Incentives in Resource Allocation under Dynamic Demands

Every computer system -- from schedulers in public clouds (Amazon, Google, etc.) to computer networks to hypervisors to operating systems -- performs resource allocation across system users. The defacto allocation policy used in most of these systems, max-min fairness, guarantees desirable properties like incentive compatibility and Pareto efficiency, assuming user demands are time-independent. However, in modern real-world production systems, user demands are dynamic, i.e., vary over time. As a result, there is now a fundamental mismatch between the resource allocation goals of computer systems and the properties enabled by classic resource allocation policies. We consider a natural generalization of the classic algorithm for max-min fair allocation for the case of dynamic demands: this algorithm guarantees Pareto optimality, while ensuring that allocated resources are as max-min fair as possible up to any time instant, given the allocation in previous periods. While this dynamic allocation scheme remains Pareto optimal, it is not incentive compatible. We show that the possible increase in utility by misreporting demand is minimal and since this misreporting can lead to significant decrease in overall useful allocation, this suggests that it is not a useful strategy. Our main result is to show that when user demands are random variables, increasing the total amount of resource by a $(1+O(\epsilon))$ factor compared to the sum of expected instantaneous demands, makes the algorithm $(1+\epsilon)$-incentive compatible: no user can improve her allocation by a factor more than $(1+\epsilon)$ by misreporting demands, where $\epsilon\to 0$ as $n\to\infty$ and $n$ is the number of users. In the adversarial setting, we show that this algorithm is $3/2$-incentive compatible, which is nearly tight. We also generalize our results for the case of colluding users and multi-resource allocation.