# Distributed generalized Nash equilibria computation of monotone games via a preconditioned proximal point algorithm

## TL;DR

This paper develops distributed algorithms for computing generalized Nash equilibria in monotone games with affine coupling constraints, leveraging a preconditioned proximal point framework and allowing inexact subgame solutions.

## Contribution

It introduces novel center-free distributed GNE algorithms for both equality and inequality constraints, based on a preconditioned proximal point approach, without requiring Lipschitz continuity.

## Key findings

- Algorithms converge under monotonicity assumptions.
- No need for inner-loop NE solving algorithms.
- Applicable to both equality and inequality coupling constraints.

## Abstract

In this paper, we investigate distributed generalized Nash equilibrium (GNE) computation of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of the coupling constraint, and can only communicate with its neighbours. We assume the game has monotone pseudo-subdifferential without Lipschitz continuity restrictions. We design novel center-free distributed GNE seeking algorithms for equality and inequality affine coupling constraints, respectively. A proximal alternating direction method of multipliers(ADMM) is proposed for the equality case, while for the inequality case, a parallel splitting type algorithm is proposed. In both algorithms, the GNE seeking task is decomposed into a sequential NE computation of regularized subgames and distributed update of multipliers and auxiliary variables, based on local data and local communication. Our two double-layer GNE algorithms need not specify the inner-loop NE seeking algorithm and moreover, only require that the strongly monotone subgames are inexactly solved. We prove their convergence by showing that the two algorithms can be seen as specific instances of preconditioned proximal point algorithms} (PPPA) for finding zeros of monotone operators. Applications and numerical simulations are given for illustration.