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We model the oligopoly competition in a dockless bike-sharing (DLB) market as a bilevel game. Each DLB operator is first committed to an action tied to a specific objective, such as maximizing profit. Then, the operators play a lower-level game to achieve their individual goals and finally reach a subgame perfect Nash equilibrium by making tactic decisions (e.g., pricing and fleet sizing). We define a Nash equilibrium under either weak or strong preference to characterize the likely outcomes of the bilevel game and formulate the demand-supply equilibrium of a DLB market that accounts for key operational features and mode choice. Using the oligopoly game model calibrated with empirical data, we show that if an operator seeks to maximize its market share with a budget constraint, all other operators must either respond in kind or be driven out of the market. When all operators compete for market dominance, even a slight efficiency edge gained by one operator can significantly shift the outcome, which signals high volatility. Moreover, even if all operators agree to focus on making money rather than ruinously seeking dominance, profitability still plunges quickly with the number of operators. Taken together, the results explain why an unregulated DLB market is often oversupplied and prone to collapse under competition. We also show that this market failure may be prevented by a fleet cap regulation, which sets an upper limit on each operator’s fleet size. Funding: This research was supported by the U.S. National Science Foundation’s Civil Infrastructure System (CIS) Program under the award CMMI no. 2225087. K. Zhang received financial support from the Swiss National Science Foundation [Grant 219232]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0846 .