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Optimum versus Nash-equilibrium in taxi ridesharing

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Abstract

In recent years, Transportation Network Companies (TNC) such as Uber and Lyft have embraced ridesharing: a passenger who requests a ride may decide to save money in exchange for the inconvenience of sharing the ride with someone else and incurring a delay. When matching passengers, these services attempt to optimize cost savings. But a possible scenario is that while passenger A is matched to passenger B, if matched to passenger C then both A and C would have saved more money. This leads to the concept of “fairness” in ridesharing, which consists of finding the Nash equilibrium in a ridesharing plan. In this paper we compare the optimum plan (i.e., benefit maximized at a global level) and the fair plan in both static and dynamic contexts. We show that in contrast to the theoretical indications, the fair plan is almost optimum. Furthermore, the fairness concept may help attract more passengers to rideshare and thus further reduce vehicle miles traveled. If social preferences are included in the total benefit, we demonstrate that the optimum ridesharing plan may be unboundedly and predominantly unfair in a sense that will be formalized in this paper.

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Notes

  1. Price of Anarchy or PoA is the maximum ratio between the benefit of the optimum plan and the fair one

  2. A coalition-structure is a ridesharing-plan in our terminology.

  3. The modification adjusts only the weights of the edges of G. The nodes and edges remain the same, thus P is an rsp on the resulting graph G’ as well.

  4. Due to this assumption, which implies a queue of taxis waiting for passengers, we are able to consider in a realistic setting ridesharing that is independent of vehicles locations and availability; these are being considered in the dynamic models.

  5. For example, the weight of an edge can be computed in constant time if the Euclidean distance saved is used as the weight. Specifically, the weight of eij is (S − L), where L = min {[(Euclidean distance from H to the destination of vi) + (Euclidean distance from the destination of vi to the destination of vj)], [(Euclidean distance from H to the destination of vj] + (Euclidean distance from the destination of vj to the destination of vi)]; and S is the sum of the two Euclidean distances from the hub to the two destinations.

  6. Observe that all the subsets of a hyper-edge are also hyper-edges in the RSH, since if requests A, B, C can be combined, then clearly they can be pairwise combined. For the purpose of constructing the e-RSH, singleton subsets of an RSH hyper-edge are also hyper-edges with weight 0 (since there is no ridesharing benefit). It means that {A}, {B}, and {C} in the example are also hyper-edges that are matched with taxis.

  7. Observe that this formulation does not consider the distance that the empty taxi travels to the pickup location.

  8. Unsatisfied requests are not taken into account to compute the total distance saved in the experiments.

  9. In fact, the cf. value matters only for the dynamic model. The reason for this is that it can be easily shown that in the static model, since there is no waiting after the pool-end time, the delay bound is satisfied for a value v1 of cf. if and only if it is satisfied for any value. However, this is not the case for the dynamic model, where the delay of a request is the sum of the travel delay and the waiting delay (which in turn may arise due to a request being transferred from one pool to the next).

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Acknowledgements

This study was supported in part by the NSF Grants IIS-1213013 and IIP-1534138.

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Correspondence to Ouri Wolfson.

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Foti, L., Lin, J. & Wolfson, O. Optimum versus Nash-equilibrium in taxi ridesharing. Geoinformatica 25, 423–451 (2021). https://doi.org/10.1007/s10707-019-00379-6

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