Two players, say A and B, play the following game: Both players have 100 marbles and may put anywhere between 1 and 100 marbles in the box each. This decision is not revealed to the other player. Then, they draw 1 marble. If the marble belongs to A, then assuming that A put a marbles in the box, A is paid 100−a monetary units from player B. Similarly if the marble belongs to B, then assuming B put b marbles in the box, B is paid 100−b monetary units from player A. Assume both players play optimally. How many marbles should player A select?
