Delegating Innovation Projects with Deadline: Committed vs. Flexible Stopping

In many contexts such as product design and development, advertising, and scouting for technical solutions, clients seek the expertise of external providers to generate innovative solutions for their business problems. Because innovation projects are beset with uncertainty, they often require multiple iterations of ideation and evaluation. Although some clients make a commitment to take the first feasible solution from the provider, other clients retain the flexibility to seek more solutions until they decide to stop the project. Which of these policies is the better way to delegate an innovation project? To answer this question, we develop game-theoretic models that capture two salient aspects of delegated innovation projects: a deadline for the project and dynamic effort adjustment by the provider. We show that the flexible stopping policy, despite its intuitive appeal, may not always benefit the client. Specifically, the committed stopping policy is optimal when the provider is highly capable of generating solutions and when the client's cost of evaluating solutions is in an intermediate range. In such situations, the committed stopping policy provides a stronger incentive to the provider to exert costly effort early on, which improves the quality of initial solutions. Considering endogenous payments, we show that the committed policy not only mitigates the provider's tendency to postpone effort but also does so with a smaller payment.