Incentivizing Shared Rides in e-hailing Systems: DynamicDiscount Pricing
G. Jiaoa , M. Ramezania,∗
a The University of Sydney, School of Civil Engineering, Sydney, Australia

gjia5714@uni.sydney.edu.au, mohsen.ramezani@sydney.edu.au∗ Corresponding author
Extended abstract submitted for presentation at the 11th Triennial Symposium on
Transportation Analysis conference (TRISTAN XI)
June 19-25, 2022, Mauritius Island

December 15, 2021
Keywords: Mobility on-demand, Matching, Ridesharing, Fare

1INTRODUCTION

Transportation Network Companies (TNCs) such as Uber, Didi and Lyft have emerged andgrown explosively over the past decade. Those TNCs offer e-hailing platforms to provide point
to point on-demand mobility services, and one of the most common services provided is ridesourcing. However, it has been shown by various studies that ridesourcing has deteriorated trafficconditions as it increases the number of unoccupied vehicles on the road (Schaller, 2017), which
subsequently lead to more crashes, pollution and congestion (Anair et al., 2020, Barrios et al.,2020). Ridesharing is another service also often provided by TNCs and is enabled by the realtime matching nature of e-hailing platforms, where passengers with similar itineraries may bepooled together in a combined trip. Though less popular among passengers (Xu et al., 2021),
ridesharing could counteract some of the negative externalities of ridesourcing, as it might increase the number of passengers on board and enables a smaller fleet to service the same numberof passenger requests. The lower popularity of ridesharing can be attributed to the potentiallylonger waiting time and detour, and the inconvenience of sharing with a stranger. Therefore,
the passengers in shared trips are generally compensated with a price discount. Higher discountoffered makes ridesharing more appealing to passengers but irrevocably lowers the profit generated per trip and vice versa. Ergo, the price discount is a crucial variable a platform has control
over. In this paper, we formulate a dynamic ridesharing discount pricing strategy for a profit
maximizing TNC and the ramifications of such strategy are evaluated.

2Methodology

We construct a dynamic model of the on-demand mobility market, where we consider a single
platform in the market, that offers both ridesourcing and ridesharing services with a fleet ofvehicles with drivers whose wage has to be paid for offering the service to passengers. The
majority of the studies on ridesharing assume all passengers are willing to share irrespective ofservice quality and price. However, in this study we explicitly consider the passengers to becost and service quality sensitive, impatient, and have a choice to decline services offered by theplatform. We use utility choice models to predict the passenger’s decision (Section 2.1). We
propose a dynamic discount pricing strategy for the platform. The strategy is integrated in theTRISTAN XI Symposium

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G. Jiao, M. Ramezani

2matching algorithm which maximizes the profit with given batches of waiting passengers and idle
vehicles, and strategically offers shared trips to selected passengers with varying price discountlevels (Section 2.2).

2.1

Passenger Choice

Consider an individual passenger pi . Once a request is made with origin and destination, theplatform will attempt to match pi to a suitable trip. If successfully matched, the service offeredto pi could either be a solo trip or a shared-trip at the will of the platform (with the overall
objective of maximizing the platform profit, see Section 2.2). However, pi may or may not bepleased with the service offered by the platform, and therefore they could choose to reject theoffer. If pi is matched in a shared trip, they make a choice between accepting it or they would
rather be in a solo trip. If pi is matched in a solo trip, they make a choice between accepting orleaving the platform for other modes of travel. We consider two binary choice models for these
two scenarios. To facilitate the choice modeling, we assume pi perceives the utilities of different
modes of travel as follows:
Solo Trip : usi = βis − βit wis − βif fis(1a)

Shared Trip : uhi = βih − βit (wih + δi ) − βif [fis (1 − θi )]Other Modes : uoi = βio

(1b)
(1c)

Where βis , βih , βio are the utility constants for the three travel modes. βit is the utility coefficient
per unit time, wis and wih are the waiting times for the solo and shared trips respectively, and δi isthe detour time for the shared trip. The waiting time and detour time are negatively correlatedwith the quality of the service, which are reflected in the utilities. βif is the utility coefficient perunit cost, fis is the solo trip fare where we assume that the fare structure consists of a fixed costand a variable cost that depends on trip distance/duration, and θi is the discount level for theshared trip. Similarly, the utilities are negatively correlated with the cost of fare.

2.2

Dynamic Discount Pricing

The platform establishes matching between a set of unmatched passengers, P = {p1 , ..., pn }, anda set of idle vehicles, V = {v1 , ..., vv } every ∆ seconds. The dynamic discount pricing strategy
is designed to determine (i) the profit maximizing matching between the two sets that consistsof solo and shared trips, and simultaneously (ii) the profit maximizing price discount for every
passenger in shared trips.
We obtain such strategy by solving a modified maximum weighted bipartite matching problem. We first construct the set of all ordered passenger pairs, Q = {p1,2 , p1,3 , ..., p1,n , p2,1 , p2,3 , ...,p2,n , ..., pn,1 , pn,2 , .., pn,n−1 }. Let R = P ∪ Q, if for consistency, we denote P = {p1,1 , ..., pn,n },then R = {p1,1 , ..., p1,n , ..., pn,1 , ..., pn,n }. Let E be the set of edges connecting each element of
R and V, where an edge (pi,j , vk ) ∈ E connects pi,j ∈ R and vk ∈ V. The modified maximum
weighted bipartite matching can be formulated as follows:
XMaxgijk xijk
(2a)
xijk ,θi,ijk ,θj,ijk(pi,j ,vk )∈E(E(πik )if i = jwhere : gijk =E(πijk ) = F (θi,ijk , θj,ijk ) if i ̸= js.t.

n Xv
X
j=1 k=1xîjk +n Xv
X

i=1 k=1nnXX

xiĵk −v
Xxîĵk ≤ 1 ∀ î = ĵ

(2b)
(2c)

k=1xijk ≤ 1 ∀k(2d)i=1 j=1

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G. Jiao, M. Ramezani

3xijk ∈ {0, 1}(2e)

θi,ijk , θj,ijk ∈ [0, 1](2f)

In Equation 2a, xijk is a binary decision variable on the edge (pi,j , vk ) ∈ E, with xijk = 1
indicating that the solo passenger pi (if i = j), or the passenger pair pi and pj (if i ̸= j) arematched to vk . Whereas, gijk is the weight of the edge, as shown in 2b, we let it be the expected
profit made by the platform under this particular arrangement. Thus, for a shared trip, gijk is afunction of θi,ijk and θj,ijk . Contrary to most maximum weighted bipartite matching problems,
where the weights of the edges are known, we formulated our problem such that each edge weightof shared arrangements is dependent on a set of decision variables, θi,ijk and θj,ijk . Note thatthe discount level has range between 0 and 1, as we assume the platform cannot charge more forthe shared trip than the original price, and it cannot give money to customers in shared trips.
Equation 2c and 2d are constraints that ensure each idle vehicle and unmatched passenger are
matched at most once.

3Results

We test the proposed dynamic discount method in an event based simulator. The simulator
depicts the road network in Manhattan New York as a directed graph. We use real passenger
demand data on a Monday from 7 - 9 am (2 hrs) and we assume there is a fleet of 4200 vehicles.
We consider benchmark scenarios where the platform offers a constant discount level for all
passengers matched in shared-trips. That is, for any given sets of unmatched passengers and∗∗= θ, where θ remains constant through each numerical= θj,ijk
idle vehicles, we assume θi,ijk
experiment, and instead of using expected profit as edge weight, we use the actual profit inEquation 2b. We conduct experiments for varying θ between the range from 0 to 0.5 (i.e. 0 to50% discount for sharing). It may be noted that under the benchmark setup, it is illogical for theplatform to offer passengers in shared trips at a discount of 50% or above, since it is always moreor equally profitable for the platform to just serve a solo trip at full price to one of the passenger
in a shared trip. Therefore, for θ ≥ 0.5, they are equivalently models of a platform that offers
ridesourcing services only. We compare the results of the benchmarks with the dynamic discountpricing strategy in Figure 1.

4Discussion

Figure 1a shows the total number of passengers that were notified with shared trips at varying
benchmark levels of θ, and correspondingly the passengers’ acceptance rate. At low levels ofdiscount, the platform is more likely to find shared trips more profitable than solo trips, hence
more passengers will be matched in shared trips. However, it is intuitive that when the discountis low, only a small fraction of passengers will accept the shared trips. As the discount level
increases, shared trips become less profitable, and thus fewer shared trips will be organized by
the platform, but a larger portion of passengers in those shared trips would accept. Consequently,
the total number of shared trips are shown in Figure 1b.
Figure 1b - 1f are the performance measures that we compare the benchmarks to the dynamic
discount pricing strategy. Figure 1c shows the total profit made by the platform during eachexperiment. Figure 1d shows the total number of cancellations by the passengers as a result ofundesired quality of service. We considered that if a customer cancels, there is a probability
they defect to other platforms and thus leading to a long-term loss. Therefore, we deduced
that each cancellation translates to roughly $4 long-term loss (e.g. based on 10-year customerprofit) for the platform, and adjusted the total profit in Figure 1e. If we assume that for thebenchmark, the platform adopts the constant 20% discount level which maximizes long term
profit (see Figure 1e). Then, the dynamic discount pricing strategy generates 12.9% more profit,
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4

20000

100%No. Passengers Notified% Passenger Accepted

60%

10000
40%
5000

20%030002000

0%048000

44000
0%

5%

10% 15% 20% 25% 30% 35% 40% 45% 50%

0%5%

10% 15% 20% 25% 30% 35% 40% 45% 50%

θ(b) No. of Shared Trips

5900

4400
3900
3400
2900

Fixed Discount
Dynamic Discount

40000

Adjusted Profit ($)

4900

38000
36000
34000
32000
30000
28000
26000

2400
10% 15% 20% 25% 30% 35% 40% 45% 50%

θ(d) No. Cancellations(c) Total Profit
95%

42000

Fixed Discount
Dynamic Discount

5400

θ

Weighted Vehicle Occupancy Rate(a) Shared Trips Notified & %Accepted

No. Total Cancellations

50000

46000

θ

5%

Fixed Discount
Dynamic Discount1000

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%0%

52000

Fixed Discount
Dynamic DiscountTotal Profit ($)

15000

No. Shared Trip

4000
80%

Shared Trip Rejection Rate

No. Passengers Notified with Shared Trip

G. Jiao, M. Ramezani

90%

Fixed Discount
Dynamic Discount85%80%

75%70%
0%5%

10% 15% 20% 25% 30% 35% 40% 45% 50%

θ(e) Adjusted Profit

0%5%

10% 15% 20% 25% 30% 35% 40% 45% 50%

θ(f) Weighted Vehicle Occupancy RateFigure 1 – Results of constant discount scenarios (Blue) and the results of the dynamic discountpricing strategy (Red). The X axis corresponds to the varying benchmark levels of the constantdiscount, θ, which is not associated with the dynamic discount pricing strategy.
reduces the number of cancellations by 30.3%, and improves the adjusted profit by 32.6%, while
conducting 30.6% more shared trips.
We also introduced a weighted vehicle occupancy rate (WVOR), where the time a vehicle
has two passengers on board are weighted twice as when there is only one passenger. The results
are shown in Figure 1f, and the dynamic discount pricing strategy increases the WVOR by
6.4%. Therefore, we show that the adoption of the dynamic discount pricing strategy creates
substantial economic benefit for the platform in both the short and long term, and improves thefleet efficiency and thus generates positive externalities for the society.

References
Anair, Don, Martin, Jeremy, Moura, MCP, & Goldman, Joshua. 2020. Ride-Hailing’s Climate Risks:
Steering a Growing Industry toward a Clean Transportation Future. Cambridge, MA: Union of Concerned Scientists.
Barrios, John M, Hochberg, Yael V, & Yi, Hanyi. 2020. The cost of convenience: ridesharing and traffic
fatalities. 2018. URL: http://yael-hochberg.com/assets/portfolio/BHY.pdf.
Schaller, Bruce. 2017. Empty seats, full streets: Fixing manhattan’s traffic problem. Schaller Consulting,1(3), 1–27.
Xu, Yiming, Yan, Xiang, Liu, Xinyu, & Zhao, Xilei. 2021. Identifying key factors associated withridesplitting adoption rate and modeling their nonlinear relationships. Transportation Research Part
A: Policy and Practice, 144, 170–188.

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Original abstract submittal