An Auction Based Mechanism for On-Demand Transport Services

Transcription

1 An Auction Based Mechanism fo On-Demand Tanspot Sevices Malcolm Egan, Ni Oen and Michal Jakob Abstact Recently, a new class of tanspot sevices, exemplified by Ube and Lyft has emeged. Such sevices use vey diffeent picing mechanisms when compaed to taditional taxis, and in this pape we chaacteize such sevices though a new agent based model, and identify a auction-based one-shot picing mechanism fo such a model which is optimal unde specific assumptions. This mechanism assumes only statistical knowledge of passenge pefeences, and uses a stategypoof elicitation of dive pefeences. We demonstate the popeties of ou mechanism including the tadeoff between pofit and efficiency, and analyze the effect of impefect infomation fo the company. Finally, we show - though simulation - that ou model yields moe pofit than taditional taxi sevices. 1 Intoduction An on-demand tanspot sevice ODTS) is one which does not follow a fixed schedule, instead poviding tanspotation in esponse to a passenge equest. Taxis ae the most common instantiation of such a sevice. Recently howeve, a new beed of on-demand tanspot sevice has emeged, as exemplified by companies such as Ube and Lyft [9]. Thei gowing populaity suggests that they have a competitive advantage ove othe taxi-like sevices. Any ODTS must be able to oute vehicles; decide which vehicle should be allocated to which passenge and when); pice passenges; and pay dives. Taditional taxi sevices pefom these functions though a mix of egulation, cental scheduling, o ad-hoc techniques. Such appoaches ae amenable to standad optimisation techniques [1; 7; 11; 4; 8; 5], but implicitly assume that passenges and dives will accept all jouneys they ae offeed. The poblem thus becomes one of matching passenges to dives in a way that minimises costs, waiting times by passenges) and dive idle times. Univesité Blaise Pascal, Fance. malcolm.egan@gmail.com Univesity of Abedeen, UK. n.oen@abdn.ac.uk Czech Technical Univesity in Pague, Czech Republic. michal.jakob@agents.fel.cvut.cz Unlike taditional ODTSs, moden sevices exploit passenge willingness to pay moe fo tanspotation at cetain times. Thus, the assumption of all jouneys being accepted no longe holds, and existing optimisation appoaches do not wok well fo such sevices. Instead, given that passenges do not eveal and often do not know) the maximum pice they ae pepaed to pay fo a jouney, picing must be based on a passenge model by analysing the lage amounts of tip infomation that ODTSs have collected. The fundamental question this pape theefoe seeks to answe is how should an ODTS be piced when both dives and passenges have pefeences ove tip costs. In answeing this question we make two distinct contibutions. Fist, we intoduce an agent-based ODTS model efeed to as the boke model which maximises the boke s pofits based on the pivate pefeences of passenges and dives. Within this model, we assume that only statistical infomation about passenge pefeences is available potentially obtained via data mining as done by existing ODTSs), and that the system has no access to dive pefeence infomation. Second, we popose a picing mechanism to solve these poblems in the boke model, consisting of two phases: 1) passenge picing and outing; and 2) passenge scheduling, and dive selection and payment. To optimize 1), we exploit statistical passenge pefeence infomation. Phase 2) is pefomed via an auction, poviding a means of simultaneously eliciting dive pefeences and selecting the dive, while optimizing pofit. In the next section we descibe ou agent-based system model. Following this, we popose a maket mechanism fo optimally picing a single jouney via ou model. Section 4 analyses some of ou solution s popeties, while Section 5 evaluates the mechanism though simulation. 2 Agent-Based System Model In ode to develop ou maket mechanism fo the boke model, we equie agent-based models fo passenges, dives, and the boke. To this end, we conside an ondemand tanspot netwok consisting of a boke, K dives and thei vehicles that can sevice a single ode at a time i.e., ideshaing is not suppoted), and N passenges which ente the netwok at diffeent times). In this section we descibe ou agent model fo passenges, dives and the boke.

2 In ou model, a passenge equests pick-up and dop-off location, which ae epesented by elements fom the set of vetices V in the diected gaph G, which in tun epesents the undelying oad netwok. As such, the set of edges E in G epesent diect outes between locations in V, which ae tavesed by the vehicles. Associated to each edge e E ae: 1. a stat location u V ; 2. an end location w V ; 3. a cost c e [0, ) fo a vehicle to tavese edge e E, due to fuel consumption, and vehicle wea and tea, etc.; 4. and an edge tavesal time τ e Z +. The edge cost c e and edge tavesal time τ e ae assumed to be computed off-line by solving the shotest path poblem between u and v on the undelying oad netwok. A new passenge entes the netwok when it makes a jouney equest to the boke, which fo passenge i consists of: 1. a pick-up location v i,p V ; 2. and a dop-off location v i,d V. 3. A maximum amount of time that they ae willing to wait fo a pickup. Note that passenges do not specify when they would like to be picked up, only how long they ae willing to wait. We assume that passenges wish to tavel immediately if possible), and thus ou mechanism opeates as a spot-maket. Ou mechanism will espond to a tavel equest by making the passenge an offe that they can accept o eject. We assume that this decision is based on a pivate maximum pice ate in, fo example, euos/km), witten i,max that epesents the uppe limit they will pay fo a jouney of unit distance. A passenge will then accept a jouney if offeed a pice ate i i,max, and eject it othewise. As an aside, we note passenges ae usually quoted a pice i R i fo a jouney, whee R i is the tip s distance, and that we theefoe assume a linea picing scheme 1. We model i,max as a andom vaiable, which is independent and identically distibuted i.i.d) fo each passenge i. This captues diffeences in pice-ate pefeences between passenges. In paticula, we assume that i,max is beta distibuted, with pobability density function 1 f i,max x ) = Bα, β ) 1 x x ) β 1 ) α 1 whee Bα, β ) = Γα)Γβ) Γα +β ) is the beta function, i,max has suppot [0, ]. The beta distibution was selected due to its flexibility. Using this distibution, we can captue a vaiety of scenaios, such as diffeent times of day simply by vaying the paametes α and β. Once passenge i accepts he jouney, each available dive bids fo the jouney descibed in detail in Section 3.1). 1 Non-linea picing schemes have been poposed [13; 14], but thei benefits have only been consideed whee total jouney pice is a function of R i o the dive commission-ate is not accounted fo. This is not the case in ou mechanism, as the pice-ate i can vay as discussed in Section 3). 1) The bid detemines dive j s commission-ate, η j. This commission-ate epesents the faction of evenue fom the passenge that the dive is willing to pay to the boke. As such, fixing η j detemines dive j s pofit fo the jouney, given by S j,i = 1 η j ) i R i c i 2) whee c i is the cost of tanspoting passenge i, given by c i = κ j R i +R j,i ) with κ j denoting the cost-ate in, fo example, euos/km) fo the dive and R j,i denoting the distance fom dive j s initial location to passenge i s pick-up location. In ode fo dive j to bid fo a passenge at commissionate η j, the jouney pofit must satisfy S min,j τ j 1 η j ) i R i κ j R i + R j,i ) 3) whee S min,j is the minimum pofit pe minute the dive will accept and τ j is the total duation of the jouney fom the dive s initial location to the passenge s dop-off). Impotantly, the minimum pofit pe minute, S min,j, is only known to the dive. The function of the boke is to pice passenges, and select and pay dives detailed in Section 3.1). In ode to pefom this function, the boke equies statistical knowledge of the maximum pice-ate, i,max, each passenge is pepaed to pay. As this infomation must be leaned, the distibution that the boke has will in geneal not exactly coespond the actual distibution of i,max, given by 1). As such, the pobability density function ˆf known to the boke is modeled by the Beta distibution; i.e., the same as 1), except with paametes α, β. The paametes α, β ae typically close, but not equal to the paametes α, β. 3 Picing Mechanism Design In this section, we descibe ou maket mechanism fo outing, scheduling and picing passenges, and selecting and paying dives in the boke model. A key featue of ou mechanism is that it uses the statistical knowledge of passenges pefeences and also elicits dive pefeences. Intuitively, using this additional infomation impoves the boke s pofit as well as the efficiency of the mechanism. In Section 5 we show that the boke model is, in ageement with this intuition, supeio to the standad dispatche model. 3.1 The Mechanism Ou mechanism consists of two phases: passenge outing and picing; and passenge scheduling, as well as dive selection and commission. In the fist phase, a new passenge equests a jouney, and negotiates the pice with the boke. The offeed pice is obtained by solving an optimization poblem exploiting statistical knowledge of the passenge s pefeences. In the second phase, dives ae selected and the commission-ate, η, is set via an auction. Phase 1: Passenge Picing Thee ae two stages to the picing negotiation between passenges and the boke: 1. Offe: The boke makes the passenge an offe, consisting of the pice of the jouney and an implicit commitment that a dive will aive within minutes.

3 2. Response: The passenge esponds by eithe ejecting o accepting the offe. Within the offe stage, the boke poposes a pice fo the passenge. This pice is the boke s goss pofit fo the jouney since a dive has not yet been selected, thei commission-ate is not yet taken into account by this pofit calculation), and the boke should thus maximise by computing the pice-ate as the solution to the following optimization poblem. whee ˆf) = ρmax maximize R i ˆfx)dx 4) subject to 0 ) α Bα, β ) ) β 1 5) Note that the optimal pice-ate will vay wheneve the distibution ˆf) changes. This may occu as passenge types change ove the couse of a day. In pactice, the boke will only make an offe to a passenge if thee ae dives which can aive to pick up the passenge within time. Howeve, thee is no guaantee that a dive, even if available, will agee to tanspot the passenge. If implemented, one could assume that the boke will efund the passenge if no dives can be found. Phase 2: Dive Selection and Commission-Rate In this phase, dives ae selected and the commission-ate is detemined. The key stages ae as follows. 1. Dive Identification: The boke identifies those dives able to each the passenge within time units Jouney Offe: The boke offes the jouney of passenge i to the dives. In paticula, the dive is infomed of the pice the passenge paid, i R i, the jouney distance, R i, and the jouney duation, τ i. The jouney distance and duation is computed stating fom the pick-up location of the passenge. The emaining paametes of Equation 3 can be computed fom this infomation. 3. Auction: The boke uns a sealed bid second pice auction [12, Chap. 11], whee each dive bids the maximum commission-ate η they ae pepaed to pay the boke, such that condition 3) is satisfied. A dive is only allowed to bid if η 0; i.e., the auction has a esevation η es = Dive Selection: The boke selects the dive with the highest bid. This dive eceives a pofit 1 η ) i R i c i, whee η is the value of the second highest bid. The mobility boke eceives the pofit η i R i. Dive selection and commission-ate detemination is built on a sealed bid second pice auction with a esevation pice. This auction has been chosen fo two easons. Fist, sealed bid second pice auctions ae Goves mechanisms [12, Chap. 10] dives have no incentive to bid untuthfully. 2 This filteing step potentially educes the numbe of dives needing to be consideed fo the emainde of this phase. Second, the auction only equies limited communication. In paticula, only a single bid is equied pe dive, saving both time and bandwidth. Scheduling is implicitly pefomed duing the dive selection phase, both duing the dive identification stage whee ineligible dives ae eliminated), and duing the auction phase, whee distant dives ae less likely to be chosen due to thei educed pofit fo the jouney. 3.2 Compaison with the Dispatche Model We now tun to the pefomance of ou mechanism and compae the boke s expected pofit with that of the dispatche in a taditional taxi sevice. The key featue of the dispatche model is that both the pice-ate and the commission-ate ae fixed. To pefom ou compaison, we seek the optimal piceand commission-ates fo this model. In the boke model, the maximum expected pofit is obtained by optimizing the following fo each passenge i. whee ρmax max max R i η j ˆfx)dx j J 6) subject to 0 S min,j τ j = 1 η j ) i R i κ j R i + R j,i ) 7) and J is the set of available dives. Note that ˆf) is the pobability density function fo the passenge types known by the boke i.e., paametized by α and β ). Fist, obseve that the ideal optimization poblem 6) cannot be solved diectly, as in ode to detemine the pice-ate, a dive must be selected and in ode to select a dive, the pice-ate must be set. In ou mechanism, 6) is decoupled: the pice-ate is fist optimized and then the dive is selected. We believe that this is a natual solution, as in ode fo the boke to negotiate with the dives, it is citical that thee is a jouney it can offe. On the othe hand, the dispatche in the dispatche model) sets the fixed pice and the commission ates by solving the optimization poblem 3 max η, E R,R 0 [ RηP )] Smin τ + cr + R 0 ) R max R R, R 0 1 η 8) whee R is the distance between the passenge s pick-up and dop-off, and R 0 is the distance fom the dive s initial location to the passenge s pick-up location. Note that the subscipts have been dopped as we ae aveaging ove all possible passenges and dives. Intuitively, this optimization poblem sets η and so that the pofit of the dispatche aveaged ove all possible jouneys is maximized; that is, pice and commission ates ae not adapted to each jouney. As fo the boke model, it is easonable to decouple this optimization poblem to fist set the pice-ate and then optimize the commission-ate 4. In paticula, the dispatche 3 Due to space constaints, and in ode to simplify the analysis, fom heeon, we assume that κ j = c fo any dive j. 4 A simila decoupling is used by sevices such as Liftago in Pague.

4 solves the two optimization poblems dis = ag max E R [RP max )] 9) and Smin τ + cr + R 0 ) η dis = ag max E R,R0 [ηp η 1 η )] R 10) In pactice, the fixed pice-ate dis and the commission-ate η dis in the dispatche model ae often chosen in an ad-hoc fashion o set accoding to outside egulations). Solving 9) and 10) instead will esult in a best-case optimized solution. The fomulations of the optimization poblems solved by the boke and dispatche claify the ole of the centalized financial and infomation exchanges at the boke. In paticula, the boke exploits explicit knowledge of R, R 0, S min via pefeence elicitation), and the pobability density function of i,max via data collection). In contast, the dispatche model elies on optimizing pofit aveaged ove R, R 0, S min, which does not account fo the unique paametes of evey jouney. Theefoe, the dispatche cannot adapt the pice- and commission-ates fo specific jouneys. 4 Pofit Analysis In this section, we analyze the expected goss pofit pe jouney i.e., the passenge s payment) fo the boke with diffeent passenge types, and when the pobability density function fo each passenge s maximum pice-ate is impefect i.e., when α, β diffe fom α, β in 1)). Moe pecisely, we analyze solutions to the optimization poblem in the fist phase of ou mechanism, descibed by 4). 4.1 Effect of Passenge Type The pobability density function of i,max can be viewed as epesenting the demogaphic o demand of the passenges, and plays a citical ole in detemining the boke s pofit. Unde the assumption that the boke has pefect knowledge of the pobability density function of i,max, we quantify the diffeence between the expected goss pofit unde two pobability density functions with paametes α = 1, β = β and α = 1, β = β, espectively 5. Theoem 1. 6 Conside two passenge types, with i,max distibuted accoding to Beta1, β) and Beta1, β ) on [0, ] with β, β > 2. Moeove, suppose that the mobility boke has pefect knowledge of the pobability density function of i,max. Then, the diffeence, E[S dif,g ], in the expected goss pofit pe jouney is given by ) E[S dif,g ] = β) 2 g 1 + β ; β ρ ) max β ) 2 g 1 + β ; β 11) 5 Space constaints limit ou analysis to these paametes, but the geneal tends hold fo moe geneal choices of α, β. 6 Poofs of theoems will be povided in a link to a sepaate technical epot following blind eviewing. whee gx; β) = 1 B1, β) 1 x)β 1 12) Figue 1 demonstates the effects of passenge type c.f. 11)). Hee, the diffeence in expected pofit gows apidly fo small inceases in β, but then slows down, causing a decease in pofit of aound 10% even fo lage diffeences in β. Note that changes in the value of will have a linea effect on the cuve s scale. Figue 1: Plot of the diffeence in expected pofit as β is vaied and β = 2.1, with = Effect of Impefect Infomation We now elax the assumption that the boke has pefect knowledge of the pobability density function i,max, bounding the expected loss in the boke s pofit pe jouney, E[L]. Theoem 2. Suppose that the actual pobability density function of i,max is Beta1, β) with suppot [0, ] and β > 2; howeve, the mobility boke uses the distibution Beta1, β ) with suppot [0, ] and β > 2 to pice passenges. Then, the loss in the expected goss pofit pe jouney due to impefect infomation is uppe bounded by E[L] 1 + β ) ) 1 β log 2 β + β β β 13) We demonstate the behaviou of this expected goss pofit loss uppe bound in Fig. 2. The loss uppe bound apidly inceases as β inceases, suggesting that it is impotant to accuately estimate the pobability density function of i,max used to pice passenges. As in Figue 1, 1 has a linea effect on these cuves. Having analyzed the effect of passenge types on the mobility boke s pofit, We now focus on the tension between pofit and efficiency in ou mechanism as the boke aises its pices, fewe passenges will make use of its sevices. We define efficiency E as E = PA p,d ) the pobability of the event that a passenge accepts an offe and that at least one dive bids fo the passenge in the second phase.

5 With the intoduction of X, we appoximate the optimization poblem in 14) to obtain Pappox = max RP max )PX R R) 18) The above povides useful insights into the tadeoff between the expected pofit pe jouney and efficiency, illustated in Fig The key featue hee is that the cuve foms a loop as the pice-ate inceases, efficiency and pofit peak befoe educing again. At a low pice-ate, no dives will accept a passenge; while at a high pice-ate, no passenges will accept a jouney. We also obseve that the pofitmaximizing pice-ate does not coespond to the efficiency maximizing pice-ate. As both factos detemine the boke s pofit, this tadeoff must be caefully accounted fo. Figue 2: Bound on the expected pofit loss as β is vaied, with = 1. Given this definition, we can conside the ole of the piceate on the pofit-efficiency tadeoff. Although the fist phase of ou mechanism optimizes the expected goss pofit pe jouney, the efficiency can be adjusted by changing the piceate. To impove the efficiency of the mechanism, we intoduce the notion of dive subsidies to ensue that dives have incentive to tanspot passenges with unpofitable jouneys. 4.3 The Role of the Pice-Rate The expected pofit optimization poblem that the boke desies to solve can be ewitten as max R 1 S ) min,j + cr 0 + R) P max ) {S min,j} R 14) Fom which we can obtain that P = max RP max ) S + C )P max ) 15) whee S is the minimum pofit, S min and C = cr+r 0 ) is the total cost fo the selected dive j. The effect of the dive supply on the pice-ate is thus to egulaize the optimization poblem. The subtacted tem in 15) esults in an optimal pice-ate that is highe than in the optimization poblem in 4), as dive pefeences ae explicitly accounted fo. To gain insight into the efficiency of ou mechanism, we conside the pobability that at least one dive accepts at pice ate. That is, thee exists a dive such that S min + cr + R 0 ) R 16) In paticula, we model the influence of jouney paametes via the andom vaiable X = S min + cr + R 0 )) 17) which is Beta distibuted with paametes α d, β d i.e., X has pobability density function given by 1), with α, β eplaced with α d, β d ). Expected Pofit Appoximation euos) Inceasing pice ate Efficiency Figue 3: Plot of expected pofit appoximation in 18) vs efficiency as the pice-ate vaies. Paametes ae: R = 1, = 1, α = 1, β = 1.1 and α d = 1, β d = Coping with Unpofitable Jouneys Efficiency is affected by the equiement that each dive eceive a minimum pofit fo each jouney see 3). As obseved in Fig. 3, this induces a loop in the pofit-efficiency cuve educing the pice-ate i.e., inceasing the pobability each passenges accepts) significantly educes total efficiency. Subsidies can be used to impove the pobability that a dive will be willing to sevice evey passenge that accepts. While an unbounded subsidy can make evey jouney pofitable fo at least one dive, in geneal the subsidy must be bound to ensue that highly unpofitable passenges ae not seviced and that the boke makes a pofit). To implement the subsidy, the esevation pice of the auction see Sec. 3.1) is modified. Instead of equiing η > 0 in each bid, the boke accepts negative bids; i.e., η > η es, whee η es < 0 is the new esevation pice. This inceases efficiency as dives with bids η = 1 S min + cr 0 + R) R < 0 19) 7 Note that the values of efficiency ae paamete dependent, thus, the values shown do not eflect system pefomance in pactice.

6 can still bid fo a jouney. To ensue that the mobility boke does not suffe a significant loss, the esevation pice η es R is bounded, thus bounding the subsidy. We investigate the choice of the subsidy paamete, η es, via simulations in the next section. 5 Evaluation: Simulation Results We now compae the behaviou of ou mechanism with the dispatche model via simulation. These simulations utilise the Mobility Sevices Testbed [3], which geneates ealistic passenge demand pofiles and uses locations in the Hague. Figue 4: Plot of expected pofit as the numbe of potential passenges vaies, fo two passenge types. Fig. 4 plots the expected pofit with N = 40, 60, 80, 100 passenges, fo both the boke and dispatche model as β which eflects passenge demand) is vaied. In the dispatche model, the taxi closest to the passenge is offeed a jouney and may efuse it). We note that a highe β can be intepeted as a lowe passenge demand. The numbe of vehicles is K = 30, the minimum pofit paamete S min,j = 0, waiting time = 10 minutes, the cost-ate is c = 1 euo/km, = 5 euos/km, and α = 1. As a compaison, we assume in the dispatche model, the pice-ate is dis = E[ max,i ] and commission-ate η dis = 0.2. The key obsevation is that ou mechanism fo the boke model has a highe expected pofit than the dispatche model fo both passenge types i.e., β = 1 and β = 3). Also obseve that thee is a significant diffeence in expected pofit between the passenge types. This is consistent with ou analysis in Theoem 1, illustated by Fig. 1, fo β > 2. η es Expected Pofit euos) Efficiency Table 1: Effect of subsidies on the expected pofit and efficiency. Table 1 shows the effect of subsidies i.e., vaying η es in Phase 2 of ou mechanism) on the expected pofit and the efficiency of ou mechanism. The paametes ae: N = 100 passenges; K = 30 dives; = 10 minutes; α = β = 1 and cost-ate c = 1 euo/km. These paametes ae consistent with eal-wold taxi opeating paametes. We also set the paamete S min,j as unifomly distibuted on [0, 5.4] euos/min, which contasts with ou expeiment in Fig. 4 whee S min,j = 0. This captues diffeences between dive pofit equiements see 3)), and also diffeences between the pofit equiements ove time fo the same dive. As the esevation bid, η es deceases, the expected pofit deceases while efficiency inceases. The eduction in pofit occus as the boke is potentially equied to pay the dive moe than the passenge paid fo the jouney. On the othe hand, the efficiency inceases as dives can be found to sevice even highly unpofitable jouneys. As Table 1 shows, using subsidies can significantly incease efficiency fom 0.29 to 0.51, while maintaining positive pofit). Also obseve that the pofit is negative when η es = 1, the boke must thus tune the esevation pice so that thee is a dive to sevice passenges while ensuing that its expected pofit is sufficient. 6 Discussion and Futue Wok We compae ou poposed model to a dispatche model athe than to a system such as Ube as such companies keep thei picing mechanisms secet. Ou esults show that the boke model geneates highe pofits than the dispatche model, validating the theoetical esults of Section 3.2, and potentially explaining the populaity of moden ODTSs. With egads to elated wok, passenge and vehicle pefeences have been consideed in the aea of demand-esponsive tanspot, whee ide-shaing is suppoted [10]. Howeve, in this appoach it is assumed that passenge picing pefeences ae known. Moeove, the total pofit is optimized via a combinatoial auction with no consideation of dive pefeences. Moe boadly in the tanspot domain, pefeence elicitation via auctions has been exploited to allocate aipot slots [2]. With egads to taxis and ODTSs, pivate passenge and dive pefeences have lagely been ignoed. Instead, pice pefeences and pofit equiements ae assumed to be known in the optimization of outing, scheduling and dive selection [1; 7; 11]. Notable exceptions ae in [6; 14], whee only statistical knowledge of passenge pefeences is assumed; howeve, individual dive pefeences wee not consideed. With egads to futue wok, this pape pices passenges individually local picing), and ignoes potential futue jouneys [14]. We ae investigating global picing mechanisms which optimise picing acoss multiple passenge equests and ove time. We ae also woking with a commecial ODTS to evaluate ou mechanism in pactice. 7 Conclusions In this pape we poposed the boke model fo ODTSs, and shown that this model yields highe pofits than the standad dispatche model. We have also shown that the model is sensitive to the boke s knowledge, and descibed how subsidies can be used to incease the system s efficiency.

7 Ou model schedules, outes and pices passenges, and selects and pays dives. It equies only a statistical model of passenge pefeences which can be obtained fom infomation eadily available to a ODTS), and elicits dive pefeences in a stategypoof manne. Finally, by filteing dives able to bid, ou model can addess scalability concens. Ou wok theefoe foms a sound basis fo ODTS picing. [13] H. Yang, C. Fung, K. Wong, and S. Wong. Nonlinea picing of taxi sevices. Tanspotation Reseach Pat A: Policy and Pactice, 445): , [14] C. Zeng and N. Oen. Dynamic taxi picing. In Poc. Euopean Confeence on Atificial Intelligence, Refeences [1] R. Bai, J. Li, J. Atkin, and G. Kendell. A novel appoach to independent taxi scheduling poblem based on stable matching. Jounal of the Opeational Reseach Society, 65, [2] L. Castelli, P. Pellegini, and R. Pesenti. Aipot slot allocation in euope: economic efficiency and fainess. Intenation Jounal of Revenue Management, 61), [3] M. Ceticky, M. Jakob, R. Pibil, and Z. Mole. Agentbased simulation testbed fo on-demand tanspot sevices demonstation). In Poc. Intenation Confeence on Autonomous Agents and Multi-Agent Systems AA- MAS), [4] J.-F. Codeau. The dial-a-ide poblem: models and algoithms. Annals of Opeations Reseach, 153:29 46, [5] C. Cubillos, F. Guido-Polanco, and C. Dematini. Madap: multi-agent achitectue fo passenge tanspotation systems. In Poc. IEEE Intenational Confeence on Intelligent Tanspot Systems, [6] M. Egan and M. Jakob. A pofit-awae negotiation mechanism fo on-demand tanspot sevices. In Poc. Euopean Confeence on Atificial Intelligence, [7] A. Glaschenko, A. Ivaschencko, G. Rzevski, and P. Skobolev. Multi-agent eal time scheduling system fo taxi companies. In Poc. Intenational Confeence on Autonomous Agents and Multiagent Systems AA- MAS), [8] M. Mes, M. van de Heijden, and A. van Haten. Compaison of agent-based scheduling to look-ahead heuistics fo eal-time tanspotation poblems. Euopean Jounal of Opeational Reseach, 1811):59 75, [9] L. Rayle, S. Shaheen, N. Chan, D. Dai, and R. Ceveo. App-based, on-demand ide sevices: compaing taxi and idesoucing tips and use chaacteistics in san fancisco. Univesity of Califonia Tanspotation Cente UCTC) Woking Pape. [10] S. Satunin and E. Babkin. A multi-agent appoach to intelligent tanspotation system modeling with combinatoial auctions. Expet Systems with Applications, 41: , [11] K. Seow, N. Dang, and D.-H. Lee. A collaboative multiagent taxi-dispatch system. IEEE Tansactions on Automation Science and Engineeing, 73), [12] Y. Shoham and K. Leyton-Bown. Multiagent Systems: Algoithmic, Game-Theoetic, and Logical Foundations. Cambidge Univesity Pess, 2009.