the boy had cleaned up his yard completely before the old man came
out, then as the battle began,
would be greater than ,
and there would be a net flow of apples to the boy's side. His agility
would do him no good if there were no apples on his side to pick
Conversely, if the battle had begun with equal concentrations of
apples on each side, then
would have been greater than
because the agility constant
is greater than .
With the same number of apples at their disposal, the boy always
can do better than the old man because he gets around faster.
In either case, a neutral observer would have found to his surprise
that the battle eventually settled down into a stalemate, or equilibrium
at a point where the extra apples on the old man's side just compensated
for the extra agility of the boy.