Stochastic Real-Time Deception in Nash Equilibrium Seeking for Games with Quadratic Payoffs

Michael Tang, Miroslav Krstic, Jorge Poveda
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:635-646, 2025.

Abstract

In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system’s long term behavior, leading to outcomes that may be beneficial to the deceiver but detrimental to victim. We study this phenomenon for a class of model-free Nash equilibrium seeking (NES) where players implement independent stochastic exploration signals to learn the pseudogradient flow. In particular, we show that deceptive players who obtain real- time measurements of other players’ stochastic perturbation can incorporate this information into their own NES action update, consequentially steering the overall dynamics to a new operating point that could potentially improve the payoffs of the deceptive players. We consider games with quadratic payoff functions, as this restriction allows us to derive a more explicit formulation of the capabilities of the deceptive players. By leveraging results on multi-input stochastic averaging for dynamical systems, we establish local exponential (in probability) convergence for the proposed deceptive NES dynamics. To illustrate our results, we apply them to a two player quadratic game.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-tang25a, title = {Stochastic Real-Time Deception in Nash Equilibrium Seeking for Games with Quadratic Payoffs}, author = {Tang, Michael and Krstic, Miroslav and Poveda, Jorge}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {635--646}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/tang25a/tang25a.pdf}, url = {https://proceedings.mlr.press/v283/tang25a.html}, abstract = {In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system’s long term behavior, leading to outcomes that may be beneficial to the deceiver but detrimental to victim. We study this phenomenon for a class of model-free Nash equilibrium seeking (NES) where players implement independent stochastic exploration signals to learn the pseudogradient flow. In particular, we show that deceptive players who obtain real- time measurements of other players’ stochastic perturbation can incorporate this information into their own NES action update, consequentially steering the overall dynamics to a new operating point that could potentially improve the payoffs of the deceptive players. We consider games with quadratic payoff functions, as this restriction allows us to derive a more explicit formulation of the capabilities of the deceptive players. By leveraging results on multi-input stochastic averaging for dynamical systems, we establish local exponential (in probability) convergence for the proposed deceptive NES dynamics. To illustrate our results, we apply them to a two player quadratic game.} }
Endnote
%0 Conference Paper %T Stochastic Real-Time Deception in Nash Equilibrium Seeking for Games with Quadratic Payoffs %A Michael Tang %A Miroslav Krstic %A Jorge Poveda %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-tang25a %I PMLR %P 635--646 %U https://proceedings.mlr.press/v283/tang25a.html %V 283 %X In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system’s long term behavior, leading to outcomes that may be beneficial to the deceiver but detrimental to victim. We study this phenomenon for a class of model-free Nash equilibrium seeking (NES) where players implement independent stochastic exploration signals to learn the pseudogradient flow. In particular, we show that deceptive players who obtain real- time measurements of other players’ stochastic perturbation can incorporate this information into their own NES action update, consequentially steering the overall dynamics to a new operating point that could potentially improve the payoffs of the deceptive players. We consider games with quadratic payoff functions, as this restriction allows us to derive a more explicit formulation of the capabilities of the deceptive players. By leveraging results on multi-input stochastic averaging for dynamical systems, we establish local exponential (in probability) convergence for the proposed deceptive NES dynamics. To illustrate our results, we apply them to a two player quadratic game.
APA
Tang, M., Krstic, M. & Poveda, J.. (2025). Stochastic Real-Time Deception in Nash Equilibrium Seeking for Games with Quadratic Payoffs. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:635-646 Available from https://proceedings.mlr.press/v283/tang25a.html.

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