Who wins the world?
Consider a world
W where there are many
xs (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
max(M(x0,t), M(x1,t), M(x2,t), ... ,M(xi,t), ...) == M(x(i),t).
x can utilise some strategy
S(x,M) to increase their
M value between
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).
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
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].