A Douglas-Rachford splitting for semi-decentralized equilibrium seeking in generalized aggregative games
For researchers in game theory and distributed optimization, this provides a more efficient algorithm for equilibrium seeking in aggregative games with coupling constraints.
This paper proposes a semi-decentralized algorithm based on Douglas-Rachford splitting for finding generalized aggregative equilibria in games with affine coupling constraints, achieving faster convergence than forward-backward methods on a resource allocation example.
We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.