A Stochastic Disaster Relief Game Theory Network Model

Abstract

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.