Computing Nash Equilibria in Potential Games with Private Uncoupled Constraints
Nikolas Patris, Stelios Stavroulakis, Fivos Kalogiannis, Rose Zhang, Ioannis Panageas
Abstract
We consider the problem of computing Nash equilibria in potential games where each player's strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network congestion games where individual drivers adhere to personal budget and fuel limitations. Despite the plethora of algorithms that efficiently compute Nash equilibria (NE) in potential games, the domain of constrained potential games remains largely unexplored. We introduce an algorithm that leverages the Lagrangian formulation of NE. The algorithm is implemented independently by each player and runs in polynomial time with respect to the approximation error, the sum of the size of the action-spaces, and the game's inherit parameters.
BibTeX
@article{Patris_Stavroulakis_Kalogiannis_Zhang_Panageas_2024, title={Computing Nash Equilibria in Potential Games with Private Uncoupled Constraints}, volume={38}, url={https://ojs.aaai.org/index.php/AAAI/article/view/28848}, DOI={10.1609/aaai.v38i9.28848}, abstractNote={We consider the problem of computing Nash equilibria in potential games where each player’s strategy set is subject to private uncoupled constraints. This scenario is frequently encountered in real-world applications like road network congestion games where individual drivers adhere to personal budget and fuel limitations. Despite the plethora of algorithms that efficiently compute Nash equilibria (NE) in potential games, the domain of constrained potential games remains largely unexplored. We introduce an algorithm that leverages the Lagrangian formulation of NE. The algorithm is implemented independently by each player and runs in polynomial time with respect to the approximation error, the sum of the size of the action-spaces, and the game’s inherit parameters.}, number={9}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Patris, Nikolas and Stavroulakis, Stelios and Kalogiannis, Fivos and Zhang, Rose and Panageas, Ioannis}, year={2024}, month={Mar.}, pages={9874-9882} }