Defection by the first player is the unique subgame perfect equilibrium and required by any Nash equilibrium, it can be established by backward induction. Suppose two players reach the final round of the game; the second player will do better by defecting and taking a slightly larger share of the pot. Since we suppose the second player will defect, the first player does better by defecting in the second to last round, taking a slightly higher payoff than she would have received by allowing the second player to defect in the last round. But knowing this, the second player ought to defect in the third to last round, taking a slightly higher payoff than he would have received by allowing the first player to defect in the second to last round. This reasoning proceeds backwards through the game tree until one concludes that the best action is for the first player to defect in the first round. The same reasoning can apply to any node in the game tree.