This paper examines an infinite horizon bargaining model, incorporating five features: two-sided incomplete information (with potentially information-revealing strategies), an infinite horizon, uncertainly concerning the potential gains from trade, an illumination of interesting qualitative bargaining issues, and plausible (free from arbitrarily specified out-of-equilibrium conjectures) equilibria. These features, motivated in the paper, have powerful implications. A Nash equilibrium exists, and is generically both unique and sequential. Comparative static implications of variations in the game's specifications are developed. We find that natural indications of bargaining strength emerge from the model, and establish the intuitive result that an increase in a player's relative bargaining strength makes that player more likely to capture the gains from bargaining.

We explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting. Our focus is on the efficiency properties of stationary equilibria of strictly superadditive games, when the discount factor δ is sufficiently large; we do, however, consider examples of other games where subgame perfectness alone is employed. It is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium, the latter for some or all orders of proposer. However, efficient stationary equilibrium payoffs converge to a point in the core, as δ → 1. Strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high δ. This vector converges as δ → 1 to the egalitarian allocation of Dutta and Ray (1989).