Zhen Lian

Zhen Lian

Postdoctoral fellow

Lyft Rideshare Labs

mail at zhenlian.me OR zlian at lyft.com


  1. Optimal Growth in Two-sided Markets. Joint work with Garrett van Ryzin. Management Science, 67(11):6862-6879.
    Abstract: We develop a theoretical model of optimal growth in two-sided markets. The model posits that market output (number of transactions) is a function of the stock of supply and demand. This market output is modeled using a homogeneous production function, which can have increasing or decreasing returns to scale. The supply and demand stock levels follow a growth model in which the rate of growth at each point in time is a function of both the surplus each side of the market receives and the attrition of supply and demand (supply and demand lifetimes). The surplus can be apportioned between the two sides of the market by changing the price paid to sellers and the price charged to buyers, which we assume the platform controls. Through these price levers, the platform can pay subsidies to one or both sides of the market. We investigate the behavior of optimal market growth, including the point at which the market becomes self-sustaining and the long-run optimal size of the market. We characterize the optimal balance between supply and demand as the market size grows and determine optimal subsidy policies that maximize discounted total profit. For the case of both increasing and decreasing returns without price constraints, we show the optimal policy is to grow using an impulse of subsidy spending (a subsidy shock) to move the market immediately to its optimal long-run size. This result is consistent with the “race to growth” observed in many two-sided markets like ride-sharing.

Working papers

  1. Capturing the Benefits of Autonomous Vehicles in Ride-Hailing: The Role of Dispatch Platforms and Market Structure. Joint work with Garrett van Ryzin. Under revision.
    Abstract: We develop an economic model of autonomous vehicle (AV) ride-hailing markets in which uncertain aggregate demand is served with a combination of a fixed fleet of AVs and an unlimited potential supply of human drivers (HVs). We analyze market outcomes under two dispatch platform structures (common platform vs. independent platforms) and two levels of supply competition (monopoly AV vs. competitive AV). A key result of our analysis is that the lower cost of AVs does not necessarily translate into lower prices; the price impact of AVs is ambiguous and depends critically on both the dispatch platform structure and the level of AV supply competition. In the extreme case, we show if AVs and HVs operate on independent dispatch platforms and there is a monopoly AV supplier, then prices are even higher than in a pure HV market. When AVs are introduced on a common dispatch platform, we show that whether the equilibrium price is reduced depends on the level of AV competition. If AVs are owned by a monopoly firm, then the equilibrium price is the same as in a pure HV market. In fact, the only market structure that leads to unambiguously lower prices in all demand scenarios is when AVs and HVs operate on a common dispatch platform and the AV supply is competitive. Our results illustrate the critical role dispatch platform and market structure play in realizing potential welfare gains from AVs.
  2. Labor Cost Free-Riding in the Gig Economy. Joint work with Sébastien Martin and Garrett van Ryzin. Under second-round review at Management Science.
    • Honorable mention, RMP 2021 Jeff McGill Student Paper Award
    Abstract: We propose a theory of gig economies in which workers participate in a shared labor pool utilized by multiple firms. Since firms share the same pool of workers, they face a trade-off in setting pay rates; high pay rates are necessary to maintain a large worker pool and thus reduce the likelihood of lost demand, but they also lower a firm’s profit margin. We prove that larger firms pay more than smaller firms in the resulting pay equilibrium. These diseconomies of scale are strong too; firms smaller than a critical size pay the minimal rate possible (the workers’ reservation wage), while all firms larger than the critical size earn the same total profit regardless of size. This scale disadvantage in labor costs contradicts the conventional wisdom that gig companies enjoy strong network effects and suggests that small firms have significant incentives to join an existing gig economy, implying gig markets are highly contestable. Yet we also show that the formation of a gig economy requires the existence of a large firm, in the sense that an equilibrium without any firms participating only exists when no single firm has enough demand to form a gig economy on its own. The findings are consistent with stylized facts about the evolution of gig markets such as ride sharing.
  3. Algorithmic Precision and Human Decision: A Study of Interactive Optimization for School Schedules. Joint work with Arthur Delarue and Sébastien Martin. Under review..
    Abstract: Motivated by a collaboration with the San Francisco Unified School District (SFUSD), this paper presents an interactive optimization framework for addressing complex pub- lic policy problems. These problems suffer from a chicken-and-egg dilemma, where policymakers understand the objectives and constraints but lack the ability to solve them (“the optimization problem”), while researchers possess the necessary algorithms but lack the necessary insights into the policy context (“the policy problem”). Our framework addresses this challenge by combining three key elements: (1) an efficient optimization algorithm that can solve the problem given certain known objectives, (2) a method for generating a large set of diverse, near-optimal solutions, and (3) an inter- face that facilitates exploration of the solution space. We illustrate the effectiveness of this framework by applying it to the problem of improving school schedules at SFUSD. The resulting schedule, implemented in August 2021, saved the district over $5 million and, to our knowledge, represents the first successful optimization-driven school start time change in the United States.


  1. Consumer Status Signaling, Wealth Inequality and Non-deceptive Counterfeits. Joint work with Li Chen and Shiqing Yao.
    Abstract: Consumers often enjoy displaying luxury consumption to signal their private wealth status. The emergence of social media has fueled such desire for status signaling. Meanwhile, the rising of e-commerce has made it easy for consumers to search and purchase cheap non-deceptive counterfeits to send a ``fake’’ status signal, posing a serious problem to the luxury (status product) industry. Motivated by these industry dynamics, we consider a market entry deterrence game between an incumbent status product firm (the firm) and a non-deceptive counterfeiter (the counterfeiter) who attempts to enter the market. A unique feature of our model is that the market demand is endogenously determined by a consumer status signaling subgame. We investigate the interaction among consumer status signaling, wealth inequality, and equilibrium market outcomes, as well as the implications of anti-counterfeit measures aimed at increasing the counterfeiter market entry cost. Our analysis yields three main insights. First, we show that without counterfeits, the firm is strictly better off from the heightened motive of consumer status signaling; however, such benefit would be neutralized by the potential counterfeiter entry. Second, we find that the presence of counterfeits lowers the firm’s profit, but may induce the firm to raise its price. It may also increase social welfare, despite enabling a fake status signal. Third, we demonstrate that increasing the counterfeiter market entry cost may not completely eliminate counterfeiting insofar as the consumer status signaling motive and wealth inequality are high, in which case the firm would settle for strategic coexistence with the counterfeiter.


  • Bartholomew Family Charitable Fund Ph.D. Student Scholarship, Cornell University, 2019-2020.
  • Byron E. Grote, MS’77, Ph.D.‘81 Johnson Professional Scholarship, Cornell University, 2017-2018.
  • Johnson Graduate School of Management Doctoral Fellowship, Cornell University, 2016-2021.

Selected talks

  • RM&P Conference, Online, 2021. Labor Cost Free-Riding in the Gig Economy.
  • RM&P Conference, Online, 2021. Autonomous Vehicle Market Design.
  • MSOM Conference, Online, 2021. Labor Cost Free-Riding in the Gig Economy.
  • MSOM Conference, Online, 2021. Autonomous Vehicle Market Design.
  • Columbia DRO PhD Workshop, Online, 2021. Labor Cost Free-Riding in the Gig Economy.
  • Marketplace Innovation Workshop, Online, 2021. Autonomous Vehicle Market Design.
  • POMS Conference, Online, 2021. Autonomous Vehicle Market Design.
  • INFORMS Annual Meeing, Online, 2020. Autonomous Vehicle Market Design.
  • Cornell Johnson OTIM Workshop, Online, 2020. Autonomous Vehicle Market Design.
  • INFORMS Annual Meeting, Seattle, 2019. Autonomous Vehicle Market Design.
  • RM&P Conference, Stanford GSB, 2019. Optimal Growth in Two-sided Markets.
  • POMS Conference, Washington DC, 2019. Luxury Pricing with Status-seeking Customers and Strategic Counterfeiters.
  • NYU Sharing Economy Seminar, NYU Stern, 2019. Optimal Growth in Two-sided Markets.
  • Cornell Johnson OTIM Workshop, 2019. Optimal Growth in Two-sided Markets.
  • INFORMS Annual Meeting, Phoenix, 2018. Optimal Growth in Two-sided Markets.


  • Reviewer for Management Science, M&SOM, OR Letters, EJOR