Ariel Rubinstein's paper "Perfect Equilibrium in a Bargaining Model" explores the dynamics of bargaining between two players who must reach an agreement on how to divide a pie of size 1. Each player takes turns making proposals, and the other player can either accept or reject the proposal, leading to a potential cycle of offers and rejections. The paper assumes certain properties of the players' preferences, including the desirability of the pie, the value of time, continuity, stationarity, and the compensation principle. Two specific models are considered: one with fixed bargaining costs and another with fixed discounting factors. In the fixed bargaining cost model, if player 1's cost is greater than player 2's, the only perfect equilibrium partition (PEP) gives all the pie to player 1. If player 1's cost is less than player 2's, the only PEP gives nothing to player 1. If the costs are equal, any partition where player 1 receives at least the cost is a PEP. In the fixed discounting factor model, the only PEP is given by the formula \((1 - \delta_2)/(1 - \delta_1 \delta_2)\), where \(\delta_1\) and \(\delta_2\) are the discounting factors of players 1 and 2, respectively. This solution is continuous and monotonic in the discounting factors, favoring the player who starts the bargaining. The paper also introduces the concept of perfect equilibrium, which requires that the strategies chosen at the beginning of the game form an equilibrium, and that the strategies planned after all possible histories (in every subgame) also form an equilibrium. This concept is crucial for isolating a single solution in most cases examined. The paper concludes with applications of the theorem to the fixed bargaining cost and fixed discounting factor models, providing specific conditions under which the PEPs are determined.Ariel Rubinstein's paper "Perfect Equilibrium in a Bargaining Model" explores the dynamics of bargaining between two players who must reach an agreement on how to divide a pie of size 1. Each player takes turns making proposals, and the other player can either accept or reject the proposal, leading to a potential cycle of offers and rejections. The paper assumes certain properties of the players' preferences, including the desirability of the pie, the value of time, continuity, stationarity, and the compensation principle. Two specific models are considered: one with fixed bargaining costs and another with fixed discounting factors. In the fixed bargaining cost model, if player 1's cost is greater than player 2's, the only perfect equilibrium partition (PEP) gives all the pie to player 1. If player 1's cost is less than player 2's, the only PEP gives nothing to player 1. If the costs are equal, any partition where player 1 receives at least the cost is a PEP. In the fixed discounting factor model, the only PEP is given by the formula \((1 - \delta_2)/(1 - \delta_1 \delta_2)\), where \(\delta_1\) and \(\delta_2\) are the discounting factors of players 1 and 2, respectively. This solution is continuous and monotonic in the discounting factors, favoring the player who starts the bargaining. The paper also introduces the concept of perfect equilibrium, which requires that the strategies chosen at the beginning of the game form an equilibrium, and that the strategies planned after all possible histories (in every subgame) also form an equilibrium. This concept is crucial for isolating a single solution in most cases examined. The paper concludes with applications of the theorem to the fixed bargaining cost and fixed discounting factor models, providing specific conditions under which the PEPs are determined.