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 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].