Rubinstein's "Perfect Equilibrium in a Bargaining Model" analyzes a bargaining scenario where two players negotiate the division of a pie. Each player takes turns proposing a division, and the other must accept or reject the offer. The paper explores two models: one where players have fixed bargaining costs and another where they have fixed discounting factors. In the fixed cost model, if player 1's cost is lower than player 2's, player 1 gets all the pie; if player 2's cost is lower, player 1 gets only the amount equal to player 2's cost. In the discounting factor model, the perfect equilibrium partition is (1 - δ₂)/(1 - δ₁δ₂), which is continuous and gives an advantage to the player who starts the bargaining. The paper introduces the concept of perfect equilibrium, which requires that strategies are optimal not only at the beginning of the game but also in all subgames. This leads to a unique solution in most cases. The analysis shows that in the fixed cost model, the outcome depends on the relative costs of the players, while in the discounting model, the outcome depends on the discounting factors. The paper also discusses the implications of these models, including the possibility of prolonged bargaining when players have incomplete information about each other's costs. The results highlight the importance of rationality and the role of strategic behavior in determining the outcome of bargaining situations.Rubinstein's "Perfect Equilibrium in a Bargaining Model" analyzes a bargaining scenario where two players negotiate the division of a pie. Each player takes turns proposing a division, and the other must accept or reject the offer. The paper explores two models: one where players have fixed bargaining costs and another where they have fixed discounting factors. In the fixed cost model, if player 1's cost is lower than player 2's, player 1 gets all the pie; if player 2's cost is lower, player 1 gets only the amount equal to player 2's cost. In the discounting factor model, the perfect equilibrium partition is (1 - δ₂)/(1 - δ₁δ₂), which is continuous and gives an advantage to the player who starts the bargaining. The paper introduces the concept of perfect equilibrium, which requires that strategies are optimal not only at the beginning of the game but also in all subgames. This leads to a unique solution in most cases. The analysis shows that in the fixed cost model, the outcome depends on the relative costs of the players, while in the discounting model, the outcome depends on the discounting factors. The paper also discusses the implications of these models, including the possibility of prolonged bargaining when players have incomplete information about each other's costs. The results highlight the importance of rationality and the role of strategic behavior in determining the outcome of bargaining situations.