Essays on Continuous-Time Bargaining

Abstract

This thesis studies bargaining games in continuous time. In chapter 1, I construct a continuous time model to study the problem of a durable good monopolist who lacks commitment power and whose marginal cost of production varies stochastically over time. Time-varying costs modify the results on the Coase conjecture. When the distribution of consumer valuations is discrete, the monopolist is able to exercise market power and the outcome is inefficient. In contrast, with a continuous distribution the monopolist is unable to extract additional surplus from buyers with higher valuations. Moreover, the outcome is efficient in this setting.

Chapter 2 introduces a new continuous time bargaining model to investigate bilateral negotiations in settings in which the relative bargaining power of the parties might change over time. The model has a unique equilibrium, in which players reach an immediate agreement. The players' payoffs are characterized by a system of ordinary differential equations. The equilibrium of the continuous time model corresponds to the limiting subgame perfect equilibrium of a discrete time bargaining game, when players can make offers arbitrarily frequently. The chapter also presents two applications of the baseline model featuring delays and inefficiencies.

Finally, chapter 3 studies legislative negotiations with supermajority requirements within the context of the continuous time bargaining model of chapter 2. The model has two key features. First, there is an exogenous diffusion process representing the parties' relative political strength, whose realization determines the identity of the party making proposals. Second, the party responding to offers incurs a concession cost c≥0 whenever it accepts a proposal put forward by its opponent. If c=0, the parties always come to an immediate agreement. On the other hand, if c>0 the equilibrium involves a delay region and an agreement region. When the diffusion process is in the delay region gridlock emerges, and policies are only implemented when this process reaches the agreement region. The model delivers positive implications concerning when legislative inaction is most likely to emerge.