Relational Contracting, Repeated Negotiations, and Hold-Up

We propose a unified framework to study relational contracting and hold-up problems in infinite horizon stochastic games. We first illustrate that with respect to long run decisions, the common formulation of relational contracts as Pareto-optimal public perfect equilibria is in stark contrast to fundamental assumptions of hold-up models. We develop a model in which relational contracts are repeatedly newly negotiated during relationships. Negotiations take place with positive probability and cause bygones to be bygones. Traditional relational contracting and hold-up formulations are nested as opposite corner cases. Allowing for intermediate cases yields very intuitive results and sheds light on many plausible trade-offs that do not arise in these corner cases. We establish a general existence result and a tractable characterization for stochastic games in which money can be transferred. This paper formulates a theory of relational contracting in dynamic games. A crucial feature is that existing relational contracts can depreciate and ensuing negotiations then treat previous informal agreements as bygones. The model nests the traditional formulation of relational contracts as Pareto-optimal equilibria as a special case. In repeated games both formulations are always mathematically equivalent. We provide ample illustrations that in dynamic games the traditional formulation is restrictive in so far that it rules out by assumption many plausible hold-up problems -- even for small discount factors. Our model provides a framework that naturally unifies the analysis of relational contracting and hold-up problems.