Market share maximizing strategies of CAV fleet operators may cause chaos in our cities

TL;DR

The paper investigates how a fleet of autonomous vehicles (CAVs) maximizing market share can influence day-to-day routing when drivers can switch between HDV and CAV modes. It develops a rigorous mathematical framework for individualized CAV offer profiles and feasible assignment plans, alongside a greedy feasibility algorithm and a discount-factor model for heterogeneous driver attitudes. The key findings show that full market penetration can be achieved in certain two-route or heterogeneously tailored/mixed routing scenarios, but in more realistic settings with bimodal travel-time distributions, mixed strategies may be needed and can induce unpredictable day-to-day travel times. The results have important policy implications, indicating that collective routing in mature CAV markets could degrade urban network reliability unless properly regulated or detected, and highlight the need for advanced behavioral and routing algorithms to manage such dynamics.

Abstract

We study the dynamics and equilibria of a new kind of routing games, where players - drivers of future autonomous vehicles - may switch between individual (HDV) and collective (CAV) routing. In individual routing, just like today, drivers select routes minimizing expected travel costs, whereas in collective routing an operator centrally assigns vehicles to routes. The utility is then the average experienced travel time discounted with individually perceived attractiveness of automated driving. The market share maximising strategy amounts to offering utility greater than for individual routing to as many drivers as possible. Our theoretical contribution consists in developing a rigorous mathematical framework of individualized collective routing and studying algorithms which fleets of CAVs may use for their market-share optimization. We also define bi-level CAV - HDV equilibria and derive conditions which link the potential marketing behaviour of CAVs to the behavioural profile of the human population. Practically, we find that the fleet operator may often be able to equilibrate at full market share by simply mimicking the choices HDVs would make. In more realistic heterogenous human population settings, however, we discover that the market-share maximizing fleet controller should use highly variable mixed strategies as a means to attract or retain customers. The reason is that in mixed routing the powerful group player can control which vehicles are routed via congested and uncongested alternatives. The congestion pattern generated by CAVs is, however, not known to HDVs before departure and so HDVs cannot select faster routes and face huge uncertainty whichever alternative they choose. Consequently, mixed market-share maximising fleet strategies resulting in unpredictable day-to-day driving conditions may, alarmingly, become pervasive in our future cities.

Figures (7)

• Figure 1: Day-to-day travel time distribution on a given route in typical urban settings (left) and likely travel time distribution when a fleet of CAVs uses probabilistic mixed routing. Note that even if the mean is the same, the $95$th percentile is shifted towards larger travel times which would inconvenience independent drivers who would need to depart significantly earlier in order to arrive on time on most days.
• Figure 2: Results of the paper at a glance. CAV fleet operator uses a multi-stage pipeline to decide which routing can maximize the market share. In most realistic cases this results in you as a road user facing the choice: either use an independent HDV and select from routes with enormous uncertainty, or join the fleet and obtain better expected utility. From the network point of view, the fleet of CAVs can generate congestion on routes in a stochastic way resulting in travel times which have two separated peaks. The human perspective and network perspective jointly make up the unpredictability of driving conditions and put human drivers at a disadvantage vs. CAVs, which generate these conditions deliberately to maximize market share.
• Figure 3: The considered system consists of $R$ independent parallel routes between Origin (O) and Destination(D).
• Figure 4: Dynamics of the considered system. Every driver $i$ makes a decision whether to use an HDV or CAV based on comparing the disutilities (perceived costs) of the two options, $u_i^{HDV}$ and $u_i^{CAV}$. If $u_i^{HDV}<u_i^{CAV}$ then they choose HDV. If $u_i^{HDV}>u_i^{CAV}$ then they choose CAV. Otherwise, they stick to the mode from the previous day. Then, on a given day of travel $j$, if HDV is the chosen mode, the driver selects one of the routes $1,\dots, R$ based typically on minimization of expected travel time and drives from Origin to Destination along the selected route. Contrariwise, if CAV is the chosen mode, then driver $i$ is assigned a route $r$ and the autonomous vehicle takes driver $i$ from Origin to Destination. After a finished day of travel, the drivers update their utilities of using an HDV (based typically on which route was the fastest on the past days). The fleet informs driver $i$ of the long-term utility it can offer to driver $i$. Periodically (every day or every several days), driver $i$ reconsiders whether to change the mode. Whether driver $i$ swaps the mode or not, they face the route choice on the following day $j+1$ and this decision - feedback process is looped indefinitely. At dynamic equilibrium the mode choice is fixed for every driver $i$ and no driver is inclined to change it. At nested equilibrium, the mode choices, the route choices of drivers using HDV and routing patterns for every $CAV$ are fixed and not only no driver is inclined to change the mode but also no HDV user is inclined to choose a different route.
• Figure 5: Summary of the technical results of the paper. An offer profile offering every driver $i$ a given mean travel time $T_i^{CAV}$ is always feasible for two routes (Proposition \ref{['Prop_AssPlans_prop']}), i.e. it admits an assigment plan $\mu(i,r)$ such that $\mu(i,r)$ is the proportion with which driver $i$ is routed via alternative $r$ and, given these proportions, the mean travel time of driver $i$ is $T_i^{CAV}$. For three or more routes, Algorithm \ref{['Alg_feasible']} and Theorem \ref{['Th_feasibility']} provide a useful criterion for verifying feasibility as well as a procedure of construction of assignment plans. Given assignment plan $\mu$, there always exists and can be constructed (Proposition \ref{['Prop_asymptotically']}) a multi-day scheme of assignment which assigns route $\rho(i,j)$ to CAV user $i$ on day $j$ such that the proportions given by assignment plan $\mu(i,\cdot)$ are fulfilled long-term for every user $i$.

Theorems & Definitions (38)

• Definition 2.1
• Remark 2.2
• Example 2.3: Examples of Fleet-Human equilibria
• Definition 3.1: CAV travel time offer profile, assignment plan
• Remark 3.2
• Example 3.3
• Proposition 3.4: Basic properties of offer profiles and assignment plans
• proof
• Definition 3.5: Multi-day assignment scheme of individual drivers to routes
• Definition 3.6