5. Consider the following variation of the centipede game in which two players take turns choosing either to take a slightly larger share of an increasing pot, or to pass the pot to the other player. The game ends in two ways: any player chooses to take their share of the pot, or the players pass the pot between themselves for 100 rounds. If a player passes the pot to her opponent and the opponent takes the pot on the next round, the player receives slightly less than if she had taken the pot on this round, but after an additional switch the potential payoff will be higher. We can represent this scenario with the following game tree: Pass 2 Pass Pass 2 Pass 1 Pass 2 Pass (100, 100) Take Take Take Take Take Take (2, 0) (1, 3) (4, 2) (97, 99) (100, 98) (99, 101) a.) Calculate the number of information sets each player has. Show your work. b.) Calculate the number of strategies sets each player has. Show your work