This paper proposes a noncooperative model of multilateral bargaining. The model can be viewed as an extension of the famous Stahl-Rubinstein bargaining game. Two players take turns proposing a division of a pie. After one player has proposed a division, the other can accept or reject the proposal. If the proposal is accepted, the game ends and the division is adopted; if it is rejected, the second player then makes a proposal, which the first player then accepts or rejects. And so on. In Stahl\u27s formulation, the game continues for a finite number of rounds; in Rubinstein\u27s extension, the number of rounds is infinite. We propose a generalization of this model to incorporate multiple players and multidimensional issue spaces. We consider a sequence of games with infinite bargaining horizons, and study the limit points of the equilibrium outcomes as the horizon is extended without bound. A novel feature of our model is that the proposer is chosen randomly by nature in each round or bargaining, according to a prespecified vector of strictly positive access probabilities
