Who wins the world?

2022-05-15

Consider a world `W` where there are many `x`s (such that `x ∈ X`). In this experiment, we define the winner of the game as having the maximum `M` value (think of it to stand for "money", perhaps), i.e. more formally, `x(i)` is the winner at some time `t` if `max(M(x0,t), M(x1,t), M(x2,t), ... ,M(xi,t), ...) == M(x(i),t)`.

Let's say,

(1) Each `x` can utilise some strategy `S(x,M)` to increase their `M` value between `t` and `t+1`, i.e. `M(x,t+1) = S(x,M(x,t))` such that `M(x,t+1) > M(x,t)`.

(2) Since this is an unfair experiment, each `x` has a different initial `M` value, i.e. `M(x=x(i),t=0) != M(x=x(j),t=0)`. In some extreme cases there could, of course, be a very large difference, `M(x=x(k),t=0) >>> M(x=x(q),t=0)`.

(3) `x=x(i)`'s strategy function `S(x(i),M(x(i),t))` at some time `t` may or may not have adverserial affect on another `x=x(j)`'s strategy function `S(x(j),M(x(j),t))`. Therefore `x(i)` and `x(j)` must know that their strategies can adverserially affect each other to one's benefit and the other's decline.

The question then that this thought experiment proposes is this -- is only the knowledge of the above three statements enough to win the game in world `W` (i.e. to pick the best strategy `S` in each epoch t, t+1, t+2 ...)?

If you wish to contribute to develop this thought experiment further, write to [email protected].