You would clarify distinctions such as those when you extended the model. The model isn't extended yet and you're trying to mash criticisms of it within its existing framework. That doesn't work, and neither does your argument.
As you said, the model has to serve a real life purpose. The real life purpose the existing model serves is it defines the potential for a solution. What purpose that is more significant does your alternative model serve with a different definition for perfect information? Thats the question one has to answer if you want to offer a better or more effective definition.
No, the model needs to accurately model reality. In this case... the existing models are assuming a perfect player, and defining perfect information based on that. What I'm saying is, in reality, no such thing exists. Yes, your conclusion is true within your irrelevant model, but there's no point to this. You don't create a model for its own sake. Hence the game theory model needs to be extended - the definition of perfect information needs to be modified - to more accurately model reality.
And that's always the way models works, that's how fields always evolve. I guarantee there is room for a game theorist to come along, and look at these problems, and extend game theory to account for them.
Basically you'd just have to create a model inwhich, instead of assuming a perfect player, you can define certain limits on the players ability to handle complexity. And you could probably model that mathematically using fields of probability and stochastic modeling. You could then tune the model to match the game... infact, your model would sort-of resemble an AI model.
To achieve the model you propsoe you have to determine the absolute point where game is too complex for theoretical limit of human interpretation. Such point cant be determined so your model is actually impractical and would solve less of a purpose than one that determines potential for a theoretically possible solution...
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I think in terms of solving the game, what is the significance of perfect information regarding the solution...
For a game that contains perfect information we can produce a solution that guarantees a certain theoretical result. For a game that hides some information this hidden information will continue to cause variance in result even with a solution at hand... We can merely come up with a strategy that provides us with the optimal odds at achieving the optimal result.
For this reason the model that currently defines games of perfect information is significant.. It defines the potential of optimal play resulting from a solution.
On the other hand what would be the purpose for defining all games that are not yet solved as games as imperfect information.. The definition would provide no value. We can just call that an unsolved game, right?
That tends to imply that the game can be solved.
Enigma could be solved but chess must be many millions of times harder to solve. Maybe it's unsolveable.
If it's finite, it's solvable within a finite amount of time. That's the only meaningful way to define solvable.
You don't have to prove that @ Octopus. As you know.
Yes its finite.
But with today's technology solving chess would take many trillions of years.
That's not practical. So the finite argument isn't a meaningful way to define solving.
But to each his own.
Its not necessary to accomodate silly 'we have to' arguments from (its not me) the particular person who makes them.
But if you also want to 'decide for others' and repeat that mistake by 'the other' that's your choice.