Assume 2 players (Ali and Baba) are bargaining over the division of a pie with value 100. Ali and Baba have a certain number of stages to reach an agreement, after that the pie is melted and its value is 0. Assume that the pie proportionally shrinks at every stage of the bargaining game. With n stages, the pie decreases by 100 of its value after each stage. For example, with n=8 stages, the pie decreases by 100/8=12.5 after any stage. in stage 1 the pie is worth 100; in stage 2 the pie is worth 100-12.5= 87.5; in stage 3 the pie is worth 87.5-12.5= 75; in stage 4 the pie is worth 75-12.5= 62.5; in stage 5 the pie is worth 62.5-12.5-50; in stage 6 the pie is worth 50-12.5= 37.5; in stage 7 the pie is worth 37.5-12.5= 25; in stage 8 the pie is worth 25-12.5=12.5; after 8 stages, the pie is worth 25-12.5=0. Ali is the proposer in every odd stage of the game (stage 1, stage 3, etc) and the receiver in every even stage (stage 2, stage 4, etc). Baba is the proposer in every even stage of the game (stage 2, stage 4, etc) and the receiver in every odd stage (stage 1, stage 3, etc)