Web platforms are reshaping resource allocation in distributed energy networks globally, from off-grid communities to lunar bases. Algorithmic decision-makers face the fundamental challenge of fairly distributing scarce resources among heterogeneous stakeholders. Traditional approaches assume complete rationality with perfect information and unlimited computation, yet distributed networks only permit local observation, requiring fairness to emerge from individual strategic interactions. Centralized optimization fails due to exponential complexity, rule-based methods cannot adapt to disruptions, and existing platforms translate economic inequality into energy access inequality. Recognizing the unattainability of complete rationality necessitates bounded rationality: pursuing provably convergent satisficing solutions under incomplete information and limited computation, translating natural language ethics into computable constraints, and designing incentives so self-interested behavior satisfies fairness at equilibrium. We propose a unified semantic-game-distributed framework. Large language models map ambiguous ethical principles into game-theoretic parameters through semantic parameterization, with contrastive learning ensuring semantic consistency and temporal stability. A two-layer Stackelberg game implements incentive design: the platform signals through differentiated pricing while nodes optimize locally, enabling fairness to emerge from equilibrium. Distributed asynchronous iteration achieves global convergence through local communication, with cognitive models adaptively adjusting step sizes and differential perturbation preserving privacy. Theoretical analysis establishes equilibrium existence and convergence guarantees, while extreme scenarios validate robustness under information scarcity and high uncertainty.