While the reader should refer to Cachon and Lariviere (2001) for the
details of the game, some definitions and concepts are needed to continue
this discussion.
The manufacturer’s private information, or type,
is her demand forecast.
There is a set of possible types that the manufacturer
could be and this set is known to the supplier, i.e., the supplier
is aware of the possible forecasts, but is not aware of the manufacturer’s
actual forecast.
Furthermore, at the start of the game the supplier
and the manufacturer know the probability distribution over the set of
types. We refer to this probability distribution as the supplier’s belief
regarding the types.
The manufacturer chooses her action first which
in this case is a contract offer and a forecast, the supplier updates his
belief regarding the manufacturer’s type given the observed action, and
then the supplier chooses his action which in this case is the amount of
capacity to build.