In this paper, we introduce a new cooperative game theory model that we call
production-distribution game to address a major open problem for operations
research in forestry, raised by R\"onnqvist et al. in 2015, namely, that of
modelling and proposing efficient sharing principles for practical
collaboration in transportation in this sector. The originality of our model
lies in the fact that the value/strength of a player does not only depend on
the individual cost or benefit of the objects she owns but also depends on her
market shares (customers demand). We show however that the
production-distribution game is an interesting special case of a market game
introduced by Shapley and Shubik in 1969. As such it exhibits the nice property
of having a non-empty core. We then prove that we can compute both the
nucleolus and the Shapley value efficiently, in a nontrivial and interesting
special case. We in particular provide two different algorithms to compute the
nucleolus: a simple separation algorithm and a fast primal-dual algorithm. Our
results can be used to tackle more general versions of the problem and we
believe that our contribution paves the way towards solving the challenging
open problem herein