Actually, you prove that there does not exist an optimal strategy for the game “Score more points that everybody else in a given competition.” The game “Score the maximum number of points possible” is subtly different.
The “maximum number of points” optimizing strategy maximizes the number of points in some average environment. In a sufficiently perverse environment, it will score low.
So, perhaps the question is how to define the “average” environment. Is it an environment containing bots with probability corresponding to their (Kolmogorov) complexity of code?
Actually, you prove that there does not exist an optimal strategy for the game “Score more points that everybody else in a given competition.” The game “Score the maximum number of points possible” is subtly different.
The “maximum number of points” optimizing strategy maximizes the number of points in some average environment. In a sufficiently perverse environment, it will score low.
So, perhaps the question is how to define the “average” environment. Is it an environment containing bots with probability corresponding to their (Kolmogorov) complexity of code?
I was going to say that there was a program which would score more than any other program in any given environment.
But when I write that out, it’s trivial to falsify.
There does not exist a strategy which is dominant in all environments.