The structure of public-private sector collaboration in travel information markets: A game theoretic analysis

Transportation Research Part A 129 (2019) 19–38

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Transportation Research Part A journal homepage: www.elsevier.com/locate/tra

The structure of public-private sector collaboration in travel information markets: A game theoretic analysis

T

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Jianlin Luan , John Polak, Rajesh Krishnan Centre for Transport Studies, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom

A R T IC LE I N F O

ABS TRA CT

Keywords: Local traffic authorities In-vehicle route guidance service providers Data exchange collaboration Collaboration strategies Non-cooperative Nash game

In recent years there has been substantial growth in the prevalence of ad-hoc data exchange arrangements between local traffic authorities and commercial traffic information service providers. Although these arrangements are widely regarded as mutually beneficial, in fact to date, no comprehensive analysis exists of the operation of this information market, nor of its consequences for the different market participants involved. To address this gap, this paper presents a new framework which enables the analysis of the long-term outcomes of various collaboration schemes for traffic information service providers, local traffic authorities and network users. The framework is based on a bi-level non-cooperative Nash game in which the upper level represents the data exchange arrangements between local traffic authorities and commercial traffic information service providers and the lower level represents the impact of the provided information services on network users. The framework is flexible and can accommodate a variety of different market structures and commercial behaviours. The game theoretic model is formulated and solved as an equivalent equilibrium problem with equilibrium constraints. Numerical experiments are undertaken using this framework to explore the consequence of a number of commonly observed real-world data exchange arrangements. This analysis leads to three general conclusions. First, the results suggest that when a local traffic authority seeks only to minimise the total network travel time and offers free collaboration schemes, it should collaborate with all the cooperating service providers in the market. Second, if conversely, a local traffic authority seeks only to maximise its revenue from selling its data to service providers, it should be aware that its revenue does not always increase by selling the data to more service providers, since the willingness of service providers to pay for data declines as more providers are granted access. And finally, if a local traffic authority seeks to establish paid schemes that balance the benefit to network users and its own revenue benefits, then circumstances can easily arise in which these two objectives are in conflict with one another.

1. Introduction In-vehicle travel information services, such as dynamic route guidance, are provided by many different service providers (SP), the majority of which are commercial companies. The resulting information market shows considerable heterogeneity both in its technical aspects (e.g., the type and volume of data inputs used by different providers) and the business models employed by the market participants. In particular, while some service providers offer real-time route guidance service on a paid subscription basis

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Corresponding author. E-mail addresses: [email protected] (J. Luan), [email protected] (J. Polak), [email protected] (R. Krishnan).

https://doi.org/10.1016/j.tra.2019.08.001 Received 21 June 2018; Received in revised form 17 June 2019; Accepted 2 August 2019 Available online 13 August 2019 0965-8564/ © 2019 Elsevier Ltd. All rights reserved.

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(CoPilot, 2016; Garmin, 2016; TomTom, 2016), other SP provide the service free to consumers at the point of use (Google, 2016b; Waze, 2016c). Recently, some SPs in the market have started to collaborate with local traffic authorities (LAs) in order to obtain the LAs’ traffic data, in the expectation that this would enable them to increase their information quality and therefore their competitiveness. The most prominent example of such collaboration is the Connected Citizen Program (CCP) of Waze (2014). The CCP programme is an example of a free data exchange scheme, whereby Waze provides data collected from Waze users to LAs for free, in exchange for the traffic data collected by LAs, typically from existing infrastructure based sensing systems (Waze, 2014). It is claimed that this type of collaboration is beneficial to LAs since it has the potential for improving network performance through enabling the provision of better information to drivers (Stern, 2016). The fact that the total number of LAs participating in the CCP scheme has increased from 10 to 70 in less than two years (Waze, 2016b) indicates that the collaboration between LAs and SPs is both seen as attractive and may well become increasingly common in the future. In addition to free data exchange schemes, there is also an emerging model of paid data exchange schemes. In these, LAs seek to offset some or all of the capital and operating costs associated with their traffic data collecting infrastructures (e.g., inductive loop detectors and ANPR camera networks) by charging SPs a fee for their data. Although public-private sector collaboration in the field of in-vehicle travel information services is gaining traction in practice, the long-term implications of such collaboration schemes for LAs and for the structure of the travel information market are currently not well understood. For example, key questions such as: “given the heterogeneity of SPs, which type of provider is the best long-term choice for LAs to collaborate with and on what basis?” have not been systematically explored. To answer questions of this type it is necessary to create a modelling framework that both represents the structure and operation of the information market and the impact of the provided information services on individual travellers and aggregate transport system performance. To the best of the authors’ knowledge, such a framework does not yet exist. To address this gap, this paper, therefore, presents a modelling framework that can be used to investigate the long-term outcomes of different collaboration schemes and provide market participants, especially LAs, with guidance regarding the design of such information markets and the strategies to guide their participation in such markets. The framework accommodates three types of collaboration schemes –free schemes, where LAs and SPs exchange their data for free; paid schemes, where LAs sell their data to SPs for data charges; and mixed schemes in which free and paid arrangements coexist – and two types of SPs – those that offer users a free information service product and those that offer users a subscription-based service. The rest of this paper is organised as follows. Section 2 presents a conceptual framework for analysing the information market considered in this paper. This structure combines treatment of the competitive market behaviour of SPs, alternative arrangements for the participation of LAs in these markets and the impact of the provided information on traveller behaviour and transport system outcomes. Section 3 reviews relevant existing literature covering existing approaches to modelling some of the elements of the conceptual framework. Building on this review, Section 4 presents the mathematical formulation of the conceptual framework as a bilevel non-cooperative Nash game. Section 5 presents numerical results from the application of this framework and discusses the implications of these results for alternative collaboration schemes. The final section presents the overall conclusions and identifies future research directions. 2. Conceptual framework for the traveller information service market To understand the outcomes of alternative market structures and market behaviours on the part of SPs and LAs, we have developed a conceptual framework for the traveller information service market. This framework is presented in Fig. 1. The structure of the framework is defined by four fundamental market participants; (a) LAs who act as network managers and also collect traffic information typically using a dedicated sensing infrastructure, (b) collaborative SPs i.e., SPs that collaborate with the LA under either a free or paid scheme, (c) non-collaborative SPs i.e., those that do not collaborate and (d) a travel information market comprising network users who consume the traffic information products provided by SPs, on either a free or subscription basis, and can potentially be influenced in their travel choices by this information. In terms of the behaviour of the market participants, both types of SPs are assumed to be monetary benefit maximisers. In the case of SPs that do not require network users to pay a subscription fee, the SP is assumed to receive benefits by monetising user’s data through related channels and advertising (e.g., Google, 2016a; TeleNav, 2016; Waz, 2016a). SPs who charge a subscription fee are assumed to also monetise user’s data and so benefit from this as well as fee income. Both types of SPs are assumed to incur only operating costs that are principally related to the costs of acquiring traffic information from their own private sensing infrastructure and/or by crowdsourcing from their user base, other costs that are less relevant to the collaboration are not considered, such as information dissemination cost. Besides, it is assumed that SPs will not exchange information with each other. Travellers are assumed to be individual utility maximisers, with a utility that depends on the performance of the transport network in satisfying their travel demands. The LA is also assumed to be an optimising agent, where the objective of its optimisation varies according to whether it participates actively or passively in the information market, as elaborated further below. Although this structure is simple, we believe it captures the essential actors and their interactions. Despite its simple structure, the competitive dynamics in this market are complex. At the simplest level, since all SPs offer information service products to the same population of travellers, there is clearly a competition for market share between SPs. Beyond this, since both SPs and travellers are assumed to be individual optimisers, seeking to maximise their own financial benefit or utility, there is also, in effect, a benefit conflict between the SPs and population of travellers as a whole, for example, with a constant information quality, a SP pursuits higher revenue (e.g. via higher service charge) whereas travellers prefer a lower cost (e.g. via lower service charge). 20

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Fig. 1. Relationship between LAs, SPs and the traveller information market.

In addition, under different schemes, LAs’ collaboration choices interact with those of SPs and travellers in different ways. Under paid schemes, it is assumed that the objective of an LA is to only maximise the revenue it obtains from selling its data; hence, the relationship between LAs and SPs is naturally a supplier-buyer relationship. In this case, their collaboration choices (which SP to collaborate with and their data charge) have a direct impact on their own benefit. In contrast, under free schemes, LAs are assumed to optimise some measure of network performance as a whole (such as total travel time); hence, their benefit comes from the traveller information market. Moreover, the impact of LA’s usage of the data from SPs on network performance is not considered in this framework, as it is intractable to quantitatively model such impact because LA may use the data in totally different ways. Therefore, LAs’ collaboration choices only have an indirect impact on their benefit via SPs’ strategies (the information quality provided to drivers and service charges). Furthermore, since SPs only seek to maximise their own benefit, which does not necessarily lead to optimal network performance for travellers, LAs must require collaborative SPs to take into account overall network performance when they optimise their own monetary benefit. This implies that a collaborative SP becomes a market actor who seeks to simultaneously maximise the network performance and its own monetary benefit. For such SPs, their benefit maximisation problem is therefore naturally a multi-objective maximisation problem. To summarise, for modelling the outcomes of collaboration schemes, this framework should have four model components:

• The model of the response of traveller information market to collaboration schemes; • The model of the benefit conflict and interaction between an SP and travellers; • The model of the competition between SPs; • The formulation of multi-objective optimisation problems of collaborative SPs. 3. Literature review Since the issue of the collaboration between LAs and commercial in-vehicle route guidance SPs has not been widely addressed, the existing literature is limited. However, a number of the model components in our framework have been studied in the literature. Hence, in this section, we review relevant existing literature dealing with some of the specific model components identified in Section 2. 3.1. Response of the traveller information market A key step in modelling the benefit conflict and interaction between SPs and the traveller information market is modelling the response of the market to the strategies of the SPs, which is essentially the result of drivers’ choice behaviour under different strategies of information provision. The effect of information on travel behaviour has been studied in a wide variety of travel choice 21

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contexts (Chorus et al., 2006; Li et al., 2012; Zito et al., 2011) but the most extensively studied context is that of the route choice (Ben-Elia et al., 2013; Rapoport et al., 2014; Szeto and Lo, 2005; Yang, 1998). Two broad approaches have emerged. The first aims to directly model the cognitive impact of travel information e.g., through the selective acquisition of information and its impact on how travellers learn and update their perceptions of network performance (Jotisankasa and Polak, 2006, 2005). The second approach models the impact of information indirectly, typically through the use of random utility based discrete choice models in which the scale of the random error is interpreted as a measure of the information quality available to the traveller (Ben-Akiva et al., 1991). Models based on the direct representation of information acquisition and learning processes tend to be complex and do not lead themselves to tractable formulations of well-defined equilibrium states with respect to choice behaviour and network performance. By contrast, indirect approaches based on e.g., probit (Van Vuren and Watling, 1991) and logit formulations (Yang, 1998) can be embedded within the framework of stochastic user equilibrium (SUE) for which good understandings of equilibrium states and computation procedures are available (Huang and Li, 2007). The logit formulation based approaches, mainly applying the Multinomial Logit Model (MNL), has been extended to account for multiple types of choice behaviour associated with information provision, including the subscription choice behaviour (Lo and Szeto, 2001, 2002; Szeto, 2007; Yang, 1998), compliance with provided information (Oh et al., 2001; Yin and Yang, 2003) as well as closely related dimensions of choice behaviour, such as departure time choice (Szeto and Lo, 2005). However, the MNL-based approach is considered to be an aggressive approximation method due to its drawbacks, including unclear association between drivers’ perception error and the scale of the random error, the assumption of independence between perception error and road links, and the assumption of equal likelihood of over-perception and under-perception (Bonsall, 2008). Nevertheless, because of the difficulty in explicitly modelling the resultant information quality of a service provider using a data processing method, and further quantifying the impact of the information quality on drivers’ route choice behaviour, this approximation method is thought to be an acceptable compromise between modelling accuracy and tractability. Another relevant line of research has focused on adapting the MNL model to mitigate the effects of the MNL’s independence from irrelevant alternatives property (Ben-Akiva and Bierlaire, 2003; Prashker and Bekhor, 2004; Prato, 2009). Amongst the most attractive such adaptations is the Path Size Logit model (PSL), first proposed in Ben-Akiva and Bierlaire (1999). Empirical studies have shown that the performance of PSL in modelling route choice behaviour is generally better than other adaptation of the MNL such as C-logit (Cascetta et al., 1996) and is, at least, not significantly worse than that of more general and computationally demanding GEV structure route choice models (Prato and Bekhor, 2006; Ramming, 2001). Moreover, in the context of this study, the PSL preserves the logic of the interpretation of the scaling parameter of MNL as a characterisation of the quality of the information available to the traveller.

3.2. Benefit conflict and interaction between an SP and drivers The benefit conflict and interaction between an SP and travellers (drivers) can be characterised as that between a single entity (the SP) and a population of entities (the travellers). Game Theory (Myerson, 2013) provides a natural framework within which to study such phenomena. From a game theoretic perspective, the benefit conflict and interaction (competition) between an SP and travellers is most naturally modelled as a Stackelberg game (also called a leader-follower game) in the literature (Farahani et al., 2013; Hollander and Prashker, 2006; Yang et al., 2007). A Stackelberg game assumes that the players (in this case, the SP and the travellers) make decisions sequentially rather than simultaneously. The SP first makes a decision based on its prediction of travellers’ responses to their strategies, and then the travellers make their choices on the basis of the strategy chosen by the SP. The SP and the travellers make their choices until neither can improve their payoffs by unilaterally changing their choices, at which point the equilibrium of Stackelberg game is achieved. The fundamental assumption of the Stackelberg game is a plausible basis for modelling the long-term relationship between a route guidance SP and drivers and hence in the context of the information market, a Stackelberg game has often been applied to model the competition between information providers and drivers (Ge et al., 2003; Jaber and O'Mahony, 2009).

3.3. Competitions between SPs In the literature, most existing studies modelling the competition between commercial entities can be broadly classified into two categories. The first category of models characterises the competition as a zero-sum non-cooperative Nash game (Bell and Cassir, 2002; Laporte et al., 2010). The fundamental assumption of a zero-sum game is that the payoff gain of one player equals to the payoff loss of the other players. In the context of the traveller information market considered in this paper, this assumption is not realistic since when an SP implements a strategy that attracts more travellers to its service, these travellers might come from the pool of traveller not currently using any SP, not just from those currently using an alternative SP. Hence, the gain to one SP is not identical to the loss to other SPs. The second relevant category of game theoretic models is those termed pure strategy non-cooperative Nash games (Nash, 1951). In a pure strategy non-cooperative Nash game, each player chooses a strategy simultaneously, and the Nash equilibrium is achieved when no player can unilaterally improve its payoff by changing its strategy. This is an acceptable assumption of how SPs compete; hence, some existing studies related to the information market also formulate the competition between SPs as a pure strategy noncooperative Nash game (Szeto, 2007; Yang and Woo, 2000; Yang and Zhang, 2002). 22

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3.4. Formulation of multi-objective optimisation problems As noted above, the behaviour of collaborative SPs is likely to be characterised by a multi-objective maximisation problem. Calculating the full Pareto front, or providing an exact description of the full Pareto front, of a multi-objective optimisation problem is often NP-hard (Caramia and Dell'Olmo, 2008). As a result, various methods that can approximate a part of the Pareto front have been proposed and extensively studied in the literature (Ehrgott, 2006). A popular approach is the scalarisation method, which transforms a multi-objective optimisation problem into a single-objective optimisation problem (Greco et al., 2005). Three types of scalarisation methods have been most commonly used (Chinchuluun and Pardalos, 2007): the weighted-sum method (Janssens et al., 2015; Zadeh, 1963; Zhang et al., 2010), the ε-constraints method (Haimes, 1971) and the goal programming method (Charnes, 1961; Chen and Xu, 2012). One of the main advantages of the weighted-sum method is that if all the weights are strictly positive, a solution of the weighted-sum formulation is strictly Pareto optimal, while it is not true for the ε-constraints method and the goal programming method (Ehrgott, 2006). This feature is consistent with the assumption used in this research that both LAs and SPs are maximising agents. Moreover, the formulated single-objective optimisation problem is usually easier to solve (Caramia and Dell'Olmo, 2008), and the weight assignment can often be adjusted to reflect the relative importance of objectives, which is helpful in analysing collaboration strategies for LAs. 4. Formulations of the non-cooperative Nash game based framework This section describes the mathematical formulation of the conceptual framework set out in Section 2. Based on the reviews in Section 3, this framework models the interaction between SPs and drivers as a Stackelberg game, with the drivers modelled using an SUE-based market equilibrium model. In addition, under free schemes, the benefit derived by a collaborative SPs is formulated using the weighted sum method. Finally, the competition between SPs is modelled as a non-cooperative Nash game, with the Stackelberg games as sub-problems. In general, the entire framework is formulated as an equilibrium problem with equilibrium constraints (EPEC). The Stackelberg game between SPs and travellers is formulated as a mathematical programme with equilibrium constraints (MPEC) sub-problem. Compared with previous studies that only considers a part of these aspects (Lo and Szeto, 2002; Szeto, 2007), this framework is substantially more comprehensive in that it considers and models the traffic conditions, driver choices, the benefits and strategies of route guidance SPs, the competition between SPs, and the collaboration between LAs and SPs, which offers highly desirable advantages for investigating the collaboration between LAs and SPs. 4.1. The lower-level Path Size Logit based market equilibrium model The market equilibrium model yields the resultant market shares of SPs’ operational strategies and network performance. In our framework, this model takes three types of traveller choice behaviour into account: the route choice, information use choice, and subscription choice. The variables used by this market equilibrium model are shown in Table 1. The model of drivers’ route choice behaviour approximates how drivers make route choices under the availability of travel information of different quality. Since under SUE, unguided drivers are assumed to also have limited information, they can be treated as drivers subscribing to a pseudo SP providing information with very poor quality. Hence, the route choice behaviour of guided and Table 1 Variables used in the market equilibrium model. θi

urod ,i Rod VOT tr ci PSrod βi

ta0 (tr0 ) Ar δas va u ¯od i, c

A dispersion parameter of SP i The utility of drivers subscribing to SP i choosing route r between od The set of all route alternatives between od The The The The

Value of Time (VOT) of drivers travel time on route r service charge of SP i to its subscribers per trip Path Size of route r between od

A scale parameter to be estimated (set to be 1/ θi here) The freeflow travel time of link a (route r ) The set of links on route r A binary indicator that is one if link a is on route s and zero otherwise The link flow of link a The average utility of users of SP i using the information provided by SP i between od

ui¯od ,n u ¯od

The average utility of users of SP i not using the information provided by SP i between od

θ' , θ c SP

dispersion parameters of subscription and information use choices respectively

i

f rod ,k

dod f

The average utility of SP i between od

The set of all SPs, including the pseudo SP unguided drivers subscribing to The route flow of driver class k on route r between od The total travel demand between od the route flow vector containing all the route flows of all classes of drivers, f = [f rod , k ], ∀ od, r , k

23

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unguided drivers is modelled in the same manner. In this paper, we use PSL as our basic model of driver route choice. In PSL, the probability of subscribers to SP i using the provided information and choosing route r between O-D pair od (Prod , i ) is calculated as follows:

Prod ,i =

exp(θi urod ,i ) ∑s ∈ Rod exp(θi usod ,i )

∀ r , i, od (1)

od urod , i = − VOTtr − ci + βi lnPSr

PSrod =

∑ a ∈ Ar

tr =

∑

(2)

ta0 1 tr0 ∑s ∈ Rod δas

(3)

ta δar

(4)

a ∈ Ar

ta = g (va)

(5)

where θi is interpreted as the information/data quality provided by SP i , a larger value of θi indicates that drivers using SP i will have a lower travel utility perception error when making route choices and are therefore more likely to choose the more efficient routes. A small PSrod indicates that route r overlaps significantly with the other route alternatives in the same route choice set. The route travel time is defined as an additive route travel time (Eq. (4)) and the link travel time is calculated by a macroscopic vehicle delay function (Eq. (5)). Drivers’ information use behaviour, namely the probability of users of SP i using the provided information between od (Ciod ), is modelled by a binary Logit model:

Ciod =

ui¯od ,c =

exp(θic ui¯od ,c ) exp(θic ui¯od ,c )

∑

+ exp(θic ui¯od ,n )

(6)

od Prod , i ur , i

(7)

r ∈ Rod

ui¯od ,n =

∑

od Prod , j ur , i

(8)

r ∈ Rod

is the probability of unguided drivers choosing route r between O-D pair od . For simplicity, the dispersion parameter θic where here is set as one. Drivers’ subscription behaviour, namely the probability of drivers subscribing to SP i (including the pseudo provider for the unguided drivers) between O-D pair od (Siod ) is modelled by an MNL:

Prod ,j

Siod =

exp(θ'ui¯od ) ¯od ) ∑sp ∈ SP exp(θ'usp

(9)

¯od od ui¯od = Ciod ui¯od , c + (1 − Ci ) ui, n

(10)

'

A larger value of θ indicates that drivers have a more accurate perception of the utility of using/subscribing to each SP. With the increase of θ' , an SP with a higher utility will have more market share. For simplicity, here, θ' is assumed to be identical for all the drivers, although this assumption could easily be relaxed without compromising the tractability of the model. Note that for the pseudo SP that unguided drivers subscribe to, ui¯od = ui¯od ,n . The equilibrium condition of this market equilibrium model can be defined as: od = 0 frod − Prrod ,k d ,k

frod =

(11)

∑ frod,k

(12)

k∈K

∑

frod = dod

(13)

r ∈ Rod

va =

∑ ∑

frod δar

(14)

od ∈ OD r ∈ Rod

where k ∈ K indexes all groups of drivers that are classified based on the combination of their subscription choice and information use choice, namely which SP they subscribe to (including the pseudo SP) and whether they use the information provided by the SP they subscribe to; and Prrod , k generalises the combined choice probability of the three choices of driver group k . Eq. (12) defines the conservation of route flows contributed by each class of drivers and the flow of each route. Eq. (13) defines the conservation of route flows and total travel demand between each O-D pair, and Eq. (14) defines the conservation of link flows and route flows. This market 24

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Table 2 Four types of SPs.

Paid Free

Collaborative

Non-collaborative

CPSP CFSP

NCPSP NCFSP

equilibrium model is formulated as a Variational Inequality problem: od F(f ) = [frod − Prrod , k d ] = 0, ,k

(f − f ∗ )TF (f  ) ≥ 0

∀ od, r , k

(15)

∑k ∈ SP mk

∀ f , f ∗ ∈ R+

(16)

subject to:

F(f ) ≥ 0

(17) m ∑ R+ k∈K k

is the set of positive real numbers with ∑k ∈ K mk dimensions; and mk is the where f  is the solution route flow vector; number of route choices of driver class k between all O-D pairs. 4.2. Modelling the competition between SPs under different collaboration schemes This section starts with formulating the Stackelberg game between SPs and drivers, namely the benefit optimisation problem of each type of SP (collaborative and non-collaborative). Based on the collaboration decisions and the business models of SPs, SPs are classified into four types, as shown in Table 2. Then, the formulation of the entire framework is completed by formulating the upperlevel game between SPs, which is a pure strategy non-cooperative Nash game. 4.2.1. Stackelberg game formulations under free collaboration schemes Under free collaboration schemes, the benefit maximisation problem of a collaborative SP is a multi-objective optimisation problem that optimises the benefit for the LA and its own monetary benefit simultaneously. In terms of LA, it is assumed that its main objective under free collaboration schemes is to reduce the total network travel time; hence the benefit accruing to LA can be characterised by the total network travel time:

BL = −t Tf ∗

tT

(18)

f ∗.

Following the assumption that LA is a benefit maximiser, the benefit where is the vector of route travel time corresponding to of LA is measured by the negative total network travel time. In terms of the benefit of SPs, to focus on the impact of the collaboration, the benefit functions only account for the revenue that is generated from private in-vehicle service subscribers and the most relevant aspects of the operational costs of SPs, namely the traffic data acquisition cost. Fig. 2 generalises the revenue sources of both free and paid SPs. The user data revenue is the value of the user data that an SP collects. Since there is a lack of published information about exactly how SPs monetise user data, an expression for the value of the user data is developed based on a number of what we believe are plausible and reasonable assumptions. In general, three assumptions are made when approximating this user data value: (1) SPs only acquire data from crowdsourcing their own users. (2) The user data value is proportional to the data quality. (3) The user data is assumed to be a type of probe vehicle data, whose quality is proportional to the number of sampling vehicles

Fig. 2. The composition of paid and free SP respectively. 25

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(subscribers). These assumptions are based on the key features of the travel information market and we believe embody an appropriate balance between on the one hand, capturing the key features of the relevant commercial behaviours of SPs and on the other, maintaining a tractable and transparent approach. Based on Assumption (2), the value of the user data can be approximated as:

DVi = αi qi

(19)

where DVi is the value of the user data of SP i ; αi is a parameter that converts the quality of the user data to a monetary value for SP i ; and qi is the quality of the user data of SP i . The next stage in the argument, building on Assumption 3, is to note that a number of authors have investigated the issue of the quality of crowdsourced estimates of traffic stream characteristics (e.g., speed and travel time) from probe vehicle data (Chen and Chien, 2000; Cheu et al., 2002; Green et al., 2004). These analyses typically focus on determining the minimum sample size of probe vehicle data required to estimate a traffic stream feature with a given precision. In particular, an approach based on the Central Limit Theorem (Rosenblatt, 1956) shows that: 2

Zα/2 σ / μ ⎞ n=⎛ e ⎝ ⎠

(20)

where μ and σ are respectively the mean and variance of the speed of the probe vehicle sample, e is the maximum tolerable error (expressed as a percentage) in the estimation of link speed from the sample, α and Zα/2 are the confidence level and the corresponding critical value of the Z-statistic respectively and n is the minimum number of probe vehicles required on a link for estimating the travel speed of the link. If it is further assumed that σ and μ are fixed, the quality of the data can be approximated by transforming Eq. (20) into:

qi = 1 − ei = 1 −

β ni (f ∗ , x i , x i−)

(21)

where ei is the relative error of the user data of SP i ; ni (f ∗ , x i , x i−) is the number of subscribers of SP i ; x i is the operational strategy vector of SP i and x i− is the strategy vector of all the other SPs; β =Zα/2 σ / μ , which is a parameter that determines the growth of the user data value with respect to the increase in the number of subscribers (users). With Eqs. (19) and (21), the value of the user data can be approximated by:

⎡ ⎛ DVi = max ⎢αi ⎜1 − ⎣ ⎝

βi ⎞ ⎤ , 0⎥ ni (f ∗ , x i , x i−) ⎟⎠ ⎦

(22)

The formulation of Eq. (22) further ensures that the value of user data will not be negative. As shown in Fig. 3, a larger number of subscribers will lead to higher user data revenue; however, with a higher number of subscribers, the increase of the user data revenue is smaller. Besides, since the user data is population-based data, when the number of subscribers (population) is too small, the user data is not representative for the entire driver population; and hence it cannot be used for applications related to drivers by other business partners and, in turn, has no monetary value when selling the data. Therefore, when the number of subscribers of a service provider is smaller than a threshold (zero-value threshold), the data value is zero. The revenue of the service charge to subscribers for a paid SP i is modelled as:

SCi = Tci ni (f ∗ , x i , x i−)

(23)

where T is the average number of trips made by a subscriber in a certain period. Free SPs principally obtain revenue from providing promotion and advertisement services to other businesses and by selling data to third parties. The pricing policy of such service is often a fixed fee per number of impressions of service subscribers on the business

Fig. 3. An example of the user data revenue function. 26

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information, where an impression on business information is each time the information is shown in the SP’s map search results (Waze, 2016a). Hence, the advertisement revenue generated by a free SP can be approximated as:

PAi = τi ni (f ∗ , x i , x i−)

(24)

where τi is a parameter that combines the fixed conversion rate (from number of subscribers to number of impressions) and the fixed average charge per number of impressions for a free SP i . In terms of the data acquisition cost, the fundamental assumption is that the shared data from the local authority can improve the information quality of a collaborative SP by a fixed level. Therefore, the data acquisition costs of non-collaborative and collaborative SPs under free schemes are modelled as:

NDCi = κθi

(25)

CDCi = max [κ (θi − θLA), 0]

(26)

where NDCi and CDCi are data acquisition costs of an SP i if it is non-collaborative or collaborative respectively; κ is a parameter that converts the data quality to a monetary cost; and θLA is the information quality improvement contributed by the LA’s data. With these benefit components, the benefit function for collaborative SPs can be formulated using the weighted-sum method, and the benefit maximisation problem for a collaborative SP can accordingly be formulated as an MPEC problem. Hence, the formulation of the benefit maximisation problem for a collaborative paid SP i is:

Vωi BL + (1 − ωi )(DVi + SCi − CDCi )

MAXθi, ci

(27)

Subject to Eqs. (16), (17) and

θun ≤ θi ≤ θimax + θLA

(28)

ci ≥ 0

(29)

ωi ∈ (0, 1)

(30)

where ωi is the weight assigned to the total network travel time for SP i ; and V is the value of time for the LA, which converts the total network travel time to a monetary value; θun is the data quality of unguided drivers; and θimax is the maximum information quality that an SP i can get without the local authority’s data. For a collaborative free SP i , the formulation is:

MAXθi

Vωi BL + (1 − ωi )(DVi + PAi − CDCi )

(31)

Subject to Eqs. (16), (17), (28) and (30). Unlike collaborative SPs, non-collaborative SPs only optimise their own monetary benefit. Therefore, the benefit maximisation problem for a non-collaborative paid SP i is formulated as:

MAXθi, ci

DVi + SCi − NDCi

(32)

Subject to Eqs. (16), (17), (29) and

θun ≤ θi ≤ θimax

(33)

For a non-collaborative free SPi , the formulation is:

MAXθi

DVi + PAi − NDCi

(34)

Subject to Eqs. (16), (17) and (33). 4.2.2. Stackelberg game formulations under paid schemes and the co-existence of free and paid schemes When LAs sell their data to collaborative SPs, the role of LAs becomes a supplier while the role of a collaborative SP becomes a buyer. Hence, LAs lose the power to force collaborative SPs to consider network performance. Therefore, it is plausible to assume that LAs aim to obtain the maximum benefit from selling their traffic data, while collaborative SPs aim only to maximise its own monetary benefit. With these assumptions, the benefit maximisation problem of an LA can be formulated as:

MAXδ co, coSP

∑

δico (coiSP − co)

(35)

i ∈ SP

coiSP

≥ co ∀ i

coiSP is the [coiSP ], ∀ i ∈

(36)

co SP

data charge that SP i pays; is a vector of the LA’s data charge to each collaborative SP, namely where co SP = SP ; co is the cost to the LA of selling the data to an SP; δico is a binary indicator, which is one if SP i is collaborative and zero otherwise; and δ co is the vector of δico . For simplicity, co is assumed to be zero here. Under paid schemes, the benefit maximisation problem of non-collaborative SPs does not change; however, the benefit maximisation problem of collaborative SPs can be formulated by incorporating the purchase cost of LA’s data into the monetary benefit of non-collaborative SPs under free schemes; hence, the formulation of the benefit maximisation problem of a collaborative paid SP i is: 27

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MAXθi, ci

DVi + SCi − CDCi − δico coiSP

(37)

Subject to Eqs. (16), (17), (28) and (29). The formulation of a collaborative free SP i can be:

MAXθi

DVi + PAi − CDCi − δico coiSP

(38)

Subject to Eqs. (16), (17) and (28). Note that in Eqs. (35), (37) and (38), the collaboration binary indicator (δico ) and the data charge to an SP (coiSP ) are decision variables in both the benefit function for the LA and the benefit function for a collaborative SP. Moreover, an increase of coiSP will always decrease the benefit of SP i , which to the contrary, will always increase the benefit of LA. Therefore, from Game Theory’s point of view, the determination of the optimal data charge is naturally a Nash bargaining game, where LA and a collaborative SP share the revenue they generate from the collaboration, namely the additional revenue the SP generates after it is granted access to LA’s data. The data charge to the SP can be treated as LA’s payoff, while SP’s payoff (benefit) is the difference between the additional revenue and the data charge. Observed from benefit functions (35), (37) and (38), the additional revenue the SP generates is fixed with respect to the change of the data charge; hence, LA’s payoff and SP’s payoff have a fixed sum. Therefore, any feasible data charge to SP i leads to an equivalent equilibrium of the bargaining game, and thus a specific data charge to an SP must be determined by both sides of the collaboration exogenously. In addition, since the outcomes of different values of a δico depend on the specific value of the corresponding coiSP , the optimal δico should also be determined exogenously. Therefore, the formulation of the framework for paid data sharing schemes reduces to a special case of the framework for free data exchange schemes; that is, each SP in the framework, whether collaborative or non-collaborative, only optimises its own monetary benefit. When two collaboration schemes co-exist (mixed schemes), the previous formulations of the benefit maximisation problems of SPs are still individually applicable. However, the objective of the LA is now to maximise the combined benefit, consisting of its own benefit due to both improvements in network performance and monetary reward from the sale of data. Hence, the benefit function of LA is formulated as the weighted sum of the two objectives:

BLC = −ωTB Vt T f ∗ + (1 − ωTB )

∑

δico coiSP

(39)

i ∈ SP

0 < ωTB < 1 where BLC is the combined benefit for an LA;

(40)

ωTB

is the weight assigned to the total network travel time.

4.2.3. Formulation of the non-cooperative Nash game between SPs With the formulations of the benefit maximisation problems for each of the four SP types, the formulation of the entire framework is completed by formulating the upper-level pure strategy non-cooperative Nash game between SPs. Since the benefit maximisation behaviour of each type of SP is formulated as an MPEC problem, the resulting Nash game, can, in consequence, be formulated as an EPEC problem, with each MPEC problem as a sub-problem. The EPEC formulation is summarised below: For each SP i , given x i−, the problem to solve is:

MAX xi B (x i , x i−, f ∗ )

(41)

Subject to Eqs. (16), (17) (the network equilibrium condition) and

x imin ≤ x i ≤ x imax

(42)

B (x i , x i−)

where Eqs. (41) and (42) generalise the formulations of the MPEC sub-problems. generalises the benefit function of an SP; and x imin and x imax are the vector of the minimum and maximum values of the strategy vector of SP i ( x i ) respectively. 5. Numerical studies on the optimal collaboration strategy This section presents three numerical studies based on the framework developed above. The aim of these numerical studies is to explore the implications of the three different collaboration schemes identified earlier – free schemes, paid schemes and co-existing free and paid schemes – and in particular to provide guidance to LAs regarding the most appropriate strategy to pursue. The well-known Sioux Falls network (Suwansirikul et al., 1987) is used as the basis for these numerical studies. The topology of which is shown in Fig. 4, where the numbers in the figure are identifiers of an origin or destination. There are assumed to be two SPs in the study; a free SP (FSP) and a paid SP (PSP). The detailed parameter settings of the experiments are listed in Table 3, which are for illustration purpose. For each O-D pair, the route choice set is generated using the link penalty approach (de la Barra et al., 1993) (penalty percentage set as 0.15), which generates sufficiently dissimilar route alternatives by iteratively adding certain impedance (e.g. a fixed percentage) to the weight of the links (e.g. link travel time) on the current shortest route alternative. The BPR function (US Bureau of Public Roads, 1964) is used as the macroscopic vehicle delay function. For solving this framework, a solution algorithm based on Particle Swarm Optimisation (PSO) and Diagonalization algorithm is proposed and applied (please refer to Appendix A for details). 28

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46

8

10

24

34

18

Fig. 4. The topology of the experimental network. (Source: Suwansirikul et al., 1987) Table 3 Parameter settings of numerical studies. Parameter

Value

Parameter

Value

Demand 10 to 34

500 vehs/h 500 vehs/h 500 vehs/h 500 vehs/h 500 vehs/h 0.01 to 1.0 0.01 to 1.0

θ' (£− ) θ of unguided drivers Number of routes each O-D Service charge of FSP Service charge of PSP Value of Time (VOT )

1

Demand 46 Demand 18 Demand 34 Demand 34 θ of FSP θ of PSP

to to to to

18 46 8 24

0.01 6 0.0 0.01to 2.0 £/trip 20 £/hour

5.1. Local authority’s strategies for utilising free schemes To investigate the optimal collaboration strategy for LAs under free schemes, numerical experiments are conducted for different collaboration states where FSP and PSP have different collaboration choices. In these experiments, the information quality improvement contributed by LA’s data is set to 0.3. The maximum data quality that FSP and PSP can achieve using their own data sources is assumed to be 1.0, which can help to avoid the cases where the weight assigned to the total network travel time becomes ineffective for a collaborative SP’s benefit. Firstly, the weight assigned to the total network travel time for each collaborative SP is changed from 0 to 1, with a 0.1 interval. The resultant total network travel time of each collaboration state is shown in Fig. 5. It can be seen from Fig. 5 that the total network travel time when both SPs are collaborative is lower than that when either of them or neither of them is collaborative, as long as the weight of the total network travel time is larger than 0. The underlying reason for this is that when more SPs collaborate, more drivers in the market can get better quality information, which means that more drivers make efficient route choices and the network performance can be improved. Hence, from LA’s perspective, the best strategy is collaborating with both SPs. From Fig. 5, it can also be seen that when only one SP is collaborative, the collaboration with the FSP is more beneficial for LA than the collaboration with the PSP, since the former leads to a lower total network travel time than the latter. To illustrate this phenomenon, Figs. 6a and 6b show the market share of the FSP and PSP, respectively, when either of them is collaborative alone. Obviously, in both collaboration scenarios, with the increase of the weight assigned to the total network travel time, the market share of the FSP is consistently much larger than that of the PSP. This is because the service charge levied by the PSP prevents it from 29

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Fig. 5. Total network travel time with different weight assignments and collaboration types.

Fig. 6a. The market share of the collaborative FSP and non-collaborative PSP.

Fig. 6b. The market share of the collaborative PSP and non-collaborative FSP.

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Table 4a The collaboration payoffs where the weight of total network travel time is 0.9. FSP

Collaborative Non-collaborative

PSP Collaborative

Non-collaborative

£16035.24, £10588.61, 1835 (h) £15325.50, £13757.85, 1853 (h)

£16496.05, £8922.17, 1838 (h) £16093.78, £12357.82, 1860 (h)

occupying a large market share. Hence, the majority of drivers will not receive the good quality data provided by PSP, meaning that the total network travel time will not be significantly reduced. Since the market share of the FSP is consistently large, however, any increase in its data quality will help the majority of drivers make more efficient route choices, and this can better reduce the total network travel time. This result indicates that if considering the order in which SPs make their decision to become collaborative, LA should first collaborate with the FSP since this will bring a more immediate improvement in the total network travel time. In addition, it can also be observed from Fig. 5 that with the increase of the weight assigned to the total network travel time, the total network travel time decreases. Firstly, this indicates that though the weight assigned to an objective in a weighted-sum formulation does not necessarily correspond to the importance of the objective (Marler and Arora, 2004), in this framework, the weight assignment correlates to the importance of the objectives. A higher weight assigned to the total network travel time can lead to a lower total network travel time, which can be interpreted as the LA is more aggressive in a bargain with an SP in the collaboration negotiation (asking for high benefit in terms of the total network travel time). This observation does not mean that the LA can always obtain more benefit when it is more aggressive, however. This is because the essence of a free scheme is that a collaborative SP sacrifices a portion of its monetary benefit to improve the network performance in exchange for the free LA’s data. If this benefit sacrifice is more than the benefit it can obtain from the free data, the SP will not collaborate, which may result in a benefit loss for the LA. To demonstrate this, Table 4a gives the payoffs for SPs when the weight assigned to the total network travel time is 0.9, and Table 4b gives the payoffs when the weight assigned to the total network travel time is 0.95. In both tables, the first element of each cell is the monetary benefit of the FSP, the second element is the monetary benefit of the PSP and the third element is the total network travel time. It can be found that when the weight is 0.9, both SPs will collaborate (θFSP = 0.82 , θPSP = 0.77 and cPSP = 0.99 £/trip) since being collaborative is the dominant strategy for them regardless of the other SP’s choice; however, when the weight increases to 0.95, only PSP will collaborate (θFSP = 0.430 , θPSP = 1.13 and cPSP = 0.97 £/trip) since being non-collaborative is the dominant strategy for FSP regardless of PSP’s choice. Furthermore, the total network travel time corresponding to the final state in Table 4a is 1835 h, which is lower than that corresponding to the final state in Table 4b (1848 h). This shows that when the LA becomes so aggressive in the setting for its data, it has the consequence of breaking the collaboration, leading to a benefit loss. Hence, under free schemes, LA should collaborate with all SPs rather than being too aggressive in bargaining with SPs in the collaboration negotiation, which may prevent SPs from collaborating. Moreover, the results also indicate that, under free exchange schemes, the LA needs to implement a regulatory requirement on collaborative SPs so that they will take into account the network performance consequences of the behaviour, not simply their own monetary benefit. When FSP is collaborative and PSP is non-collaborative and the weight of the total network travel time is 0, then the optimal strategy of FSP is θFSP = 0.44 , which is much lower than that when the weight of the total network travel time is 0.9 (θFSP = 0.83). Hence, when collaborating with FSP, the LA should establish standards of minimum data quality. Similarly, when FSP is non-collaborative, PSP is collaborative and only considers its own monetary benefit, the optimal strategy of PSP is (θPSP = 0.75, cPSP = 1.17 £/trip). Compared to the optimal strategy when the weight of the total network travel time is 0.9 (θPSP = 0.95, cPSP = 1.10 £/trip), PSP’s data quality is lower but the service charge is higher. Hence, when collaborating with PSP, LA needs to set up requirements of minimum data quality and maximum service charge. In addition, a higher quality of LA’s data will bring a more significant improvement in the collaborative SP’s data quality, which can, in turn, increase the feasibility of the collaboration for collaborative SPs and the potential benefit accruing to collaborative SP. Fig. 7 gives an intuitive example of the feasibility of the collaboration for the FSP with different levels of quality improvement contributed by the LA’s data, given that the cooperation choice of the PSP is fixed. The solid double arrow represents the benefit accruing to the FSP when it is non-collaborative, which is the distance between its revenue and data acquisition cost. Since being collaborative is a dominant strategy for the FSP if the benefit of FSP is not worse than that when it is non-collaborative, the maximum feasible data quality of the FSP when it is collaborative can be determined by moving the double arrow in Fig. 7 to its right until it just

Table 4b The collaboration payoffs where the weight of total network travel time is 0.95. FSP

Collaborative Non-collaborative

PSP Collaborative

Non-collaborative

£14234.45, £9422.22, 1827 (h) £14527.72, £12720.73, 1848 (h)

£14905.02, £8129.28, 1831 (h) £16093.78, £12357.82, 1860 (h)

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Fig. 7. An example of the effect of the quality of the local traffic authority’s data on the feasibility of the collaboration.

intersects the curve of the FSP’s revenue and the curve of the new data acquisition cost. The feasible data quality range for the FSP is then the distance between its optimal data quality, when it is non-collaborative, and its new maximum feasible data quality. Clearly, when the quality of the local traffic authority’s data is high, the feasible data quality range of the FSP will be wider. This also indicates that with the increase of LA’s data quality, SPs are more likely to provide better quality and driver are more likely to make efficient route choices, which will improve the network performance. 5.2. Local authority’s optimal strategy under paid schemes This numerical study aims to provide suggestions for LAs under paid schemes. Here, the information quality improvement contributed by the LA’s data is set to 0.3. The maximum data quality the FSP and PSP can achieve using their own data sources is assumed to be 0.3, which means that FSP and PSP can only achieve their optimal data quality via the collaboration with LA (according to the optimal strategies in Section 5.1). Otherwise, when FSP and PSP can achieve their optimal data quality using their own data sources, their optimal strategy will always be disseminating the data with the optimal quality, regardless of the other SPs’ collaboration choice; and hence, an SP will only purchase LA’s data when it is cheaper than their own data sources, and this will prevent the experiment to reveal the full interactions between LA and SP under paid schemes. To calculate the maximum benefit for LAs from selling their data, it is assumed that an SP will collaborate as long as its benefit after the collaboration is not lower than that before the collaboration. Based on this assumption, the maximum data selling benefit can be calculated based on the maximum acceptable data charge to FSP and PSP in each collaboration state:

BLCcsmax =

∑ i ∈ SP

δico (BSic, cs − BS n ') i, cs

(43)

where BLC max is the maximum benefit for the LA’s data selling benefit in a collaboration state cs (cs = (δico, δ jco) ); BSic, cs is the benefit of a collaborative SP i in cs ; and BS n ' is the benefit of an SP i in the state cs ' (cs ' = (¬δico, δ jco) ). i, cs Fig. 8 shows each SP’s maximum acceptable data charge in each collaboration state. It can be seen that the optimal collaboration strategy of the LA is collaborating with both SPs with the data charges to FSP and PSP being £1767 and £2661 respectively. In addition, both FSP and PSP will collaborate under such data charges since it is at least a weakly dominant strategy, regardless of the collaboration choice of the other SP. It can also be seen from Fig. 8 that when one of the SPs becomes collaborative, the maximum acceptable data charge to the other SP decreases, and the direct reason for this is that there is a collaboration benefit loss for the other SP. For example, when FSP becomes collaborative, the maximum acceptable data charge to PSP decreases from £3459 to £2661, which results from the loss of the maximum collaboration benefit (when the data charge is zero) for PSP from £15730 (£3459 + £12271) to £13774 (£2661 + £11113). Hence, the conclusion of the LA’s optimal strategy in this experiment is to collaborate with both SPs because the benefit loss of either SP when its competitor becomes collaborative is less than the maximum acceptable data charge to its competitor. This indicates that if the maximum acceptable data charge to an SP is lower than the benefit loss of the other collaborative SP when this SP becomes collaborative, collaborating with both SPs will not be the optimal strategy for the LA. Hence, when LAs aim to 32

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Fig. 8. A SP’s maximum acceptable data charge and its corresponding benefit in each collaboration state.

maximise their revenue from selling its data to SPs, they should be aware that their revenue does not always increase by selling the data to more SPs. The underlying reason for this finding is that the effect of the LA’s data is not only on the data acquisition cost of a collaborative SP but also on its relative utility difference from the other SPs (competitiveness). Each SP’s benefit depends on its market share, which is determined by an MNL, a fundamental assumption of which is that only the utility difference between alternatives matters. Hence, the benefit experienced by an SP depends on its competitiveness. Thus, when an SP becomes collaborative, its absolute utility will increase because of its increased maximum information quality due to the access to LA’s data. Since the other SP’s data quality is unchanged, the competitiveness of the other SP will decrease because of the decrease of its relative utility. This naturally leads to the loss of the other SP’s market share and the loss of the other SP’s benefit. Therefore, this finding is not just specific to this experiment.

5.3. Local authority’s strategies for utilising mixed schemes This numerical study focuses on the co-existence of free and paid schemes. The parameter and network settings here generally follow the settings for Section 4.2. In particular, the weight assigned to the total network travel time against a collaborative SP’s benefit and that to the total network travel time against data selling benefit are set as 0.9. Table 5 is the payoff table for the maximum LA’s collaboration benefit calculated using Eq. (38). Clearly, Table 5 indicates that in this case, the optimal collaboration strategy for the LA is collaborating with FSP and PSP under paid schemes. Note that collaborating with all SPs via paid schemes is not always the optimal collaboration strategy for the LA. This is because its collaboration benefit via free schemes may exceed that via paid schemes given different weight assignments in the free schemes from the one used in this example. More importantly, even though the objective function of the LA considers the total network travel time, which, to some degree, represents the benefit of all drivers, the resultant optimal collaboration strategy for the LA does not necessarily lead to the optimal average generalised driver benefit (public benefit). To demonstrate this, the average generalised benefit/utility of drivers in each collaboration state is computed as: Table 5 The maximum local traffic authority’s collaboration benefit via mixed schemes. FSP

Free scheme Paid scheme Non-collaborative

PSP Free scheme

Paid scheme

Non-collaborative

−£25137 −£25034 −£25424

−£24863 −£24796 −£25096

−£25225 −£25218 −£25586

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Table 6 Average driver benefit in each collaboration state.

U¯ =

FSP collaboration choice

PSP collaboration choice

Average driver benefit (£)

Free scheme Free scheme Free scheme Paid scheme Paid scheme Paid scheme Non-collaborative Non-collaborative Non-collaborative

Free scheme Paid scheme Non-collaborative Free scheme Paid scheme Non-collaborative Free scheme Paid scheme Non-collaborative

−15.097 −15.101 −15.103 −15.164 −15.174 −15.223 −15.314 −15.330 −15.353

−VOT × t Tf ∗ − ∑sp' ∈ PSP n sp' × c sp' ∑sp ∈ SP nsp

(44) '

where PSP is the set of all paid SPs in the market; andc sp' is the service charge to a subscriber per trip of a paid SP sp . The average benefit for drivers in each collaboration state in Table 5 is listed in Table 6. It is clear that drivers can have the optimal average benefit when both SPs collaborate via free collaboration schemes. More importantly, the optimal collaboration strategy for the LA actually leads to an average driver benefit that is even worse than that when the FSP collaborates via a free scheme and the PSP is non-collaborative. To explain this phenomenon, Table 7 shows the optimal strategies for PSP in four of the collaboration states. From this table, it can be seen that service charge drivers paying when PSP collaborates via a paid scheme is higher than that when the PSP collaborates via a free scheme, and this is more significant when the FSP collaborates via a paid scheme. In addition, the number of PSP’s subscribers also decreases when it switches to a paid scheme from a free scheme. Table 7 shows that, in fact, it is the drivers who help to pay for the data that the LA sells to a paid SP via paying the increased service charge. Besides, the service charge increase also prevents more drivers to access the better-quality information. These two reasons lead to a sub-optimal average driver benefit. Although the average driver benefit can be measured in other ways, this numerical study generally shows that there may be an inconsistency between optimal public benefit and the optimal LA’s benefit. Therefore, there may be public concern about whether LA’s data is appropriately utilised for improving public benefit, even if the LA considers the public benefit when it sells its data to SPs. 6. Concluding remarks This paper develops a novel modelling framework based on a non-cooperative Nash game for investigating the strategies for LAs in their data exchange collaboration with in-vehicle route guidance SPs. This framework explicitly considers the commercial (benefit maximising) behaviour of SPs in the collaboration. The framework is formulated as an EPEC, and the benefit optimisation behaviour of SPs is formulated as an MPEC sub-problem. The framework also accommodates the business models of both free and paid SPs. Three types of collaboration schemes are considered in this paper: free schemes, paid schemes, and the co-existence of free and paid schemes. Under free schemes, the benefit functions of two types of collaborative SPs are formulated as a multi-objective optimisation problem using the weighted-sum method. Compared to existing modelling frameworks in the literature, this framework more comprehensively considers and models the traffic conditions, driver choices behaviour, the benefits and strategies of route guidance SPs, the competition between SPs, and the collaboration between LA and SPs, which offers highly desirable advantages for investigating the collaboration between LA and SPs. Numerical studies based on this framework provide three suggestions and implications for LA regarding how to make collaboration with SPs beneficial both to itself and the travelling public. Firstly, when an LA is purely public benefit driven (i.e., it is seeking to maximise network performance as a whole) and offers free collaboration schemes, it should collaborate with all SPs in the market. This results in more drivers making efficient route choices based on better guidance information. Secondly, when an LA aims only to maximise its revenue from selling its data to collaborative SPs, it should be aware that its revenue does not always increase by selling the data to more SPs. This is because selling the data to a new SP will reduce the data charge that it can command from the SPs it is already collaborating with. Thirdly, because of the inconsistency between the authority’s objective and the average public Table 7 Optimal strategies of PSP in four collaboration states. FSP collaboration choice

PSP collaboration choice

PSP data quality

PSP service charge

PSP subscribers

Free scheme Free scheme Paid scheme Paid scheme

Free scheme Paid scheme Free scheme Paid scheme

0.5 0.5 0.5 0.5

0.98 1.03 0.99 1.06

513.39 422.08 540.63 447.44

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Fig. 9. Pseudo code of the solution algorithm.

benefit, when an LA considers selling its data to collaborative SPs, whether it also takes account of the public benefit or not, there may be a public concern about whether the LA’s data is appropriately utilised for improving public benefit. It is worth noting that, with minor modifications, this framework can also be applied to investigate other types of public-private sector collaboration in travel information markets. For example, when investigating the case where LAs want to buy data from service providers to reduce their data collecting cost, this framework can be modified by changing the benefit functions of LAs and SPs respectively, while the general framework structure preserves. In addition, when SPs are market share maximisers rather than benefit 35

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maximisers, this framework can also be applied by only changing the benefit functions of SPs. This research is one of the first attempts we are aware of to comprehensively study the recent phenomenon of data exchangebased collaboration between LAs and in-vehicle route guidance SPs, and it opens several directions for further research. For example, the framework could be extended to deal with a wider range of collaboration schemes, including the cases where LAs selling their data with a discount in return for obligations of an SP to consider the network performance. Another important direction for future work, which we are currently developing, is the application in real-world contexts. Although the key insights we have obtained from the numerical experiments performed on the Sioux Falls network are general in nature, it would clearly be desirable to apply the framework in a more realistic context, so that the magnitude of the effects can be quantified in a manner that is directly meaningful for practical policy analysis. As part of this work, the extension of the framework to accommodate explicitly time limited collaboration arrangements is being addressed. Acknowledgement This research was partially supported by the UK Engineering and Physical Sciences Research Council’s Digital City Exchange project, under award EP/I038837/1. Appendix A. . Solution algorithm In the literature, the Diagonalization algorithm has been widely applied to solves an EPEC, which decomposes the problem into a series of MPEC problems and then solves these problems separately (Haghighat and Kennedy, 2012; Hu and Ralph, 2007; Zhao et al., 2011). One of the main advantages of the Diagonalization algorithm is that it does not rely on the partial derivatives of the payoff functions with respect to link or route flows; hence, its implementation is relatively simple. Also, it has been proven that it is able to find at least the local Nash equilibrium (Su, 2004). Common methods utilising this Diagonalization approach include the Gauss-Seidel method and the Jacobi method (Leyffer and Munson, 2005). Here, the Gauss-Seidel method is chosen as the main solution algorithm since it is shown to have better convergence performance than the Jacobian method (Su, 2004). For solving the MPEC sub-problems, we use PSO (Clerc, 2011; Kennedy and Eberhart, 1995). Generally speaking, PSO is a population-based metaheuristics algorithm that iteratively searches through the solution space using a number of particles, the position of each of which in the solution space is a vector of values of decision variables. In each iteration, each particle moves in the solution space based on its velocity, which is calculated based on its personal best position and the personal best positions of some or all of the other particles (neighbours). A personal best position is one of its previous positions that result in the best objective value (commonly called fitness). PSO terminates either when the maximum number of iterations has been run or particles concentrate closely enough to one solution in the solution space. The global optimal objective value is obtained based on the best personal best position among all the particles. PSO is chosen for solving the MPEC sub-problems because it does not rely on the information of the partial derivatives of the payoff functions with respect to link or route flows and hence is applicable even when this framework is further extended by embedding more realistic and complex traffic propagation models. Moreover, numerical studies have shown that PSO has comparatively better performance than the other metaheuristic algorithms in solving various types of optimisation problems (Elbeltagi et al., 2005; Poli, 2008; Shi and Eberhart, 1999). In addition, the parameter configuration of PSO is straightforward, which makes it simple to achieve a reasonable balance between its computational efficiency and optimisation accuracy, and this is critical for successfully applying a metaheuristic algorithm. The descent algorithm proposed in Han and Lo (2004) is embedded in the PSO to solve the market equilibrium model, whose performance in solving models with similar structures has been proven in previous studies (Lo and Szeto, 2004; Szeto and Lo, 2005) and is very simple to implement. To summarise, this paper proposes a PSO-based Gauss-Seidel method to solve the entire framework, whose pseudo code is shown in Fig. 9.

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