# Game theory Centipede game

Players $A$ and $B$ alternately had the opportunity to claim or pass a growing pile of dimes (maximum of 10) placed on the table.

Suppose rules of game were changed so that

Two rounds of game are played with the same two players $A$ and $B$. In the first round, $A$ may not keep more than five dimes, and $B$ may not keep more than nine. Find the rollback equilibrium strategies for each player.

My question is

I am not understanding this statement In the first round, $A$ may not keep more than five dimes, and $B$ may not keep more than nine. In original game as shown below, whosever ($A$ or $B$) turn is take entire amount or pass it. But here it is stated that $A$ may not keep more than five dimes and $B$ may not keep more than nine, than where does remaining amount in growing pile goes?

I am assuming rounds here mean the same game (entire upto amount $100$) is played multiple times?

In original centipede game will stop at very first step; that is player $A$ choose to take $10$ dime. Does playing same game two times build confidence among players and game will not stop at very first step? In odd rounds, when $A$ has the right to claim, he collects up to five dimes and the rest stays in the pile (to be collected by $B$).
Similarly, in even rounds, $B$ has the right to claim but she collects up to nine dimensions (and leaves the rest to $A$).