Dynamic Linear Production Games under Uncertainty

In situations where uncertain costs are shared over time, static cooperative game-theoretic models and solution concepts like the core may prove inadequate. This holds in multi-period supply chain settings where inventories, capacities and resources must be managed over time in the presence of uncertainty. Motivated by these applications, we propose dynamic linear production games under uncertainty, generalizing classical linear production games to multiperiod models with stochastic parameters. We construct a dynamic cost allocation in the strong sequential core, the core’s natural extension to this setting. This allocation enjoys two additional appealing properties: First, it can be computed using only primal and dual optimal solutions, requiring no additional effort beyond the model’s optimization; second, each period’s allocation requires information only from itself and its immediate successor, and thus is amenable to on-line computation when special-purpose methods are available. We extend our result to infinite horizon models under mild additional assumptions.