[Paper Review] Efficient Carpooling and Toll Pricing for Autonomous Transportation

Saurabh Amin, Patrick Jaillet+1 more|arXiv (Cornell University)|Feb 18, 2021

Transportation and Mobility Innovations21 references4 citations

TL;DR

This paper proposes a mechanism for efficient carpooling and toll pricing in autonomous transportation networks, using linear programming and combinatorial auction theory to ensure market equilibrium with individual rationality, budget balance, and stability. It proves that a socially optimal equilibrium exists and can be computed in polynomial time when the network is series-parallel and riders have homogeneous carpool disutility.

ABSTRACT

In this paper, we address the existence and computation of competitive equilibrium in the transportation market for autonomous carpooling first proposed by [Ostrovsky and Schwarz, 2019]. At equilibrium, the market organizes carpooled trips over a transportation network in a socially optimal manner and sets the corresponding payments for individual riders and toll prices on edges. The market outcome ensures individual rationality, stability of carpooled trips, budget balance, and market clearing properties under heterogeneous rider preferences. We show that the question of market's existence can be resolved by proving the existence of an integer optimal solution of a linear programming problem. We characterize conditions on the network topology and riders' disutility for carpooling under which a market equilibrium can be computed in polynomial time. This characterization relies on ideas from the theory of combinatorial auctions and minimum cost network flow problem. Finally, we characterize a market equilibrium that achieves strategyproofness and maximizes welfare of individual riders.

Motivation & Objective

• To establish conditions under which a competitive market equilibrium exists in autonomous carpooling systems with heterogeneous rider preferences.
• To develop a computationally efficient method for computing such equilibria using linear programming and network flow optimization.
• To design a strategyproof mechanism that maximizes individual rider utility while ensuring market clearing and budget balance.
• To characterize the existence of integer optimal solutions in the primal linear program as equivalent to market equilibrium existence.
• To extend the framework to handle toll pricing that reflects edge capacity usage and incentivizes socially optimal route choices.

Proposed method

• Formulates the carpooling problem as a linear program (primal) and its dual, linking market equilibrium existence to the existence of an integer optimal solution in the relaxed primal.
• Uses the theory of combinatorial auctions and minimum cost network flow to model rider preferences and route assignment with capacity constraints.
• Applies a greedy algorithm to select routes in increasing order of travel time, allocating network capacity to minimize total cost under series-parallel network topology.
• Introduces an augmented trip value function that satisfies monotonicity and gross substitutes conditions, enabling the use of lattice-based equilibrium analysis.
• Employs strong duality of linear programming to derive equilibrium outcomes from optimal primal and dual solutions.
• Uses the ellipsoid method to compute toll prices satisfying feasibility constraints, with polynomial-time separation oracles based on the augmented value function.

Experimental results

Research questions

• RQ1 Under what network and preference conditions does a competitive market equilibrium exist for autonomous carpooling with toll pricing?
• RQ2 Can a socially optimal and stable carpooling outcome be computed efficiently in polynomial time?
• RQ3 How can a mechanism be designed to ensure strategyproofness while maximizing individual rider utility?
• RQ4 What role does network topology—specifically series-parallel structure—play in ensuring the existence of integer solutions to the linear programming relaxation?
• RQ5 How can toll prices be set to reflect edge capacity usage and incentivize efficient route and trip organization?

Key findings

• A market equilibrium exists if and only if the linear programming relaxation of the optimal trip organization problem admits an integer optimal solution.
• When the network is series-parallel and riders have homogeneous carpool disutility, the primal LP is guaranteed to have an integer optimal solution, ensuring equilibrium existence.
• The optimal trip assignment can be computed in polynomial time using a greedy algorithm that prioritizes routes by increasing travel time and allocates capacity accordingly.
• A strategyproof equilibrium that maximizes individual rider utility is achieved by selecting the maximum Walrasian equilibrium price vector, which also minimizes total toll revenue collected.
• Toll prices satisfying market clearing constraints can be computed in polynomial time using the ellipsoid method, with separation oracles solvable in O(|M|) time per route.
• The equilibrium outcome ensures individual rationality, stability of carpooled trips, budget balance, and market clearing, with all properties derived from strong duality and lattice structure of the solution space.