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About this paper
Lacra Pavel
A fully distributed algorithm is introduced to compute variational Generalized Nash Equilibria (GNE) in non-cooperative games featuring shared coupling constraints under partial-decision information. The approach, based on a doubly-augmented operator splitting method, ensures global convergence with fixed step-sizes, as verified through network Nash-Cournot game simulations.
Key insights
- Lifting the problem to a "doubly-augmented" space enables effective local management of primal (decision estimates) and dual (multiplier estimates) variables through neighbor-to-neighbor communication to achieve global consensus.
- The algorithm's global convergence with fixed step-sizes is established by demonstrating a weaker property, "restricted cocoercivity," for the pseudo-gradient-related operator, relaxing common assumptions in operator-splitting GNE methods.
- A carefully chosen preconditioning metric matrix within a forward-backward iteration allows for a rigorous convergence analysis using monotone operator theory, ensuring distributed computability of the resolvent.
Summary by alphaXiv.
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