Abstract
In this paper, we present a new Generalized Nash Equilibrium (GNE) model for post-disaster humanitarian relief by introducing novel financial funding functions and altruism functions, and by also capturing competition on the logistics side among humanitarian organizations. The common, that is, the shared, constraints associated with the relief item deliveries at points of need are imposed by an upper level humanitarian organization or regulatory body and consist of lower and upper bounds to ensure the effective delivery of the estimated volumes of supplies to the victims of the disaster. We identify the network structure of the problem, with logistical and financial flows, and propose a variational equilibrium framework, which allows us to then formulate, analyze, and solve the model using the theory of variational inequalities (rather than quasivariational inequality theory). We then utilize Lagrange analysis and investigate qualitatively the humanitarian organizations’ marginal utilities if and when the equilibrium relief item flows are (or are not) at the imposed demand point bounds. We illustrate the game theory model through a case study focused on tornadoes hitting western Massachusetts, a highly unusual event that occurred in 2011. This work significantly extends the original model of Nagurney (Dynamics of Disasters: Key Concepts, Models, Algorithms, and Insights. Springer International Publishing, Switzerland, 2016), which, under the imposed assumptions therein, allowed for an optimization formulation, and adds to the literature of game theory and disaster relief, which is nascent.
Presented at the 3rd International Conference on Dynamics of Disasters Kalamata, Greece, July 5–9, 2017.
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Acknowledgements
This paper is dedicated to the memory of Professor Martin J. Beckmann, Professor Emeritus at Brown University, who passed away on April 11, 2017 at the age of 92. He was a renowned scholar in transportation science, regional science, and operations research, and his work on network equilibria has had a profound impact on both theory and practice.
The first author acknowledges support from the Radcliffe Institute for Advanced Study at Harvard University where she was a 2017 Summer Fellow. The second author acknowledges support from the project PON SCN_00451 CLARA—CLoud plAtform and smart underground imaging for natural Risk Assessment, Smart Cities and Communities and Social Innovation.
The authors acknowledge the co-organizers of the 3rd Dynamics of Disasters conference as well as the participants for a stimulating conference and discussions. They also thank the anonymous reviewer for helpful comments and suggestions on an earlier version of this paper.
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Nagurney, A., Daniele, P., Flores, E.A., Caruso, V. (2018). A Variational Equilibrium Network Framework for Humanitarian Organizations in Disaster Relief: Effective Product Delivery Under Competition for Financial Funds. In: Kotsireas, I., Nagurney, A., Pardalos, P. (eds) Dynamics of Disasters. DOD 2017. Springer Optimization and Its Applications, vol 140. Springer, Cham. https://doi.org/10.1007/978-3-319-97442-2_6
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