Game-Theoretic Drone Swarm Defense: A Case Study in Applied Differential Game Theory

Ross E. Allen

cs.GTSep 3, 2026

Game-Theoretic Drone Swarm Defense: A Case Study in Applied Differential Game Theory

Authors: Ross E. Allen

Organizations: MIT Lincoln Laboratory

Abstract

This technical report is a study of the use of differential game (DG) theory to solve the target-assignment and midcourse guidance problems of drone swarms tasked with intercepting opposing swarms in defense of high-value assets. The game-theoretic tactics---which treat the intruder swarm as a rational agent and seek a Nash equilibrium between defenders and intruders---are compared against baseline tactics that model the defense problem as a unilateral optimization of the defenders' maneuvers. Monte Carlo simulation and Bayesian analysis show that the game-theoretic approach has a higher probability of successfully intercepting all intruders than the baseline techniques. This improvement in successful defense probability is most pronounced when the intruder swarm is capable of evasive maneuvers: relative to baseline optimization tactics, differential-game tactics increase estimated defense success from 94.6% to 96.8%, closing approximately 41% of the remaining gap to perfect defense. To add statistical credibility to this result, a paired-trial Bayesian analysis assigns a 99.9% posterior probability that differential-game tactics have a higher probability of successful asset defense than baseline tactics in this scenario.

Figures & tables

Panel of Figure 1 — Figure 1: Conceptual drone swarm defense problem posed as a many-agent Lady-Bandit-Guard problem [ 7 ] . The guard drone $G_{i}$ , which is one of a large set of guard drones, attempts to intercept a particular bandit drone $B_{j}$ before it reaches a high-value asset $L_{\ell}$ , while considering the trade-offs of potentially pursuing different bandits.

Panel of Figure 2 — Figure 2: High-level control flow for guard/defender tactics.

Category	Parameter	Value or sampling range	Scenario
Campaign	Integration time step, maximum steps	$1~\mathrm{s}$ , $500$ ( $500~\mathrm{s}$ maximum duration)	B1, B2
Team size	Assets $N_{L}$	$\operatorname{UnifInt}\{4,\ldots,8\}$	B1, B2
	Bandits $N_{B}$	$\operatorname{UnifInt}\{8,\ldots,12\}$	B1, B2
	Guards $N_{G}$	$\operatorname{UnifInt}\{\max(10,N_{B}),\ldots,16\}$	B1, B2
Vehicle	Guard speed	$[70,80]~\mathrm{m/s}$	B1, B2
	Bandit speed	$[45,55]~\mathrm{m/s}$	B1, B2

Table 1: Monte Carlo trial parameters for non-evasive (B1) and evasive (B2) bandit scenarios. Parameters marked with ∗ apply only to the B2 evasive-bandit scenario.

Metric	Per-trial observation	Bayesian model and prior	Posterior quantities reported
defense-success	$Y_{\mathrm{sd}}\in\{0,1\}$ , equal to one only if no asset is reached and every bandit is intercepted; zero otherwise	Bernoulli likelihood with $\theta_{\mathrm{sd}}\sim\mathrm{Beta}(1,1)$	$\mathbb{E}[\theta_{\mathrm{sd}}\mid D]$ and its $95\%$ credible interval estimated from $100{,}000$ posterior samples; higher is better
HVAs-reached	$S_{\mathrm{lr}}\in[0,1]$ , the fraction of assets reached in one trial	One hundred equal-width bins on $[0,1]$ ; multinomial likelihood with symmetric $\mathrm{Dirichlet}(1/K,\ldots,1/K)$ prior for $K=100$ bins (total concentration one)	$\mathbb{E}[\mu_{\mathrm{lr}}\mid D]$ and its $95\%$ credible interval estimated from $100{,}000$ posterior samples; lower is better
Bandits intercepted	$S_{\mathrm{bi}}\in[0,1]$ , the fraction of bandits intercepted in one trial	One hundred equal-width bins on $[0,1]$ ; multinomial likelihood with symmetric $\mathrm{Dirichlet}(1/K,\ldots,1/K)$ prior for $K=100$ bins (total concentration one)	$\mathbb{E}[\mu_{\mathrm{bi}}\mid D]$ and its $95\%$ credible interval estimated from $100{,}000$ posterior samples; higher is better
mean-control-saturation	$S_{\mathrm{sat}}\in[0,1]$ , the mean across guards of the fraction of recorded active control steps on which the requested action is clipped	One hundred equal-width bins on $[0,1]$ ; multinomial likelihood with symmetric $\mathrm{Dirichlet}(1/K,\ldots,1/K)$ prior for $K=100$ bins (total concentration one)	$\mathbb{E}[\mu_{\mathrm{sat}}\mid D]$ and its $95\%$ credible interval estimated from $100{,}000$ posterior samples; lower is better

Table 2: Per-trial performance metrics and Bayesian analyses. The reported posterior intervals are central

95\%

credible intervals.

Guard tactic	Defense success $\mathbb{E}[\theta_{\mathrm{sd}}\mid D]$	HVAs reached $\mathbb{E}[\mu_{\mathrm{lr}}\mid D]$	Bandits intercepted $\mathbb{E}[\mu_{\mathrm{bi}}\mid D]$	Control saturation $\mathbb{E}[\mu_{\mathrm{sat}}\mid D]$
Nearest-bandit (NB)	0.157 $[0.135,0.180]$	0.182 $[0.172,0.194]$	0.828 $[0.821,0.835]$	0.007 $[0.007,0.009]$
Coverage-aware (CA)	0.958 $[0.939,0.974]$	0.013 $[0.010,0.018]$	0.990 $[0.987,0.992]$	0.008 $[0.007,0.011]$
Differential-game (DG)	0.966 $\mathbf{[0.949,0.980]}$	0.011 $[0.008,0.016]$	0.991 $[0.988,0.993]$	0.006 $[0.005,0.009]$

Table 3: Bayesian performance summary for non-evasive bandit tactics . Each entry gives the posterior mean and central

95\%

credible interval (in brackets). The nearest-bandit baseline uses 1,000 Monte Carlo trials; the coverage-aware baseline and differential-game tactics each use 500. Posterior summaries use 100,000 samples.

Guard tactic	Defense success $\mathbb{E}[\theta_{\mathrm{sd}}\mid D]$	HVAs reached $\mathbb{E}[\mu_{\mathrm{lr}}\mid D]$	Bandits intercepted $\mathbb{E}[\mu_{\mathrm{bi}}\mid D]$	Control saturation $\mathbb{E}[\mu_{\mathrm{sat}}\mid D]$
Nearest-bandit (NB)	0.146 $[0.125,0.168]$	0.192 $[0.181,0.203]$	0.802 $[0.794,0.810]$	0.009 $[0.008,0.010]$
Coverage-aware (CA)	0.946 $[0.925,0.964]$	0.015 $[0.011,0.019]$	0.990 $[0.986,0.992]$	0.009 $[0.008,0.013]$
Differential-game (DG)	0.968 $\mathbf{[0.951,0.982]}$	0.011 $[0.009,0.016]$	0.991 $[0.988,0.993]$	0.006 $[0.005,0.009]$

Table 4: Bayesian performance summary for evasive bandit tactics . Each entry gives the posterior mean and central

95\%

Panel of Figure 3 — Figure 3: Median evasive-bandit (B2) episode selected independently for each tactic by HVA-reached percentage: (a) nearest-bandit baseline (0.167), (b) coverage-aware baseline (0.000), and (c) differential-game tactics (0.000).

Panel of Figure 4 — Figure 4: Worst observed evasive-bandit (B2) episode selected independently for each tactic by HVA-reached percentage: (a) nearest-bandit baseline (0.800), (b) coverage-aware baseline (0.250), and (c) differential-game tactics (0.250).

Game Theory

Game theory studies how interacting decision-makers choose strategies, form agreements, and shape outcomes under competition and cooperation.

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Unmanned Aerial Vehicles (UAVs) are valuable for mission-critical systems like surveillance, rescue, or delivery. Not surprisingly, such systems attract cyberattacks, including Denial-of-Service (DoS) attacks to overwhelm the resources of mission drones (MDs). How can we defend UAV mission systems against DoS attacks? We adopt cyber deception as a defense strategy, in which honey drones (HDs) are proposed to bait and divert attacks. The attack and deceptive defense hinge upon radio signal strength: The attacker selects victim MDs based on their signals, and HDs attract the attacker from afar by emitting stronger signals, despite this reducing battery life. We formulate an optimization problem for the attacker and defender to identify their respective strategies for maximizing mission performance while minimizing energy consumption. To address this problem, we propose a novel approach, called HT-DRL. HT-DRL identifies optimal solutions without a long learning convergence time by taking the solutions of hypergame theory into the neural network of deep reinforcement learning. This achieves a systematic way to intelligently deceive attackers. We analyze the performance of diverse defense mechanisms under different attack strategies. Further, the HT-DRL-based HD approach outperforms existing non-HD counterparts up to two times better in mission performance while incurring low energy consumption.

Abstract

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