Equilibria in routing games with connected autonomous vehicles will not be strong, as exclusive clubs may form

TL;DR

The paper addresses whether routing equilibria remain robust in mixed-autonomy networks when connected autonomous vehicles can form coalitions. It develops a coalitional routing model on a two-route network, integrating NE, $SE$, and club dynamics, and demonstrates that a small AV club can deviate from the NE to improve its members’ travel times, while harming others and reducing system efficiency; this requires adaptive traffic signals to realize the effect. A concrete demonstration shows a coalition of three AVs achieving gains and establishing a new stable state, with externalities spreading to humans and non-members, raising equity and policy concerns for future smart cities. The work highlights the potential emergence of exclusive AV coalitions that distort traditional equilibria, emphasizing the need for design and policy interventions to mitigate inequitable and inefficient outcomes in urban road networks.

Abstract

User Equilibrium is the standard representation of the so-called routing game in which drivers adjust their route choices to arrive at their destinations as fast as possible. Asking whether this Equilibrium is strong or not was meaningless for human drivers who did not form coalitions due to technical and behavioral constraints. This is no longer the case for connected autonomous vehicles (CAVs), which will be able to communicate and collaborate to jointly form routing coalitions. We demonstrate this for the first time on a carefully designed toy-network example, where a `club` of three autonomous vehicles jointly decides to deviate from the user equilibrium and benefit (arrive faster). The formation of such a club has negative consequences for other users, who are not invited to join it and now travel longer, and for the system, making it suboptimal and disequilibrated, which triggers adaptation dynamics. This discovery has profound implications for the future of our cities. We demonstrate that, if not prevented, CAV operators may intentionally disequilibrate traffic systems from their classic Nash equilibria, benefiting their own users and imposing costs on others. These findings suggest the possible emergence of an exclusive CAV elite, from which human-driven vehicles and non-coalition members may be excluded, potentially leading to systematically longer travel times for those outside the coalition, which would be harmful for the equity of public road networks.

Figures (7)

• Figure 1: CAV coalition formation. We depart from User Equilibrium (top left) on a simple Two Route Network, where each driver decides to go straight (Route 0), as traveling Route 1 would be slower for each of them. When 10 out of 15 vehicles mutate to autonomous vehicles, they reconsider their choices. None of them would benefit by individually deviating to Route 1 (bottom left); however, vehicles 1, 5, and 6 discover that by deviating together, they can arrive faster (bottom center). Not only on average, but also individually. This benefit for the few invited club members is at the cost of other users and system performance (bottom right).
• Figure 2: Illustration of the club dynamics graph $\mathcal{G}^I$ with $I = \{1,5,6\}$, the only coalition identified with Algorithm 1. However, both players 0 and 7 would like to join it given that it is formed (eq. \ref{['eq:externalstab']}). However, when both of them join, it is no longer attractive to player number 7. This leads to one terminal node, a coalition $\{0,1,5,6\}$ - which happens to be a strong Nash equilibrium.
• Figure 3: The topology of the network studied in this paper.
• Figure 4: Snapshot from SUMO of the Two Route Yield network employed in this work. The club of deviating agents driving through Route 1 is colored in red.
• Figure 5: Travel times of 10 CAVs in NE $x^0$ (a) and in four considered club compositions $\mathds{1}_{\{1,5,6\}}, \mathds{1}_{\{1,5,6,7\}}, \mathds{1}_{\{0,1,5,6,7\}}, \mathds{1}_{\{0,1,5,6\}}$ (b-e). Travel times are normalized across the 5 plots, such that the travel time of all agents in $x^0$ is 1. Black (respectively red) arrows show how much time each agent would lose (respectively gain) by changing route unilaterally from a given joint action. The absence of red arrows is therefore equivalent to the joint action being a Nash equilibrium (a) and (e). Club members (deviating to Route 1) are marked with white circles, and those not invited (remaining at Route 0) with black ones. Blue arrows connect cases where an agent can gain time by changing route unilaterally to the state resulting from this change (vertices of graph $\mathcal{G}$).

Theorems & Definitions (1)

• proposition 1