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In this paper, we construct a novel game theory model for multiple humanitarian organizations engaged in disaster relief. Each organization is faced with a two-stage stochastic optimization problem associated with the purchase and storage of relief items pre-disaster, subject to a budget constraint, and, if need be, additional purchases and shipments post the disaster. The model integrates logistical and financial components, in that the humanitarian organizations compete for financial donations, as well as freight service provision, and each seeks to maximize its expected utility. The expected utility function of each humanitarian organization depends on its strategies and on those of the other organizations, and their feasible sets do, as well, since the organizations are subject to common lower and upper bound demand constraints. The governing concept is that of a stochastic generalized Nash equilibrium. We provide alternative variational inequality formulations of the model and propose an algorithmic scheme, which at each iteration yields closed form expressions for the product purchase/storage/shipment variables and the associated constraint Lagrange multipliers. Numerical examples illustrate the modeling and computational framework.

In this paper, we develop a unified variational inequality framework in the context of spatial price network equilibrium problems that handles multiple products with multiple demand and supply markets in multiple countries as well as multiple transportation routes. The model incorporates a plethora of distinct trade measures, which is particularly important in the pandemic, as PPEs and other essential products are in high demand, but short in supply globally. In the model, product flows as well as prices at the supply markets and the demand markets in different countries are variables that allows us to seamlessly introduce various trade measures, including tariffs, quotas, as well as price floors and ceilings. Qualitative properties are analyzed. Numerical examples are provided to illustrate the impacts of the trade measures on equilibrium product path and link flows, and on prices, and demand and supply quantities. Given the relevance of the trade measures in the world today and discussions concerning the impacts, the framework constructed in this paper is especially timely.