Flexible contracting with heterogeneous agents and stochastic demand

Dashi I. Singham, Wenbo Cai, Armin Fügenschuh

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Article number107840
JournalInternational Journal of Production Economics
StatePublished - Jan 2021

All Science Journal Classification (ASJC) codes

  • General Business, Management and Accounting
  • Economics and Econometrics
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


  • Contracts
  • Heterogeneous agents
  • Pricing
  • Principal–agent model
  • Stochastic demand


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