Many knowledge-intensive projects such as new product and software design, research and high technology development have flexible scope and involve co-production between a client and a vendor. In such projects, it is often challenging to estimate how much progress can be achieved within a certain time window or how much time may be needed to achieve a certain degree of progress, especially because the client and vendor often adjust their efforts as a function of the project's progress, the time until the deadline, and the incentives in place. Effective contracts should therefore be flexible in scope and foster collaboration. In this paper, we characterize the collaborative work dynamics of a client and a vendor who are engaged in a multi-state, multi-period stochastic project with a finite deadline. We show that when the client can verify the vendor's effort, it is optimal that they both exert high effort in one of two situations: when either not enough progress has been made and the deadline is close (deadline effect), or conversely, when so much progress has been made that the project state is close to a completion state set by the client (milestone effect). Hence, in this case, progress will typically be faster when the project is about to be stopped, due to either reaching the deadline or reaching the client's desired completion state. However, when the client cannot verify the vendor's effort, the vendor is prone to free-riding. Considering a time-based contract, which pays the vendor a per-period fee and a fixed completion bonus, we show that the equilibrium completion state is decreasing in the per-period fee and increasing in the bonus, justifying the use of both incentive mechanisms in practice. Moreover, we show that, under such contracts, some form of milestone effect arises in equilibrium, but the deadline effect does not. Hence, in those cases, early progress will typically lead to early project conclusion at a high state; whereas, slow progress will typically make the project drag until the deadline while still at a low state
