The Cost of Differential Privacy in Linear-Quadratic Dynamic Games
Abstract
Multi-agent coordination often requires strategic agents to share sensitive information about their states or objectives, creating a tension between performance and privacy. Our paper studies this tradeoff in stochastic linear-quadratic (LQ) dynamic games with heterogeneous agent objectives. In our framework, agents share noise-perturbed state and reference information with a cloud computer that computes feedback Nash equilibrium strategies, with the injected noise calibrated to provide differential privacy. We derive an analytical expression for each agent's infinite-horizon steady-state cost of privacy relative to the non-private game. Then, we prove that when agents' objectives are sufficiently aligned, the injection of privacy noise necessarily incurs a positive performance cost. In contrast, we characterize a class of games with sufficiently misaligned objectives across agents for which an agent's cost of privacy can be strictly negative. Thus, counterintuitively, noise can simultaneously protect privacy and improve the equilibrium performance of an agent when the objectives of interacting agents are sufficiently misaligned. Finally, we present numerical experiments which corroborate our theoretical contributions.
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BibTeX
@misc{chiu2026cost,
title = {{The Cost of Differential Privacy in Linear-Quadratic Dynamic Games}},
author = {Chih-Yuan Chiu and Matthew Hale},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07238},
eprint = {2610.07238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07238},
}
RIS
TY - UNPB
TI - The Cost of Differential Privacy in Linear-Quadratic Dynamic Games
AU - Chih-Yuan Chiu
AU - Matthew Hale
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07238
UR - https://arxiv.org/abs/2610.07238
AB - Multi-agent coordination often requires strategic agents to share sensitive information about their states or objectives, creating a tension between performance and privacy. Our paper studies this tradeoff in stochastic linear-quadratic (LQ) dynamic games with heterogeneous agent objectives. In our framework, agents share noise-perturbed state and reference information with a cloud computer that computes feedback Nash equilibrium strategies, with the injected noise calibrated to provide differential privacy. We derive an analytical expression for each agent's infinite-horizon steady-state cost of privacy relative to the non-private game. Then, we prove that when agents' objectives are sufficiently aligned, the injection of privacy noise necessarily incurs a positive performance cost. In contrast, we characterize a class of games with sufficiently misaligned objectives across agents for which an agent's cost of privacy can be strictly negative. Thus, counterintuitively, noise can simultaneously protect privacy and improve the equilibrium performance of an agent when the objectives of interacting agents are sufficiently misaligned. Finally, we present numerical experiments which corroborate our theoretical contributions.
ER -