A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917417845784576 |
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| author | Yan, Junji Yorulmaz, Asrin Efe Zhou, Hanchen Başar, Tamer |
| author_facet | Yan, Junji Yorulmaz, Asrin Efe Zhou, Hanchen Başar, Tamer |
| contents | Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity cost. In multi-tenant GPU cloud platforms, this trade-off is inherently dynamic because workload demand is endogenous; specifically, pricing shapes the submissions of heterogeneous tenants, which subsequently impact congestion and delay. We formulate the joint pricing-and-scaling problem as a large-population Stackelberg game problem, and we derive an explicit equilibrium demand map. The resulting closed-loop model reveals a structural failure mode in which delay-insensitive workloads sustain a residual demand floor, making the backlog undrainable under bounded price and service capacity. This observation motivates a computable drainability guardrail that certifies uniformly negative drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish a unique operating point and global convergence towards it under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer-agnostic action shield for the full dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16802 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms Yan, Junji Yorulmaz, Asrin Efe Zhou, Hanchen Başar, Tamer Computer Science and Game Theory Systems and Control Optimization and Control Modern Graphics Processing Unit (GPU)-backed services must satisfy strict latency service-level objectives (SLOs) while controlling spare-capacity cost. In multi-tenant GPU cloud platforms, this trade-off is inherently dynamic because workload demand is endogenous; specifically, pricing shapes the submissions of heterogeneous tenants, which subsequently impact congestion and delay. We formulate the joint pricing-and-scaling problem as a large-population Stackelberg game problem, and we derive an explicit equilibrium demand map. The resulting closed-loop model reveals a structural failure mode in which delay-insensitive workloads sustain a residual demand floor, making the backlog undrainable under bounded price and service capacity. This observation motivates a computable drainability guardrail that certifies uniformly negative drift in the residual-demand regime. For any fixed price-capacity pair satisfying the drainability guardrail, we establish a unique operating point and global convergence towards it under a checkable step-size condition. Building on this fixed-pair analysis, we further develop an optimizer-agnostic action shield for the full dynamic problem and show empirically that it improves safety and robustness for model-free reinforcement learning (RL) in this setting. |
| title | A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms |
| topic | Computer Science and Game Theory Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2604.16802 |