Consider two players, designated by i = 1,2, involved in a dynamic bargaining over a perfectly divisible surplus of size 1. At the beginning of the interaction (at timet 1), player 1 chooses x1 in [0, 1]. Player 2 observes this offer and decides whether or not to accept it. If player 2 accepts this offer, the game ends and the utilities of player 1 and 2 equal x1 and 1- x1, respectively. If player 2 does not accept this offer, the game goes into the second round with a probability of \pi = 2|1/2-x11, while with probability 1 -\ pi the game ends and both players get a payoff of 0. If the game reaches the second round, t = 2, player 2 makes a counter-offer x2 in [0, 1] observing the whole past. Player 1 sees this offer and decides whether or not to accept it. If player 1 accepts x2, then the game ends and player 1 gets a payoff of x2 and player 2 a utility of 1 - x2. Both players get a payoff of zero when player 1 rejects player 2's offer x2 and the game ends. We assume that the game is common knowledge among the players. So, we have perfect information. Moreover, we concentrate on pure actions. Further, both players are risk - neutral von Neumann-Morgenstern expected utility maximizers when evaluating risky prospects. (0.) Formulate this strategic interaction via an extensive - form game in pure actions under perfect information. (a.) Identify the dynamic best responses, the set of subgame perfect equilibrium outcome paths and the set of subgame perfect equilibrium strategies.