Game theoretic models of bargaining frequently do not represent an ongoing bargaining process, but focus on equilibrium outcomes and assume that one party makes an offer corresponding to the equilibrium outcome, which is immediately accepted by the other party. Immediately identifying the equilibrium of a bargaining situation is a very strong assumption about the rationality of players, which is clearly violated in many actual bargaining situations. We present a model that takes a more myopic view of the players’ decision process: At each stage of the negotiation, players decided on acceptance of their counterpart’s offer, a possible counteroffer, or termination of the negotiation based on their expectations about what could be the final outcome of a prolonged negotiation. We show that the process depends mainly on the negotiator’s confidence (whether they expect the final outcome to be closer to their own or their opponent’s current offer), and that the process will (under some additional assumptions) converge to the nonsymmetric Nash bargaining solution. This connects the approach to the Zeuthen-Hicks bargaining model. We furthermore test this model empirically using data from negotiation experiments and find that it represents actual bargaining processes well, but that outcomes systematically deviate from the model predictions.