Perfect Equilibrium in a Bargaining Model

Two players have to reach an agreement on the partition of a pie of size 1. Each has to make in turn, a proposal as to how it should be divided. After one player has made an offer, the other must decide either to accept it, or to reject it and continue the bargaining. Several properties which the players' preferences possess are assumed. The Perfect Equilibrium Partitions (P.E.P.) are characterized in all the modesls satisfying these assumptions. Specially, it is proved that when every player bears a fixed bargaining cost for each period (c"1 and c"2), then: (i) if c"1 < c"2 the only P.E.P. gives all the pie to 1; (ii) if c"1 > c"2 the only P.E.P. gives to 1; only c"2. In the case where each player has a fixed discounting factor (@d"1 and @d"2) the only P.E.P. is (1 - @d"2)/(1 - @d"1@d"2).