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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 . 

As one of the most fundamental concepts in transportation science, Wardrop equilibrium (WE) has always had a relatively weak behavioral underpinning. To strengthen this foundation, one must reckon with bounded rationality in human decision-making processes, such as the lack of accurate information, limited computing power, and suboptimal choices. This retreat from behavioral perfectionism in the literature, however, was typically accompanied by a conceptual modification of WE. Here, we show that giving up perfect rationality need not force a departure from WE. On the contrary, WE can be reached with global stability in a routing game played by boundedly rational travelers. We achieve this result by developing a day-to-day (DTD) dynamical model that mimics how travelers gradually adjust their route valuations, hence choice probabilities, based on past experiences. Our model, called cumulative logit (CumLog), resembles the classical DTD models but makes a crucial change; whereas the classical models assume that routes are valued based on the cost averaged over historical data, our model values the routes based on the cost accumulated. To describe route choice behaviors, the CumLog model only uses two parameters, one accounting for the rate at which the future route cost is discounted in the valuation relative to the past ones and the other describing the sensitivity of route choice probabilities to valuation differences. We prove that the CumLog model always converges to WE, regardless of the initial point, as long as the behavioral parameters satisfy certain mild conditions. Our theory thus upholds WE’s role as a benchmark in transportation systems analysis. It also explains why equally good routes at equilibrium may be selected with different probabilities, which solves the instability problem posed by Harsanyi. Funding: This research is funded by the National Science Foundation [Grants CMMI #2225087 and ECCS #2048075]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0132 . 

The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution, is often used to address the challenge. Built on a recently proposed day-to-day discrete-time dynamical model called cumulative logit (CumLog), this study provides a new behavioral underpinning for the maximum-entropy user equilibrium (MEUE) route flow. It has been proven that CumLog can reach a UE state without presuming that travelers are perfectly rational. Here, we further establish that CumLog always converges to the MEUE route flow if (i) travelers have no prior information about routes and thus, are forced to give all routes an equal initial choice probability or if (ii) all travelers gather information from the same source such that the general proportionality condition is satisfied. Thus, CumLog may be used as a practical solution algorithm for the MEUE problem. To put this idea into practice, we propose to eliminate the route enumeration requirement of the original CumLog model through an iterative route discovery scheme. We also examine the discrete-time versions of four popular continuous-time dynamical models and compare them with CumLog. The analysis shows that the replicator dynamic is the only one that has the potential to reach the MEUE solution with some regularity. The analytical results are confirmed through numerical experiments. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This research was funded by the United States National Science Foundation’s Division of Civil, Mechanical and Manufacturing Innovation [Grant 2225087]. The work of J. Xie was funded by the National Natural Science Foundation of China [Grant 72371205]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0525 . 

This paper proposes a novel quantity-based demand management system that aims to promote ridesharing. The system sells a time-dependent permit to access a road facility (conceptualized as a bottleneck) by auction but encourages commuters to share permits with each other. The commuters may be assigned one of three roles: solo driver, ridesharing driver, or rider. At the core of this auction-based permit allocation and sharing system (A-PASS) is a trilateral matching problem (TMP) that matches permits, drivers, and riders. Formulated as an integer program, TMP is first shown to be tightly bounded by its linear relaxation. A pricing policy based on the classical Vickrey–Clarke–Groves (VCG) mechanism is then devised to determine the payment of each commuter. We prove that, under the VCG policy, different commuters pay exactly the same price as long as their role and access time are the same. Importantly, by controlling the number of shared rides, any deficit that may arise from the VCG policy can be eliminated. This may be achieved with a relatively small loss to system efficiency, thanks to the revenue generated from selling permits. Results of a numerical experiment suggest A-PASS strongly promotes ridesharing. As sharing increases, all stakeholders are better off: the ridesharing platform receives greater profits, the commuters enjoy higher utility, and society benefits from more efficient utilization of the road infrastructure.