This is a sequential game with two players A and B. In this game a dime is put on the table. A can take it or pass. If A takes a dime, the game ends; if A passes, then B can take 2 dimes or pass; if B takes 2 dimes, the game ends; if B passes, then A can take 3 dimes or pass; and so on until a choice of a dollar. This process is shown in the game tree below. The rollback equilibrium of this game is that B is sure to take the dollar at last round, so A should take 90 at the penultimate stage, and so on. Thus, A should take the first dime and end the game.

True

False

A B. A Pass Pass Pass B Pass B Pass 0,0 Take Dime Take Dimes Take Dimes Take Dimes Take Dimes 10,0 0,20 30,0 0,40 0,100