Consider the following game between two players. The player takes turns moving a rock among the cells of an 3 x 4 matrix. At the beginning of the game (before the first move by the first player), the rock is placed at the top left of the matrix. Player 1 goes first. At each turn, the player with the move must push the rock into one of the three cells below or to the right (or both) of the cell where the rock currently sits. That is the player may move the rock in following three actions: To the right of the current cell (labelled as R) To the bottom of the current cell (labelled as B) To the cell diagonal to the current position in the bottom right direction (labelled as D) A player may not move the rock outside of the matrix. The player who is forced to move the rock into the bottom left right that is cell (3,4) losses the game. The winner gets a payoff of 1 and the loser get a payoff of 0. a) Represent the given game in the Extensive form game. Clearly labelled each of the nodes, branches, and player. At each of the terminal node, gives the payoff vector. Suppose that at a node, ex node e, after the player make decision and the opponent were forced to make only 1 decision sequentially until bottom right of the matrix, then the game end after the decision branch of node e with terminal nodes where payoff 1 goes to the winner and payoff 0 goes to loser. b) Using backward induction, solve the game and state the strategy profile. Which player have a strategy that guarantees a victory?