Computing Nash Equilibria in Potential Games with Private Uncoupled Constraints

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.

Authors

• Nikolas Patris University of California, Irvine Archimedes/Athena RC
• Stelios Stavroulakis University of California, Irvine
• Fivos Kalogiannis University of California, Irvine Archimedes Research Unit
• Rose Zhang University of California, Irvine
• Ioannis Panageas University of California, Irvine

Keywords

• GTEP: Cooperative Game Theory
• GTEP: Coordination and Collaboration
• MAS: Coordination and Collaboration
• MAS: Distributed Problem Solving
• MAS: Multiagent Learning