🤖 AI Summary
This paper addresses the fair allocation challenge in multi-stakeholder horizontal collaboration for forestry transportation, specifically focusing on a linear production-distribution game integrated with market demand.
Method: Departing from conventional cooperative game models based solely on individual costs, we introduce firms’ market shares—i.e., customer demand—as a key component of the coalition value function, yielding a novel, practice-grounded collaborative game model. We prove this model is a special case of the Shapley–Shubik market game and possesses a nonempty core. Algorithmically, we propose the first polynomial-time separation algorithm and a fast primal-dual algorithm tailored to this model.
Contribution/Results: Our methods enable exact and efficient computation of both the nucleolus and the Shapley value. The resulting allocation mechanism is provably fair, computationally tractable, and implementable—providing a rigorous foundation for equitable resource sharing in forestry logistics.
📝 Abstract
. 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 non-trivial 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.
