Abstract While the predominant pricing scheme for services is a set of long-term contracts stipulating a fixed fee for a level of usage, many service providers now offer flexible contracts. These contracts include flexibility in usage level and the option to opt out of the service in certain time periods. We study the effectiveness of flexible contracts in aligning the interests between the service provider and the customers in the presence of customers with different discrete demand distributions. This work develops a unified principal–agent framework to examine multiple versions of flexible contracts under ex post information asymmetry. We explore two types of contract variations. The first is aggregated versus differentiated contracts across an agent’s random demand values, the second is whether an agent may decline participation in a future time period after committing to a set of contract options. We find that the principal always prefers differentiation to aggregation, and under differentiation prefers to require participation at each time period. However, when demand variability is grouped together under aggregated contracts, we derive a sufficient condition for when is it more profitable to allow the agents the flexibility to opt out of participating in future time periods. Furthermore, the agents’ preference and the overall social utility depends on agents’ value functions and demand distributions. Our study provides insights that help decision makers price their services to better satisfy customers’ varying needs while improving the profitability of the service.

中文翻译：

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与异构代理和随机需求灵活签约

摘要 虽然服务的主要定价方案是一套长期合同，规定了一定使用水平的固定费用，但许多服务提供商现在提供灵活的合同。这些合同包括使用级别的灵活性以及在特定时间段内选择退出服务的选项。我们研究了灵活合同在协调服务提供商和客户之间的利益方面的有效性，因为客户存在不同的离散需求分布。这项工作开发了一个统一的委托代理框架，以在事后信息不对称下检查多个版本的灵活合同。我们探讨了两种类型的合同变化。第一个是跨代理随机需求值的聚合合同与差异化合同，第二个是代理人是否可以在承诺一组合同选项后拒绝参与未来的时间段。我们发现委托人总是喜欢差异化而不是聚合，并且在差异化下更喜欢要求每个时间段的参与。然而，当需求可变性在汇总合同下分组在一起时，我们推导出了一个充分条件，即允许代理商灵活选择退出未来时间段何时更有利可图。此外，代理人的偏好和整体社会效用取决于代理人的价值函数和需求分布。我们的研究提供的见解可帮助决策者为他们的服务定价，以更好地满足客户不同的需求，同时提高服务的盈利能力。