Bargaining Between Collaborators of a Stochastic Project

41 Pages Posted: 24 Sep 2020 Last revised: 10 Jan 2022

See all articles by Z. Eddie Ning

Z. Eddie Ning

Cheung Kong Graduate School of Business

Date Written: January 1, 2022


Some projects require collaboration between two firms to implement. The expected return from such a project can change over time due to evolving market conditions or arrival of new information. Each firm may also choose an outside option rather than collaborating. In such a case, when is the joint project implemented, and how do firms split the return? To address these questions, the paper studies a continuous-time model of bilateral bargaining with a stochastic cake and outside options. I show that the combination of stochastic cake, outside options, and uneven bargaining power creates a hold-up problem that leads to insufficient delay. The joint project is implemented too early or firms take outside options too quickly, causing both the ex-ante probability of agreement and its timing to be sub-optimal. Increasing the frequency of counteroffers, which balances bargaining power, improves efficiency by reducing the hold-up. More importantly, the paper finds that a more balanced bargaining power can lead to Pareto improving outcomes.

Keywords: stochastic bargaining, optimal stopping, joint decision-making, continuous-time game

Suggested Citation

Ning, Z. Eddie, Bargaining Between Collaborators of a Stochastic Project (January 1, 2022). Available at SSRN: or

Z. Eddie Ning (Contact Author)

Cheung Kong Graduate School of Business ( email )

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