A model of the N-player multiple period bargaining game with equal discounting rate

This study extends the classical ultimatum bargaining game to consider a case when there are multiple players who are alternatively making their offers in multiple states. The game begins by letting the first player makes an offer, then the subsequent players will decide whether to accept or reject the offer in order. The approach of backward induction was used to solve for subgame perfect equilibria. The equilibrium depends on whether the final state is even or odd. One result shows that when discounting factors are equal for all players, all players except player 1 receive equal payoffs; however, player 1 does not always have the advantage. Another interesting result shows that the discounting factor must be less than one divided by the number of player minus one; otherwise, player 1 has no incentive to offer anything in the first stage.