Position Bidding for Algorithm-Assisted Drivers
38 Pages Posted: 9 Apr 2020
Date Written: March 20, 2020
Drivers on roads and highways have different levels of urgency and, consequently, different valuations of time. Yet, since the origins of vehicular traffic, the most common responses to having a high time valuation have been either to drive more aggressively, which compromises safety; or to do nothing, which compromises the efficiency of traffic flow. Effectively, there have been no means for drivers to negotiate or coordinate on the fly, which would allow them to reach better outcomes. The recent advent of algorithm-assisted driving, vehicle-to-vehicle and vehicle-to-infrastructure technologies promise to change this reality. To fully exploit the possibilities that lie ahead though, a paradigm shift is necessary: algorithm-assisted drivers should be viewed as rational economic agents, while traffic regulators should, in turn, play the role of mechanism designers, setting the rules of the game so as to lead vehicular traffic to safe and efficient equilibria. We study the possibilities that these new technologies open, very concretely, in the context of a common forced-merging scenario: a single driver on the blocked-lane of a road segment has to merge into a dense platoon of cars, on the free lane. Drivers are heterogeneous in terms of their time valuations, but this information is private. The only public information is the common probability distribution from which valuations are drawn, as well as the exact positions of different cars in the platoon. We propose a sequential bidding mechanism, where the merging driver bids for the ability to merge ahead of each of the free-lane drivers, from tail to head of the platoon, and is only allowed to move forward if all free-lane drivers up to that point have accepted her bids. We demonstrate that this mechanism: (i) imposes no negative externalities on free-lane drivers; (ii) leads to equilibrium bids that can be succinctly characterized via a simple Dynamic Program; (iii) results in total utility that is close to the social optimum. Furthermore, we propose Approximate Dynamic Programming approaches that are extremely fast, computationally, and lead to bids that are very close to the equilibrium ones, making them suitable for practical implementation.
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