Entropy-Regularized Mean-Field Games with Average-Reward Criterion: Span-Seminorm Contractions and Model-Free Learning
We study stationary discrete-time mean-field games with finite state and action spaces under the average-reward criterion, with an entropy-regularized objective and population-dependent dynamics and rewards. Under a minorization condition, the soft Q-operator is a span-seminorm contraction for the full transition kernel, so relative value iteration does not require the minorizing measure. When the Lipschitz constant of the kernel is below the minorization mass and the temperature exceeds an explicit threshold, the equilibrium fixed-point operator is a contraction: an equilibrium exists, its population distribution is unique, and a fixed-point iteration converges to it geometrically. We th...
| Authors | Gunes Akbas, Naci Saldi, Berkay Anahtarci et al. |
|---|---|
| Primary category | math.OC |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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