[Paper Review] Prospect Theory for Enhanced Cyber-Physical Security of Drone Delivery Systems: A Network Interdiction Game

Anibal Sanjab, Walid Saad+1 more|arXiv (Cornell University)|Feb 11, 2017

Infrastructure Resilience and Vulnerability Analysis10 references4 citations

TL;DR

This paper proposes a zero-sum network interdiction game between a drone delivery vendor and an attacker, modeling cyber-physical security using prospect theory to capture subjective perceptions of risk and delivery time relative to a target. It shows that subjective decision-making leads to riskier path choices, increasing expected delivery time beyond the target, even surpassing the Nash equilibrium under classical game theory.

ABSTRACT

The use of unmanned aerial vehicles (UAVs) as delivery systems of online goods is rapidly becoming a global norm, as corroborated by Amazon's "Prime Air" and Google's "Project Wing" projects. However, the real-world deployment of such drone delivery systems faces many cyber-physical security challenges. In this paper, a novel mathematical framework for analyzing and enhancing the security of drone delivery systems is introduced. In this regard, a zero-sum network interdiction game is formulated between a vendor, operating a drone delivery system, and a malicious attacker. In this game, the vendor seeks to find the optimal path that its UAV should follow, to deliver a purchase from the vendor's warehouse to a customer location, to minimize the delivery time. Meanwhile, an attacker seeks to choose an optimal location to interdict the potential paths of the UAVs, so as to inflict cyber or physical damage to it, thus, maximizing its delivery time. First, the Nash equilibrium point of this game is characterized. Then, to capture the subjective behavior of both the vendor and attacker, new notions from prospect theory are incorporated into the game. These notions allow capturing the vendor's and attacker's i) subjective perception of attack success probabilities, and ii) their disparate subjective valuations of the achieved delivery times relative to a certain target delivery time. Simulation results have shown that the subjective decision making of the vendor and attacker leads to adopting risky path selection strategies which inflict delays to the delivery, thus, yielding unexpected delivery times which surpass the target delivery time set by the vendor.

Motivation & Objective

• To address the lack of comprehensive cyber-physical security analysis in drone delivery systems, especially against interdiction attacks.
• To model the strategic interaction between a drone vendor (evader) and an attacker (interdictor) as a zero-sum network interdiction game.
• To incorporate prospect theory into the game to capture subjective perceptions of attack probability and delivery time relative to a target.
• To analyze how bounded rationality and loss aversion affect path selection and expected delivery time.
• To demonstrate that subjective behavior leads to longer delivery times than predicted by classical game theory.

Proposed method

• Formulate a zero-sum network interdiction game where the vendor selects a path to minimize expected delivery time, and the attacker chooses nodes to interdict and maximize delay.
• Prove that the Nash equilibrium of the game can be computed via two linear programming problems, with the value function yielding the expected delivery time under equilibrium strategies.
• Integrate prospect theory by introducing a probability weighting function and a value function that distorts objective probabilities and delivery time outcomes based on a reference point (e.g., target delivery time).
• Model the vendor’s and attacker’s subjective valuations using a loss-averse utility function with parameters for risk sensitivity and loss aversion.
• Use the rationality parameter γ to control the degree of probability weighting, with lower γ indicating higher distortion of probabilities.
• Simulate the game under different values of γ and loss aversion parameter λU to evaluate the impact on path selection and expected delivery time.

Experimental results

Research questions

• RQ1 How does incorporating prospect theory into a network interdiction game affect path selection and expected delivery time in drone delivery systems?
• RQ2 To what extent does subjective perception of attack success probability distort optimal path strategies compared to classical game theory?
• RQ3 How does loss aversion in the vendor’s decision-making influence the choice of path and resulting delivery time?
• RQ4 What is the impact of varying rationality (γ) on the expected delivery time and attacker’s interdiction strategy?
• RQ5 Does subjective decision-making lead to delivery times that exceed the target delivery time, even when the target is known?

Key findings

• Lower rationality (γ = 0.1) leads to a 11% increase in expected delivery time compared to higher rationality (γ = 0.9), due to distorted probability weighting.
• When γ = 0.1, the vendor perceives all nodes as equally risky and selects the shortest path with 94% probability, despite high attack probability at key nodes.
• Under prospect theory, the attacker shifts focus to nodes 5 and 8—critical to the shortest path—rather than the most probable attack nodes, altering interdiction strategy significantly.
• Increased loss aversion (λU) leads the vendor to favor the shortest path more strongly, increasing its selection probability from 51% to 81% as λU rises from 1 to 10.
• The expected delivery time under prospect theory exceeds both the classical game theory equilibrium and the target delivery time (T⁰ = 30), indicating that subjective behavior can degrade system performance.
• The results demonstrate that bounded rationality and subjective risk perception can cause delivery delays beyond the vendor’s target, especially in time-critical applications like medical delivery.