Evolution of labour supply in ridesourcing

Figures & data

Figure 1. Conceptual framework of the proposed dynamic ridesourcing model, including references to subsections in which a particular submodel is explained.

Table 1. Scenario design.

Label	N (–)	$W_d$ (€)	$(-)$	π (-)	$C_d$ (€)
DP200	200	80	0.2	0.25	20
DP400	400	80	0.2	0.25	20
DP600	600	80	0.2	0.25	20
DP800	800	80	0.2	0.25	20
DP1000*	1000	80	0.2	0.25	20
RW50	1000	50	0.2	0.25	20
RW60	1000	60	0.2	0.25	20
RW70	1000	70	0.2	0.25	20
RW80*	1000	80	0.2	0.25	20
RW90	1000	90	0.2	0.25	20
RW100	1000	100	0.2	0.25	20
RW110	1000	110	0.2	0.25	20
HR0*	1000	$\mathcal{N}$(80,0)	0.2	0.25	20
HR10	1000	$\mathcal{N}$(80,10)	0.2	0.25	20
HR20	1000	$\mathcal{N}$(80,20)	0.2	0.25	20
HR30	1000	$\mathcal{N}$(80,30)	0.2	0.25	20
IV005	1000	80	0.05	0.25	20
IV010	1000	80	0.1	0.25	20
IV020*	1000	80	0.2	0.25	20
IV050	1000	80	0.5	0.25	20
IV100	1000	80	1.0	0.25	20
CF5	1000	80	0.2	0.05	20
CF15	1000	80	0.2	0.15	20
CF25*	1000	80	0.2	0.25	20
CF35	1000	80	0.2	0.35	20
CF45	1000	80	0.2	0.45	20
CF55	1000	80	0.2	0.55	20
RC0	1000	80	0.2	0.25	0
RC10	1000	80	0.2	0.25	10
RC20*	1000	80	0.2	0.25	20
RC30	1000	80	0.2	0.25	30
RC40	1000	80	0.2	0.25	40

*Reference scenario

Table 2. KPIs in equilibrium for all scenarios.

Label	Informed drivers	Registered drivers	Participating drivers	Expected income, mean (€)	Expected income, std. among drivers (€)	Experienced income, mean (€)	Experienced income, std. among drivers (€)	Satisfied requests (%)	Average waiting time (s)	Daily platform profit (€)	Convergence criterion satisfied (day)
DP200	200	198	125	85.96	10.49	89.36	19.93	100.0	162.8	5217	47.0
DP400	400	301	136	77.56	10.62	82.25	20.75	100.0	153.6	5217	58.8
DP600	600	350	140	75.04	10.57	80.38	21.15	100.0	151.1	5217	68.2
DP800	800	377	142	73.79	10.77	79.48	20.85	100.0	150.5	5217	61.3
DP1000	1000	425	145	71.83	10.29	77.58	21.47	100.0	148.8	5217	64.8
RW50	1000	572	228	45.11	11.38	51.19	21.27	100.0	127.0	5351	58.1
RW60	1000	504	192	54.17	11.33	60.63	22.49	100.0	137.7	5351	68.5
RW70	1000	454	167	63.34	11.21	69.41	22.02	100.0	145.5	5351	62.0
RW80	1000	422	147	72.42	11.03	78.36	21.51	100.0	153.5	5351	64.2
RW90	1000	396	133	81.53	10.81	86.49	21.92	100.0	164.2	5351	74.2
RW100	1000	368	118	90.98	10.21	96.56	20.89	100.0	185.3	5351	75.8
RW110	1000	339	106	100.33	9.76	105.14	17.58	99.7	227.9	5334	71.0
HR0	1000	398	143	71.56	13.62	78.98	23.22	100.0	152.8	5230	70.0
HR10	1000	382	149	67.46	14.23	75.76	24.07	100.0	149.2	5230	55.4
HR20	1000	393	168	60.95	14.01	67.51	24.12	100.0	138.0	5230	52.4
HR30	1000	410	188	55.43	14.49	60.56	22.90	100.0	130.5	5230	53.6
IV005	1000	401	158	70.36	10.67	72.51	22.33	100.0	150.0	5312	56.5
IV010	1000	415	148	72.86	10.32	77.48	20.77	100.0	155.8	5312	60.3
IV020	1000	432	137	74.15	10.30	83.11	20.94	100.0	161.3	5312	65.5
IV050	1000	482	125	75.86	10.63	90.79	21.00	100.0	173.8	5312	68.5
IV100	1000	538	120	77.67	10.51	93.86	20.70	100.0	176.9	5312	91.7
CF5	1000	472	181	73.23	16.91	85.61	30.94	100.0	129.2	1042	56.4
CF15	1000	441	163	72.95	13.11	82.15	25.47	100.0	137.5	3125	62.4
CF25	1000	400	144	72.85	10.24	77.94	20.29	100.0	148.0	5195	72.6
CF35	1000	356	120	72.25	7.61	75.25	14.24	100.0	166.1	7265	73.4
CF45	1000	240	70	70.70	3.88	72.04	8.26	86.7	363.3	7962	77.0
CF55	1000	52	11	67.03	2.08	67.29	4.14	16.9	194.1	1751	18.4
RC0	1000	885	168	62.52	10.73	69.30	22.75	100.0	143.4	5394	68.3
RC10	1000	632	157	66.57	10.95	74.35	21.72	100.0	148.6	5388	63.0
RC20	1000	429	149	72.12	11.19	78.13	20.49	100.0	152.9	5384	68.7
RC30	1000	287	138	78.87	11.08	84.04	20.53	100.0	158.0	5384	60.0
RC40	1000	205	128	85.84	11.24	89.75	19.09	100.0	164.1	5383	55.7

Figure 2. (a) The evolution of the number of registered, informed and participating drivers, (b) the evolution of the average expected and experienced income, and (c) the distribution of expected income for participating drivers versus registered drivers in equilibrium.

Figure 3. The effect of the size of the driver pool on the evolution of (a) the expected income of registered drivers as ratio of their reservation wage, (b) the share of requests that are satisfied, (c) the average waiting time for pick-up for travellers, (d) daily participation volumes, (e) the total number of registered drivers, and (f) the share of registered drivers that participate.

Figure 4. The effect of (homogeneous) reservation wage on the evolution of (a) the expected income of registered drivers as ratio of their reservation wage, (b) the share of requests that are satisfied, (c) the average waiting time for pick-up for travellers, (d) daily participation volumes, (e) the total number of registered drivers, and (f) the share of registered drivers that participate.

Figure 5. The effect of heterogeneity in reservation wage on (a) the evolution of the average expected income of registered drivers as ratio of their reservation wage, (b) the evolution of the total number of registered drivers, (c) the evolution of daily participation volumes, (d) the probability density function of reservation wage for registered drivers, (e) the evolution of average experienced income of participating drivers as ratio of their reservation wage and (f) the evolution of the average waiting time for pick-up for travellers.

Figure 6. The effect of the valuation of income in participation choice on (a) the evolution of the average expected income of registered drivers as ratio of their reservation wage, (b) the evolution of average experienced income of participating drivers as ratio of their reservation wage, (c) the evolution of daily participation volumes, (d) the probability density function of expected income (as ratio of their reservation wage) for registered drivers, (e) the evolution of the total number of registered drivers and (f) the evolution of the average waiting time for pick-up for travellers.

Figure 7. The effect of platform commission rate on the evolution of (a) expected income of registered drivers as ratio of their reservation wage, (b) the share of requests that are satisfied, (c) the average waiting time for pick-up for travellers, (d) daily participation volumes, (e) the total number of registered drivers, and (f) daily platform profit.

Figure 8. The effect of registration costs on the evolution of (a) the total number of registered drivers, (b) daily participation volumes, (c) average experienced income of participating drivers as ratio of their reservation wage, (d) the average expected income of registered drivers as ratio of their reservation wage, (e) average experienced income of participating drivers as ratio of the sum of their reservation wage and daily share of registration costs and (f) the average waiting time for pick-up for travellers.

Figure 9. Optimality of supply in a system with fare-based driver payouts (assuming a platform commission rate of 25%) and a system with wage-based driver payouts, for (a) the service provider, aiming at maximum profit, (b) the traveller union, minimising costs from waiting and rejected requests, (c) the driver union, maximising driver earnings over the reservation wage, and (d) an authority that evaluates the three previous objectives equally, maximising the summed net value.

Figure 10. The effect of the rate of learning on (a) the evolution of the average expected income of registered drivers as ratio of their reservation wage, (b) the probability density function of expected income (as ratio of their reservation wage) for registered drivers, (c) the evolution of daily participation volumes, (d) the evolution of average experienced income of participating drivers as ratio of their reservation wage, (e) the evolution of the average waiting time for pick-up for travellers and (f) the evolution of the total number of registered drivers.

Figure 11. The effect of the information transmission rate on the evolution of (a) the number of informed agents, (b) daily participation volumes, (c) the average expected income of registered drivers as ratio of their reservation wage, (d) the average waiting time for pick-up for travellers, (e) platform profit and (f) the total number of registered drivers.