Optimal Pricing of Cloud Services: Committed Spend under Demand Uncertainty

TL;DR

This paper develops an optimal dynamic contract model for cloud services where buyers have uncertain demand and noisy signals, extending classic screening to multi-unit settings, and shows how practical contracts like two-part tariffs can implement the optimal mechanism.

Contribution

It introduces a novel nonlinear multi-unit screening framework for demand uncertainty and demonstrates practical contract forms that implement the optimal mechanism.

Findings

Optimal contracts provide discounts for higher signals with larger fixed payments.

Two-part tariffs and committed spend contracts can implement the optimal mechanism.

Extensions analyze effects of commitment costs and spot markets on contract design.

Abstract

We consider a seller who offers services to a buyer with multi-unit demand. Prior to the realization of demand, the buyer receives a noisy signal of their future demand, and the seller can design contracts based on the reported value of this signal. Thus, the buyer can contract with the service provider for an unknown level of future consumption, such as in the market for cloud computing resources or software services. We characterize the optimal dynamic contract, extending the classic sequential screening framework to a nonlinear and multi-unit setting. The optimal mechanism gives discounts to buyers who report higher signals, but in exchange they must provide larger fixed payments. We then describe how the optimal mechanism can be implemented by two common forms of contracts observed in practice, the two-part tariff and the committed spend contract. Finally, we use extensions of our base model to shed light on policy-focused questions, such as analyzing how the optimal contract changes when the buyer faces commitment costs, or when there are liquid spot markets.