Cost allocation in a robust two-stage resource allocation game: Fairness and robustness

This paper considers a two-stage resource allocation game within a cooperative game framework from a platform perspective, where the customers’ demands are uncertain. To incentivize all customers (players) into the grand coalition for joint cost sharing in resource allocation, a critical issue for the platform is determining a fair and robust cost allocation solution. To address the challenge, we introduce the concept of the strict robust core to the operations research (OR) game with constraints and propose the Two-stage Resource Allocation-Robust Cost Sharing Problem (TRA-RCSP). Our approach integrates distributionally robust optimization (DRO) and distributionally favorable optimization (DFO) to improve computational tractability. By leveraging the polyhedral ambiguity set to model demand uncertainty, we calculate the worst-case cost for grand coalition and the best-case costs for subcoalitions. Additionally, we develop an iterative constraint generation algorithm to mitigate the exponential growth of constraints in TRA-RCSP. Numerical experiments demonstrate that our algorithm achieves excellent computational efficiency and the strict robust core significantly outperforms the cost allocation of SAA model across both robustness performance metrics, ensuring the formation of the grand cooperation and its long-term stability under uncertain demands.