A Game-Theoretic Framework for Incentive-Compatible AI training Under Renewable-Energy Constraints

As artificial intelligence systems increasingly rely on distributed and collaborative training, the energy footprint of these processes becomes a shared responsibility. Modern AI training often unfolds across heterogeneous compute nodes-ranging from cloud clusters to edge devices-whose energy availability is spatially and temporally variable. At the same time, renewable energy grids experience growing levels of excess generation, creating opportunities to align computational workloads with low-carbon energy supply. In this work, we develop a game-theoretic model of carbon-aware AI training in which autonomous agents strategically choose whether to participate and how intensively to train under limited renewable energy availability. Each agent balances diminishing learning returns, rewards for remaining within green-energy budgets, and penalties for grid consumption. While our framework applies broadly to distributed AI training, we examine Federated Learning as a representative case study due to its decentralized structure and flexible scheduling. We analyze equilibrium existence, efficiency, and adaptive dynamics, and provide simulation evidence that appropriately designed incentives can eliminate grid-based energy usage while preserving model performance. Our findings demonstrate how incentive-compatible training mechanisms can enhance energy efficiency and sharply reduce carbon emissions under renewable-energy constraints.