A Stackelberg Game Framework with Drainability Guardrails for Pricing and Scaling in Multi-Tenant GPU Cloud Platforms

TL;DR

This paper models pricing and scaling in multi-tenant GPU cloud platforms as a Stackelberg game, identifying a structural failure mode and proposing a guardrail to ensure stable operation and improve RL safety.

Contribution

It introduces a novel game-theoretic framework with explicit equilibrium analysis, a drainability guardrail, and an action shield to enhance robustness in dynamic GPU cloud management.

Findings

Identifies a residual demand floor causing undrainable backlog.

Proposes a drainability guardrail ensuring negative drift.

Demonstrates improved safety and robustness of RL policies.

Abstract

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.