Subsidies in Interdependent Security With Heterogeneous Discount Rates

Abstract

Optimizing resource allocation in interdependent security problems is a serious challenge for homeland security. In this article, we present the equilibrium strategies for multiple interdependent defenders in a model where threats occur over time. We show that the existence of myopic agents can make it undesirable for non-myopic agents to invest in security when it would otherwise be in their interests to do so. The phenomena of tipping and cascading are discussed, and we explore how to target subsidies for security investment in order to achieve the best results from tipping. The above findings are illustrated in numerical examples, and their policy implications are discussed.

ACKNOWLEDGMENTS

This material is based upon work supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office under grant number DAAD19-01-1-0502, by the U.S. National Science Foundation under grant number DMI-0228204, and by the U.S. Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE) under grant number N00014-05-0630. Any opinions, findings, and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the sponsors. We also thank Larry Samuelson of the University of Wisconsin–Madison for his helpful comments and suggested references.

Notes

*The costs for subsidized agents are the same with P _i ( s _i , s _{− i} ) of investing agents subtracting the investment cost C.

*No equilibrium is possible with 1 ≤ M ≤ (N − Ñ)⁺.