I study alternating-offer bargaining games with two-sided incomplete information about the players' discount rates. For both perfect Bayesian equilibrium and a rationalizability-style notion, I characterize the set of expected payoffs which may arise in the game. I also construct bounds on agreements that may be made. The set of expected payoffs is easy to compute and incorporate into applied models. My main result is a full characterization of the set of perfect Bayesian equilibrium payoffs for games in which the distribution over the players' discount rates is of wide support, yet is in a weak sense close to a point mass distribution. I prove a lopsided convergence result: each player cannot gain from a slight chance that she is a strong type, but the player can suffer greatly if there is a slight chance that she is a weak type.

This paper develops a model of private bilateral contracting, in which an exogenous network determines the pairs of players who can communicate and contract with each other. After contracting, the players interact in an underlying game with globally verifiable productive actions and externally enforced transfers. The paper investigates whether such decentralized contracting can internalize externalities that arise due to parties being unable to contract directly with others whose productive actions affect their payoffs. The contract‐formation protocol, called the “contracting institution,” is treated as a design element. The main result is positive: There is a contracting institution that supports efficient equilibria for any underlying game and connected network. A critical property is that the institution allows for sequential contract formation or revision. The equilibrium construction features assurance contracts and cancellation penalties .

This paper develops a theoretical framework for studying contract and enforcement in settings with nondurable trading opportunities and complete but unverifiable information. The framework explicitly accounts for the parties' individual trade actions. The sets of implementable state-contingent payoffs, under various assumptions about renegotiation opportunities, are characterized and compared. The results indicate the benefit of modeling trade actions as individual, rather than as public, and they highlight the usefulness of a structured game-theoretic framework for applied research.

THE ECONOMIC LITERATURE concerning agents' reputations has grown steadily since the seminal work of Kreps, Milgrom, Roberts, and Wilson.2Early work focused on how incomplete information leads to equilibria that are vastly different (but more intuitive) than those possible in the complete information game.Recently, however, game theorists have been studying how incomplete information might refine the set of equilibria.3One important class of games is that in which a single long-run agent plays a simultaneous move (stage) game with a sequence of opponents, each of whom plays only once, yet observes all previous play.Fudenberg and Levine (1989) study the reputation of the long-run player in this type of game.They argue that the "'most reasonable' equilibrium is the one which the long-run player most prefers."Their intuition is sustained when one perturbs the game with the "Stackelberg strategy."Fudenberg and Levine show that in the perturbed game the equilibrium payoffs of the long-run player are bounded below by a number that converges to the "Stackelberg payoff."Fudenberg and Levine (and the others who have developed reputation models) take the notion of Nash equilibrium as fundamental in the analysis.However, it would seem as though our intuition about reputations relies little on equilibrium concepts.This leads to two questions.First, can meaningful reputations develop apart from equilibria?Second, if so, under what circumstances can reputations develop?As I will demonstrate, equilibrium concepts are not required in order for players to establish significant reputations.I study (following Fudenberg and Levine (1989)) games in which a long-run player faces a sequence of short-run opponents.Like Fudenberg and Levine, I consider perturbations of the game involving the Stackelberg strategy.However, whereas they focus on equilibria, I will only require that players "best-respond" to their beliefs.Whenever the conjectures of the short-run players are "generally comparable" (e.g.contained in a compact set), I obtain the same refinement as do Fudenberg and Levine, but without an equilibrium assumption.What is important for reputations is that the beliefs of the short-run agents not be too dispersed in a sense to be made precise.Players can thus establish meaningful reputations from within the loose confines of individual rationality.This paper borrows heavily from the work of Fudenberg and Levine (1989).In fact, their statistical result (their Lemma 1), which establishes the potential gain of building a reputation, requires no notion of equilibrium.It does require that the short-run agents hold the same belief, which is implied by equilibrium.I simply invoke their lemma in a more general setting (in which short-run players may hold different beliefs) and study the type of beliefs which allow it to refine the set of rational outcomes.Note that a similar style of research has been followed on another front as well.Cho (1991) extends the Coase conjecture to a nonequilibrium setting.Cho's work is similar to mine in that we both take as fundamental a rationalizability notion.Our analyses require additional restrictions, however, and it is the nature of these restrictions in which our 11 am grateful to David Kreps, Marco LiCalzi, two referees, and the editor for comments.This is Chapter 2 of my Ph.D.

CONSIDER A REPEATED GAME with incomplete information in which a patient long run player, whose type is unknown, faces a sequence of short run opponents (as in Fudenberg and Levine (1989)). The standard result is that the patient long run player can obtain an average long payoff almost equal to the payoff of the stage game by consistently playing as a leader. In the analysis, one generally takes as fundamental an assumption that the players have common prior beliefs on the states of the world and that behavior is consistent with the concept of Bayesian Nash equilibrium. However, these related suppositions have been called into question as unrealistic and too stringent (cf. Gul (1991)). In many games of incomplete information a player's prior probabilities on types (or states of the world) are best regarded as purely subjective psychological parameters, unknown to the modeler and to this player's opponents. Therefore, it is important to understand whether the standard reputation results (among others) are implied by weaker assumptions on the knowledge and behavior of the players. In fact, as Watson (1993) demonstrates, the reputation result does not require equilibrium. It is implied by a weak notion of rationalizability with some restrictions on the beliefs of the players. Here we qualify Watson's (1993) study and extend the line of inquiry of Watson (1993) and Battigalli (1994) concerning settings in which reputations are effective. As Watson shows, two main conditions on the beliefs of the players, along with weak rationalizability, imply the reputation result. First, there must be a strictly positive and uniform lower bound on the subjective probability that players assign to the Stackelberg type. Second, the conditional beliefs of the short run players must not be too dispersed. Watson (1993) does not explicitly indicate on what the updated beliefs of the short run players are conditioned. We make this explicit and show that it is necessary to assume that the conditional beliefs of the short run players satisfy a stochastic independence property (cf. Battigalli (1996)). We also comment on the dispensability of equilibrium regarding the reputation result in games with two long run players.

This paper proposes a new approach to equilibrium selection in repeated games with transfers, supposing that in each period the players bargain over how to play. Although the bargaining phase is cheap talk (following a generalized alternating-offer protocol), sharp predictions arise from three axioms. Two axioms allow the players to meaningfully discuss whether to deviate from their plan; the third embodies a “theory of disagreement”—that play under disagreement should not vary with the manner in which bargaining broke down. Equilibria that satisfy these axioms exist for all discount factors and are simple to construct; all equilibria generate the same welfare. Optimal play under agreement generally requires suboptimal play under disagreement. Whether patient players attain efficiency depends on both the stage game and the bargaining protocol. The theory extends naturally to games with imperfect public monitoring and heterogeneous discount factors, and yields new insights into classic relational contracting questions.

This paper considers propagation of aggregate shocks in a dynamic general-equilibrium model with labor-market matching and endogenous job destruction. Cyclical fluctuations in the job-destruction rate magnify the output effects of shocks, as well as making them much more persistent. Interactions between capital adjustment and the job-destruction rate play an important role in generating persistence. Propagation effects are shown to be quantitatively substantial when the model is calibrated using job-flow data. Incorporating costly capital adjustment leads to significantly greater propagation.

We study relational contracting and renegotiation in environments with external enforcement of long-term contractual arrangements. A long-term contract governs the stage games that the contracting parties will play in the future (depending on verifiable stage-game outcomes) until they renegotiate. In a contractual equilibrium, the parties choose their individual actions rationally, jointly optimize when selecting a contract, and exercise their relative bargaining power. Our main result is that in a wide variety of settings, the optimal contract is semi-stationary, with stationary terms for all future periods but special terms for the current period. In each period the parties renegotiate to this same contract. For example, in a simple principal-agent model with a choice of costly monitoring technology, the optimal contract specifies mild monitoring for the current period but intense monitoring for future periods. Because the parties renegotiate in each new period, intense monitoring arises only off the equilibrium path after a failed renegotiation.