Dynamic Proportional Sharing: A Game-Theoretic Approach

Sharing computational resources amortizes cost and improves utilization and efficiency. When agents pool their resources, each becomes entitled to a portion of the shared pool. Static allocations in each round can guarantee entitlements and are strategy-proof, but efficiency suffers because allocations do not reflect variations in agents' demands for resources across rounds. Dynamic allocation mechanisms assign resources to agents across multiple rounds while guaranteeing agents their entitlements. Designing dynamic mechanisms is challenging, however, when agents are strategic and can benefit by misreporting their demands for resources. In this paper, we show that dynamic allocation mechanisms based on max-min fail to guarantee entitlements, strategy-proofness or both. We propose the flexible lending (FL) mechanism and show that it satisfies strategy-proofness and guarantees at least half of the utility from static allocations while providing an asymptotic efficiency guarantee. Our simulations with real and synthetic data show that the performance of the flexible lending mechanism is comparable to that of state-of-the-art mechanisms, providing agents with at least 0.98x, and on average 15x, of their utility from static allocations. Finally, we propose the T -period mechanism and prove that it satisfies strategy-proofness and guarantees entitlements for T łe 2.