Day-to-day Supply Side Evolution of Ride-Sourcing

Abstract

2 In contrast to more traditional transit services in which the service provider employs drivers and thus has full 3 control over supply, ride-sourcing supply is the result of a decentralized participation decisions by self-employed 4 drivers, that each day decide to work for a ride-sourcing platform or not. Research on the dynamics of supply 5 in ride-sourcing is scarce. One of the few works in this field has modeled the choice to work on a day based on 6 expected income with a binary threshold, in which drivers are dependent on the experiences of others to decide 7 to start working again after opting out. This study introduces an agent-based probabilistic participation 8 choice model to account for the stochasticity to which drivers are exposed in daily ride-sourcing operations. 9 The logic behind this is that when drivers expect earnings to be under a minimally desired reference income, 10 they are aware of the fact that there is also a positive probability of having an income above the reference, and 11 vice versa. With a day-to-day learning model, in which drivers weigh their latest and all previous experiences, 12 we aim to find whether decentralized fleet evolution in ride-sourcing leads to an optimal fleet on a system 13 level, considering the perspective of service providers, transit authorities and the community of drivers. The 14 approach is applied to the road network of Amsterdam, with a maximum available fleet of 200 drivers and 15 artificial demand. We find that decentralization in ride-sourcing supply can lead to oversupply, with high 16 system costs and a low income for drivers. In addition, we conclude that the starting expectation of drivers 17 does not have an affect on emergent supply.

19 Keywords: Ride-sourcing, decentralization, participation choice, fleet planning, day-to-day learning

1 1 Introduction 2 One of the main motivations for drivers to work for ride-sourcing platforms is the flexibility offered by 3 these platforms in terms of their supply of labour (Hall & Krueger, 2018; Ashkrof et al., 2020). Because these 4 drivers are self-employed, they can make daily decisions on whether to work (in labour theory also called 5 ’participation choice’) and if so, decide on their working hours (Wang & Yang, 2019). Both types of labour 6 decisions have an impact on the service supply that is, at a specific moment in time, offered by a ride-sourcing 7 platform. Ride-sourcing platforms have instruments to steer supply, such as surge pricing and setting the 8 commission fee charged. Notwithstanding, their control under the gig-economy model is limited compared to 9 a system where the daily vehicle schedule is centrally planned. 10 Previous research that investigated the effect of daily participation choices on service supply (Banerjee et 11 al., 2015; Djavadian & Chow, 2017; Taylor, 2018; Bai et al., 2019) has assumed that drivers participate in a 12 platform only when their expected earnings for a given day exceed their reservation wage. The latter is defined 13 in the labor choice literature as the minimum daily income for which people are willing to work (Franz, 1980), 14 thus representing the opportunity cost of working. With drivers’ participation decisions modelled using a fixed 15 threshold, past studies do not allow for incorporating earning uncertainty in drivers’ daily participation choice. 16 Uncertainty can follow from day-to-day stochasticity in ride-hailing operations that result from variations in 17 supply and demand. Cachon et al. (2017) and Gurvich et al. (2019) constitute the first attempts to capture 18 the effect of uncertainty in ride-hailing operations on participation choice. In these studies drivers at the start 19 of each day draw an estimation of the expected supply and demand conditions for that given day from a 20 probability distribution, which is then used to determine their daily expected income. These studies assumed 21 that drivers opt out from the platform when their expected income is lower than a pre-defined threshold. 22 Day-to-day variability in driver’s earnings may lead drivers to choose with a certain probability to work 23 on a given day even if the expected value of the earning distribution falls short of the earning target. To 24 this end, we propose in this study a probabilistic participation choice model to represent supply elasticity 25 under uncertainty. We integrate this day-to-day learning choice model in an agent-based simulation model 26 which represents ride-hailing operations including within-day traffic and demand variability. We investigate 27 the effect of decentralized supply of ride-hailing services by comparing the fleet of active drivers obtained in 28 equilibrium with the optimal, centrally set, fleet size for service providers, transit authorities and ride-sourcing 29 driver unions that represent drivers collectively. 30 Furthermore, we examine the effect of the starting income expectation on the ride-sourcing supply 31 equilibrium, which has not been done before. Our day-to-day driver participation approach is applied to a 32 relatively large case study in Amsterdam with up to 200 drivers, compared to 20 in previous day-to-day works.

33 2 Methodology 34 Agent-based models are typically used to investigate emerging system effects from (potentially complex) 35 strategies of individual agents (Abou-Zeid et al., 2013). Its bottom-up approach is suitable for modelling 36 supply side ride-sourcing adoption, since ride-sourcing systems are decentralized in the sense that self-employed 37 drivers can make individual and independent working choices, which will jointly determine to the fleet size on 38 the system level. 39 Our agent-based approach consists of a few elements, as shown in Figure 1. First, we model the participation 40 choice of ride-sourcing drivers on a given day based on the income that they expect to earn on this day 41 (explained in more detail in Subsection 2.1). The outcome of the probabilistic participation choice model 42 determines the ride-sourcing supply on this day, which we use as input in a within-day ride-hailing operations 43 model (2.2). This model not only determines the level of service for travellers but also yields individual driving 44 experiences for drivers (2.3). Those in turn will update their expected income based on their experienced 45 income, if they decided to work. The day-to-day learning model (2.4) specifies how drivers weigh their last 46 driving experience compared to the experience accumulated over all previous days. 47 This section also includes a description of the simulation stopping criterion (2.5), the main key performance 48 indicators (2.6) and the model implementation (2.7).

Figure 1: Overview of the methodology with a reference to the subsections that explain the respective parts of the approach in more detail

1 2.1 Participation choice 2 Similarly to Banerjee et al. (2015), Taylor (2018) and Bai et al. (2019), we assume that drivers’ decision on 3 whether to join the platform on a given day or not depends on their reservation wage. Notwithstanding, drivers 4 experienced income might be higher than their expected income, resulting from stochasticity in within-day 5 ride-hailing operations and the participation choices of other drivers. Consequently, in our model, a driver’s exp 6 participation choice has a probabilistic element. Based on driver’s expected income Id,t we determine the 7 probability of driving on a given day using the Logit model, in which the utility of driving is tested against 8 the utility of not driving, which is represented by driver’s reservation wage Idres , i.e. opportunity cost. The 9 parameter βI determines the degree of randomness in the participation choice model, and thus represents the 10 extent to which drivers are willing to try their luck when their expected income is below their reservation 11 wage. 12 The utility of working (w) and not working (n), respectively, for a driver d on day t, is specified as follows: w exp Ud,t = βI · Id,t +ε (1)

n Ud,t = βI · Idres + ε (2) 13 The corresponding probability of working (wd,t = 1) and not working (wd,t = 0) on day t is: w exp(Ud,t ) P (wd,t = 1) = w n ) (3) exp(Ud,t ) + exp(Ud,t

P (wd,t = 0) = 1 − P (wd,t = 1) (4)

14 2.2 Within-day operations 15 A simple ride-hailing matching algorithm is adopted in which pending requests are assigned to available 16 drivers based on the minimum time required for a driver to reach a request. Formally, assignment takes place 17 whenever there exists both a queue of pending drivers Qdriver and a queue of pending requests Qreq :

arg min ttd,r (5) r∈Qreq ,d∈Qdriver

18 In this study, drivers do not re-position, i.e. they remain idle at their last drop-off location until assigned 19 to a new request.

20 2.3 Experienced income 21 Self-employed drivers who offer their labour to ride-sourcing platforms do not receive an hourly wage, but 22 rather make earnings based on the requests that they serve. Commonly, they receive the ride fare minus a 23 commission fee π for each satisfied request. Assuming that the fare is comprised of a base fare fbase and a 24 per-kilometer fare fkm , the payout to driver Pr for serving a single request is:

Pr = (fbase + fkm · sr ) · (1 − π) (6) 1 The total payout to driver d on a specific day t is then the sum of the payouts from all requests that are 2 served by this specific driver on this day. Defining ar,d,t as a binary variable indicating whether driver d picks 3 up request r on day t, we can formulate driver’s daily payout as follows: X Pd,t = Pr · ar,d,t (7) r∈R

4 Since freelance drivers have to cover for their own capital and operational costs, we have to subtract these 5 costs from their payout to obtain drivers’ daily income. In this study, we limit ourselves to variable costs, i.e. 6 fuel, depreciation and maintenance costs, which we define with parameter okm . The total operational costs 7 Od,t of a driver on a specific day are formulated as follows: X Od,t = ( sr · ar,d,t + DHd,t ) · okm (8) r∈R

8 in which DHd,t indicates a driver’s deadheading distance. The (actual) income of a driver d on a day t is: act Id,t = Pd,t − Od,t (9)

9 2.4 Day-to-day learning 10 As stated earlier, the participation choice for a driver is dependent on the expected income for a given day. exp 11 We assume that drivers assess what they expect to earn at the start of a day (Id,t ) by integrating their latest act exp 12 experienced income from the previous day Id,t−1 into their accumulated experienced Id,t−1 , except if they 13 were not active on the previous day. The parameter κ represents how much value a driver attaches to the last 14 experienced income as opposed to the expected income at the start of the previous day, which encompasses 15 the driver’s experiences from all past days. This corresponds to a reinforced learning Markov decision making 16 process. The expected income of a driver for a specific day is thus defined as follows: ( exp exp (1 − (Ed,t )−κ ) · Id,t−1 + (Ed,t )−κ · Id,t−1 act wd,t−1 = 1 Id,t = exp (10) Id,t−1 wd,t−1 = 0 17 in which Ed,t is defined as the number of days during which the driver gained a driving experience: X Ed,t = wd,i (11) i∈{1,...,t−1}

18 If κ is equal to 1, a driver weighs all his previous experiences equally. If lower, more value is given to his 19 latest experience. Note that in contrast to the work of Djavadian and Chow (2017), the value drivers attach 20 to their latest experience as opposed to all previous ones is not constant but rather dependent on the number 21 of experiences, which is arguably more likely to mimic learning behaviour in reality.

22 2.5 Stopping criterion 23 The fleet size of a ride-sourcing platform on a given day is the outcome of a random process. The simulation 24 is terminated when the degree of learning expected income for all drivers has become fairly limited, which 25 means that the expected fleet size also has converged. More specifically, the simulation is terminated when 26 the following condition is first met: exp exp |Id,t+1 − Id,t | exp ≤ϕ ∀d ∈ D (12) Id,t 27 and the convergence parameter ϕ is set to approach 0.