Angeloudis, P

Karamanis, R

Sivakumar, A

Stettler, M

English

Spiral - Imperial College Digital Repository

Market dynamics between public transport and competitiveride-sourcing providersRenos Karamanis ∗1, Panagiotis Angeloudis1, Aruna Sivakumar1, and Marc Stettler11Centre for Transport Studies, Imperial College LondonMarch 15, 20181 IntroductionRecent advances in communications and IT technology have underpinned the rapid development of trans-portation network companies (TNCs) in recent years [8]. Although the competitive prices offered by TNCshave been well-received by users, recent studies indicate that the resulting increase in public welfare [6] istemporary, as passengers are likely to be steered away from public transport. Indeed, a recent study by[5] has presented evidence that such shifts have already occurred and can be directly linked to increasedcongestion in major cities.Many studies in taxi pricing [e.g. 4, 9] have adopted an economic theory perspective, using aggregatedemand and supply models to represent the dynamics of urban taxi operations. Dynamic pricing hasalso been considered, for example by [7] who adopt a Vickrey-Clarke-Groves (VCG) bidding mechanismfor shared autonomous taxi rides to maximise social welfare. The impact of dynamic pricing to TNCoperations was investigated in [3], suggesting that a dynamic increase in trip price significantly increasesthe supply of rides in the system.However, the relationship between dynamic TNC pricing strategies and public transport provisionremains unexplored to this date. To address this issue, we propose a novel, game-theoretic, dynamicpricing model that accounts for multiple TNCs operating alongside public transport services. This isapplied to a city-wide service scenario, and compared to an alternative static pricing model that serves asa baseline. Finally, we perform a comparative analysis of expected utilities for travellers and operators,while monitoring mode share fluctuations across a range of competitive scenarios and market structures.2 Model DescriptionThe key actors in our model are two symmetric TNC firms offering an identical product (rides) of equivalentquality. A centralised platform receives ride requests from the public. Both firms are expected to respondto these requests, with quotes for service and estimates of anticipated wait and travel times. Travellerscan then decide (using a generalised costing mechanism) whether to accept an offer or to revert to publictransport.TNCs are expected to operate with a profit maximization objective and are allowed to introducesurcharges upon the base prices for each trip. These are based upon current demand levels, and a TNC’sperception on the ability of its competitors to serve a specific trip request. Using dynamic pricing, thefinal bid price is the sum of a variable base price r per time of travel set by the platform, and the TNC’schoice of an extra variable tariff per time of travel fi.∗Corresponding author: renos.karamanis10@imperial.ac.uk (R. Karamanis)1The price pi for company i is calculated using (1) and (2):pi = fi + r ∀ i (1)fi ∈ R+ ∀ i (2)The variable base price level r is set by the platform and assumed to apply to both firms. This dependsupon the number of available vehicles Qi for each firm i, and the total number of trip requests D currentlyin the queue. The minimum value of r, denoted r0, is the lowest value in the set C of marginal costs perunit travel time, with ci being the cost for each TNC i.We use equations (3), (4) and (5) to determine r, with α, β and γ determined through calibration:r = r0 +αβ(∑iQiD)2 + γ(3)r0 ≥ minC (4)D ∈ Z+, Qi ∈ N ∀i (5)Equation (3) stipulates that for high ratios of vehicle availability against demand, r approaches r0.Where very low availability levels are observed, the value of r approaches r0 +αγ. It is assumed thatfirms do not adjust their value of Qi at each request. Vehicle availabilities in our model are influenced bytraveller origins and vehicle proximities. As such, following from Bertrand competition [2], firms can onlycontrol bid values through fi.In turn, travellers in our model evaluate the utility of each company bid using a nested logit modelwith a degree of stochasticity to account for heterogeneity in traveller preferences. Customer utilities foreach modal options are calculated using (6) for TNC firms UTi and (7) for public transport UP :UTi = VTi + εTi = αi − β1 wi − β2 tT − β3 pi × tT + εTi ∀i (6)UP = VP + εP = −β1 wP − β2 tP − β3 pP + εP (7)where pP and wP are the price and waiting times for trips using public transport, wi is the waitingtime for firm i, tP and tT are the in-vehicle travel times via public transport and TNC respectively. Theparameter αi is used to represent the inherent preferences for the TNCs due to unobserved factors suchas comfort, brand image and trust. In turn, β1, β2 and β3 are random variables representing the marginaldisutility of waiting time, travel time and travel cost, and are assumed to vary across the client populationfollowing a normal distribution with standard errors σβ1 , σβ2 , σβ3 .The stochastic error terms εTi and εP are randomly distributed variables following a type 1 extremevalue distribution, which is the assumption underlying the nested logit model structure. The latter assumesa heightened correlation between the stochastic error terms for the TNCs (i.e. εTi) thus allowing for agreater elasticity between the TNC alternatives. The values of pP , wP , wi, tP and tT vary between clientsand depend on network characteristics and vehicle distributions across the network at the time of therequest.For the nested logit model choice probabilities are computed as follows for the high level choice of TNCT or public transport P [1]:P (b) =eµ Vbeµ VT + eµVP∀ b = {T, P} (8)Where µ is the scale of the stochastic error terms, assumed to be 1 between the high-level options(TNCs versus public transport). The probability of choosing one of the TNC firms is given by:P (Ti) = P (Ti|T )P (T ) ∀ i (9)P (T ) =eµ VTeµ VT + eµVP(10)VT = IVT is the inclusive value of the TNC nest and is calculated using equation (11):2IVT =1µTln[∑ieµT×VTi](11)Where µT is the scale of the error terms for the TNC options, which captures the heightened correlationbetween the different TNC choices as shown in equation (12):corr = 1−(µµT)2(12)The value of P (Ti|T ) is calculated using equation (13):P (Ti|T ) =eµT VTi∑nj=1 eµT VTj(13)For each trip request, the firms evaluate the probability of winning the bid based on the estimatedtraveller utilities for each option. Estimates are required as firms are not privy to the real value ofclient-specific parameters αi, β1, β2 and β3, nor the real values of their competitors wi. To estimate thetraveller utilities, each firm i uses random variables from the distributions of the parameters calibratedfrom observed behaviour, denoted as α̂i, β̂1, β̂2, β̂3, σ̂β1 , σ̂β2 , σ̂β3 and µ̂TNC . Firm i also uses an estimate w̄j,ifor the waiting time of firm j, weighted by firms i waiting time and their ratio of vehicle availabilities asshown in equation (14):w̄j,i = wi ×QiQj∀ i, j (14)Hence the estimate by firm i of the utility V̄j,i of choosing firm j to the customer in question is givenby equations (15), (16) and (17):V̄j,i = α̂i − β̂1 w̄j,i − β̂2 tT − β̂3 p̄j,i × tT ∀ i, j (15)p̄j,i = f̄j,i + r ∀ i, j (16)f̄j,i ∈ R+ ∀ i, j (17)Similarly, the estimate by firm i of the utility V̄i of choosing firm i to the customer and the estimateof the utility V̄P of choosing public transport to the same customer is given by equations (18) and (19)respectively:V̄i = α̂i − β̂1 wi − β̂2 tT − β̂3pi × tT ∀ i (18)V̄P = −β̂1 wP − β̂2 tP − β̂3pP (19)Firms choose the price of their bids to maximise their expected profit. Since the utility values used inthe probability calculations are estimates, so is the expected profit. For simplicity, we assume a scenariowhere only two TNCs operate. Hence, the expected profits E(P̄ rTi) and E(P̄ rTj,i), given the marginal costci per time of travel for each firm are:E(P̄ rTi) = P̄ (Ti | f̄j,i)× ((fi + r)− ci) ∀ i (20)E(P̄ rTj,i) = P̄ (Tj,i | fi)× ((f̄j,i + r)− cj) ∀ i, j (21)If a pair of values f ∗i and f̄∗j,i exists for which both E(P̄ rTi) and E(P̄ rTj,i) are maximised, this constitutesa Nash Equilibrium. Hence, the algebraical solution for the Nash Equilibria, if they exist, could be foundby solving the system of non-linear equations for fi and f̄j,i as defined in equations (22) and (23). Fixedcosts are not considered in equations (20) and (21) since they do not influence the choice of fi which isdefined by (22) and (23):∂(E(P̄ rTi))∂fi= g(fi, f̄j,i) = 0 ∀ i (22)3∂(E(P̄ rTj,i))∂f̄j,i= h(fi, f̄j,i) = 0 ∀ i, j (23)3 Expected ResultsThe Nash Equilibrium in the proposed model is expected to be different than the Bertrand model [2], whereequilibrium price is the marginal cost. This is due to allowing for variation in the inherent preference andwaiting times between TNCs. This variation gives the competitive advantage to the firm with the highestsum of the inherent preference and waiting time terms in equations (15) and (18) to set the equilibriumvalue of extra variable tariff above 0. We test the model for the presence of Nash Equilibria, solving thesystem of non-linear equations (22) and (23). Simulation is used to evaluate the impact of this model inrealistic network scenarios.References[1] M. Ben-Akiva and M. Bierlaire. Discrete Choice Methods and their Applications to Short Term TravelDecisions. pages 5–33, 1999.[2] J. Bertrand. Theorie Mathematique de la Richesse Sociale. Journal des Savants, pages 499–508, 1883.[3] M. K. Chen and M. Sheldon. Dynamic Pricing in a Labor Market: Surge Pricing and Flexible Work onthe Uber Platform. Ec’16: Proceedings of the 2016 ACM Conference on Economics and Computation,page 455, 2016.[4] G. W. Douglas. Price Regulation and Optimal Service Standards: The Taxicab Industry, 1972.[5] S. R. Gehrke, A. Felix, and T. Reardon. Fare Choices: A Survey of Ride-Hailing Passengers in MetroBoston. Technical report, MAPC, Boston, Massachusetts, 2018.[6] J. Horpedahl. Ideology Über Alles? Economics Bloggers on Uber, Lyft, and Other TransportationNetwork Companies. Econ Journal Watch, 12(3):360–374, 2015.[7] A. Y. Lam. Combinatorial Auction-Based Pricing for Multi-Tenant Autonomous Vehicle Public Trans-portation System. IEEE Transactions on Intelligent Transportation Systems, 17(3):859–869, 2016.[8] X. Qian and S. V. Ukkusuri. Taxi market equilibrium with third-party hailing service. TransportationResearch Part B: Methodological, 100:43–63, 2017.[9] H. Yang, S. C. Wong, and K. I. Wong. Demand-supply equilibrium of taxi services in a network undercompetition and regulation. Transportation Research Part B: Methodological, 36(9):799–819, 2002.4

Market dynamics between public transport and competitive ride-sourcing providers

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Market dynamics between public transport and competitive ride-sourcing providers

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