This paper extends the Stahl-Rubinstein model of bilateral bargaining to incorporate many players and multidimensional issue spaces. A central feature of our framework is that in each round of negotiations, a proposer is selected randomly. Our bargaining model consists of a sequence of finite-horizon games, in which the horizon increases without bound. A solution to our model is a limit of equilibrium outcomes for the finite-horizon games. A necessary condition for existence of a deterministic solution is that the limit outcome belongs to the core of the underlying bargaining problem. Solutions, if they exist, are generically unique. Two sets of sufficiency conditions for existence are presented. The paper concludes with examples and applications. In particular, we consider bipolar negotiations between two factions, and show that there is a positive relationship between the cohesiveness of one faction relative to the other and its effectiveness in securing the common goals to its members.