done only in response of his use. However, maybe a superposition can be created of two Earths (two universes) – in the first, the nuclear war has not started, and in the second, this dictator had pushed the button. Like in the Elitzur–Vaidman bomb experiment, the information that the dictator has pressed the button will be accessible in the first universe so the states will have the right to nuke the country of this dictator.

I remember that this forum does not like politics and philosophy, but my question relates physics only and is sufficiently specific and clear. We can discuss it without politics. Besides that, I have a question, what applications of the game theory are mostly useful. My idea is a suggestion of a new science, which combines the quantum mechanics and the game theory; the game theory has important use with the strategy of nuclear wars, and if the nuclear wars are not a good subject for this forum, I can think about combining quantum mechanics with other applications of the game theory.

So they create two artificial universes and see into the future of each. That seems too speculative for PhysicsForums, as we can't even remotely imagine how to do either of these things. Maybe you would be better off in the Science Fiction World Building section.

And why two universes? Why not 1,667,901 of them? Suppose country A is the bad guy in 36% of them while country B is bad in 24%. Then what?

What if your own country is statistically the bad guy. Do you then nuke yourself?

 

[Spathi]

Maybe you would be better off in the Science Fiction World Building section

What is the World Building? I see only the "Science Fiction and Fantasy Media Forum" section. Ok I can create such threads in this section, and I hope that good experts at this forum visit it.

​

 

[Hornbein]

What is the World Building? I see only the "Science Fiction and Fantasy Media Forum" section. Ok I can create such threads in this section, and I hope that good experts at this forum visit it.

​

It's a subforum of the science fiction forum. https://www.physicsforums.com/forums/sci-fi-writing-and-world-building.220/

 

[Spathi]

It's a subforum of the science fiction forum. https://www.physicsforums.com/forums/sci-fi-writing-and-world-building.220/

I didn't pay attention to this section. Maybe it is here only recently?
Previously I thought that this forum is totally anti-philosophycal: no speculation, no philosophy, no political science. Maybe now something has changed?

 

[Hornbein]

I didn't pay attention to this section. Maybe it is here only recently?
Previously I thought that this forum is totally anti-philosophycal: no speculation, no philosophy, no political science. Maybe now something has changed?

The goal of that section is to help science fiction authors. Though usually they are just told to not worry about it and do whatever fantastic thing they want.

 

[Spathi]

The goal of that section is to help science fiction authors. Though usually they are just told to not worry about it and do whatever fantastic thing they want.

It is interesting for me, how many fiction writers do use the knowledge of modern quantum physics? For example, as far as I know, the MWI becomes more popular than the CI, and this means that there are a lot of alternative universes; and an author can describe an idea that some people have superpowers of travelling through these universis (something similar was in the "Chronicles of Amber" by Roger Zelazny). Is there any fiction (maybe fantasy) about that? And is such fantasy fiction allowed in the Science Fiction World Building section?

 

[Hornbein]

It is interesting for me, how many fiction writers do use the knowledge of modern quantum physics? For example, as far as I know, the MWI becomes more popular than the CI, and this means that there are a lot of alternative universes; and an author can describe an idea that some people have superpowers of travelling through these universis (something similar was in the "Chronicles of Amber" by Roger Zelazny). Is there any fiction (maybe fantasy) about that? And is such fantasy fiction allowed in the Science Fiction World Building section?

I dunno. I read very little science fiction these days and don't follow the genre. And I have no input into PhysicsForums policies. It might be a good idea to ask the mentors. You can do that by reporting your own post with that button in the lower left corner.

 

[Spathi]

As I have mentioned, I am a fan of ethology and I want to give two refs which describe mathematical models of evolution, which provide the basic understanding of what I say:

https://en.wikipedia.org/wiki/The_Evolution_of_Cooperation

 

[Hornbein]

The aliens came down to Earth and said "take me to your leader." They were informed that Earth had 169 nations hence 169 leaders. "Very well," said they, "take us to 169 leaders." While the hideous aliens were unflaggingly polite during the course of this tour it was noticed that their first request was always to see the forests of each nation. They showed polite interest in factories and armies but never asked to be shown such things.

Now the leader of Moldova was a volitile and touchy individual. One day he exploded, saying to the entourage, "trees! trees! all you want to see is za trees! You'd think that za trees ruled this world!" Aghast, the aliens held a short but busy conference in their as-yet-untranslateable language. Then their ambassador approached the President of Moldova. "Do you mean to say sir," he asked gracefully, "that you didn't know?"

 

[Spathi]

https://www.physicsforums.com/threads/time-patrol.1064714/#post-7109061