The paper analyzes an infinite-horizon sequential bargaining game (with one-sided offers) between a buyer and a seller when the buyer's valuation depends on the seller's; the seller knows the value of the object and the buyer does not. The influence of relative discount factors on the solution is studied. It is shown, for example, that an impasse may result if the buyer (offeror) is too impatient relative to the seller: the buyer makes a single take-it-or-leave-it offer.

According to standard theory, the set of implementable outcome functions is reduced if the mechanism or contract can be renegotiated ex post.In some cases contracts can achieve nothing and so, for example, the holdup problem may be severe.This paper shows that if the mechanism is designed in such a way that sending a message involves a small cost (e.g., the opportunity cost of time spent attending a hearing) then ex post renegotiation essentially does not restrict the set of implementable functions.Any Pareto-efficient, bounded social choice function can be implemented in subgame-perfect equilibrium, for any strictly positive message cost.

This paper studies a general model of holdup in a setting encompassing the models of Segal (1999) and Che and Hausch (1999) among others. It is shown that if renegotiation is modeled as an infinite-horizon noncooperative bargaining game, then, with a simple initial contract, an efficient equilibrium will generally exist. The contract is robust in the sense that it does not depend on fine details of the model. The contract gives authority to one party to set the terms of trade and gives the other party a nonexpiring option to trade at these terms. The difference from standard results arises because the initial contract ensures that the renegotiation game has multiple equilibria; the multiplicity of continuation equilibria can be used to enforce efficient investment.

We show that, in repeated common interest games without discounting, strong ‘perturbation implies efficiency’ results require that the perturbations must include strategies that are ‘draconian’ in the sense that they are prepared to punish to the maximum extent possible. Moreover, there is a draconian strategy whose presence in the perturbations guarantees that any equilibrium is efficient. We also argue that the results of Anderlini and Sabourian (1995) using perturbation strategies that are cooperative (and hence nondraconian) are not due to computability per se but to the further restrictions they impose on allowable beliefs.

The authors consider a repeated game between two long-run players, one of whom is relatively patient. Each player has a small amount of uncertainty about the other's strategy. Given a weak assumption about the support of this uncertainty, the more patient player obtains (in any Nash equilibrium) approximately the highest payoff consistent with the individual rationality of the other player, if the latter is patient enough. If the less patient player is relatively impatient, any Nash equilibrium gives the more patient player at least the Stackelberg payoff: this generalizes K. M. Schmidt's (1993) result, which applies only to games of conflicting interests.