COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1888 Relational Contracting, Repeated Negotiations, and Hold-Up Sebastian Kranz February 2013 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. |
