Online Incentive-Compatible Mechanisms for Traffic Intersection Auctions

TL;DR

This paper introduces online incentive-compatible auction mechanisms for traffic intersections that dynamically estimate waiting times using Markov models, ensuring truthful user bidding and maximizing social welfare.

Contribution

It develops two novel Markov chain models for dynamic waiting time estimation and designs incentive-compatible mechanisms that outperform static approaches.

Findings

Online mechanisms are incentive-compatible in the dynamic sense.

Static mechanisms may cause users to misreport delay costs.

Proposed models improve social welfare in traffic auctions.

Abstract

We present novel online mechanisms for traffic intersection auctions in which users bid for priority service. We assume that users at the front of their lane are requested to declare their delay cost, i.e. value of time, and that users are serviced in decreasing order of declared delay cost. Since users are expected to arrive dynamically at traffic intersections, static pricing approaches may fail to estimate user expected waiting time accurately, and lead to non-strategyproof payments. To address this gap, we propose two Markov chain models to determine the expected waiting time of participants in the auction. Both models take into account the probability of future arrivals at the intersection. In a first model, we assume that the probability of future arrivals is uniform across lanes of the intersection. This queue-based model only tracks the number of lower- and higher-bidding users on access lanes, and the number of empty lanes. The uniformness assumption is relaxed in a second, lane-based model which accounts for lane-specific user arrival probabilities at the expense of an extended state space. We then design a mechanism to determine incentive-compatible payments in the dynamic sense. The resulting online mechanisms maximize social welfare in the long run. Numerical experiments on a four-lane traffic intersection are reported and compared to a static incentive-compatible mechanism. Our findings show that static incentive-compatible mechanisms may lead users to misreport their delay costs. In turn, the proposed online mechanisms are shown to be incentive-compatible in the dynamic sense.