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Policy analysis of third party electronic coupons for public transit fares
Transportation Research Part A 66 (2014) 238–250
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Policy analysis of third party electronic coupons for public transit fares Joseph Y.J. Chow ⇑ Ryerson University, Toronto, ON, Canada
a r t i c l e
i n f o
Article history: Received 16 May 2013 Received in revised form 14 May 2014 Accepted 29 May 2014 Available online 24 June 2014 Keywords: Public transport Automated fare collection Marginal cost theory Revenue management Game theory Electronic coupon
a b s t r a c t Mobile technologies are generating new business models for urban transport systems, as is evident from recent startups cropping up from the private sector. Public transport systems can make more use of mobile technologies than just for measuring system performance, improving boarding times, or for analyzing travel patterns. A new transaction model is proposed for public transport systems where travelers are allowed to pre-book their fares and trade that demand information to private firms. In this public-private partnership model, fare revenue management is outsourced to third party private firms such as big box retail or large planned events (such as sports stadiums and theme parks), who can issue electronic coupons to travelers to subsidize their fares. This e-coupon pricing model is analyzed using marginal cost theory for the transit service and shown to be quite effective for monopolistic coupon rights, particularly for demand responsive transit systems that feature high cost fares, non-commute travel purposes, and a closed access system with existing pre-booking requirements. However, oligopolistic scenarios analyzed using game theory and network economics suggest that public transport agencies need to take extreme care in planning and implementing such a policy. Otherwise, they risk pushing an equivalent tax on private firms or disrupting the urban economy and real estate values while increasing ridership. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Urban sustainability depends on making public transport systems attractive to travelers (Kennedy, 2002; Sinha, 2003). Without high ridership, public transport requires costly subsidies (Parry and Small, 2009) partly because few riders results in lower operating frequency and consequently higher user costs such as wait and access time (Mohring, 1972). However, many transport systems around the world operate with low ridership outside of the peak periods, and in some cases for all periods. This problem is especially endemic in low population density suburban communities in the United States. Of course, there are exceptions where transit ridership is so high compared to the available capacity that congestion at a station or in a vehicle is a recurrent problem (Lam et al., 1999; Hamdouch and Lawphongpanich, 2010). For fixed route and fixed schedule services, low ridership during off-peak periods, combined with demand uncertainty, can lead to lower cost efficiency of a system. Ridership concern is even greater when operating demand responsive transit (DRT) systems (Schofer et al., 2003): paratransit, dial-a-ride, or personal DRT. These systems operate with relatively smaller capacity vehicles compared to buses or rail, and they can spend significant portions of their time running empty after dropping off passengers. ⇑ Tel.: +1 416 979 5000. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.tra.2014.05.015 0965-8564/Ó 2014 Elsevier Ltd. All rights reserved.
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Proper revenue management, which involves dynamic pricing and marketing strategies to maximize revenue, can improve ridership and other system performance measures (Li et al., 2009). As those authors pointed out, the challenge that the public transport industry faces compared to the airline or car rental industries is that it is an open-access system that does not require pre-booking. The result is that travel demand and behavior remain difficult to forecast. In cases where reservations can be made, such as intercity rail, revenue management models are being developed (e.g. Cirillo et al., 2011). However, urban public transport systems at best can implement pricing differentiation strategies—time-based pricing, directional pricing, regional pricing, usage-based pricing, or demand-based pricing (Li et al., 2005)—because of the inherent open access structure. Technology may perhaps change this outlook. Automated fare collection (AFC) systems have enabled many of the pricing strategies presented by Li et al. (2005). Smart card technologies reduce the amount of time it takes to board a transit vehicle, which can ultimately improve operational efficiency (Tirachini and Hensher, 2011; Tirachini, 2013). The technology allows transit system performance measures to be collected (Morency et al., 2007), and for travel patterns to be estimated (Chakirov and Erath, 2011; Nassir et al., 2011; Munizaga and Palma, 2012). With the growing use of mobile devices, further opportunities in fare collection are possible. In Helsinki, Finland, public transport users have been able to pay their fares with their mobile phones since 2001 (Mallat et al., 2008). Böhm et al. (2005) explained the practical advantage of paying fares through mobile devices, which reduces the cost of transit infrastructure for AFC and also presents opportunities for location-based services to link with fare payment. Páez et al. (2011, 2012) saw an opportunity to engage private sector with the transit demand information available from smart cards, and proposed spatial analysis methods to identify local business opportunities or to market to particular demographics. If we consider the near-future scenario where the majority of the population owns mobile devices that can purchase fares offsite from a transit system, what can be done to improve ridership? Besling et al. (2002) introduced the idea of using smart cards to allow payment of electronic coupons. With mobile devices, there is potential for a new form of fare transaction model where the public transport system’s revenue management can be outsourced to third party private firms, as suggested by Páez et al. (2011) in the form of rebates, offers, and/or loyalty points. These firms would issue electronic coupons to travelers to subsidize their fares. Traditional coupons already exist, but only in limited form, for example for intercity bus services to take tourists to casinos. In an urban area, traditional coupons would not work because there is no centralized control; for example, a traveler may just take a paid transit fare to multiple vendors at a destination and ask for rebates if they all participated in the model. This is why this business model is used by intercity destinations like casinos but has not yet found its way to urban destinations. Even existing businesses that currently provide free transportation service to their customers can benefit, because they are investing in the free transportation due to insufficient capacity or demand from other modes like driving. In these cases, the businesses would be transferring the cost to an alternative that may be less costly while increasing transit ridership. In this example of a public-private partnership, the public transport system serves as a platform for fare transactions. Firms that operate large destinations for travelers, such as a sports stadium, a theme park, or big box retail, can issue electronic coupons on the platform. Users are allowed to book their transit fares in advance (pre-book), and in doing so, have the option to claim a coupon if they intend to travel to that destination. When they arrive at the destination and check in to that location, the platform gets informed of completion of the travel transaction, and their trip fare is reimbursed in the amount of the coupon. The advantages of such a system are three-fold: (1) the firms can attract more customers, or may seek customers arriving by other modes due to limited parking availability; (2) ridership goes up for the transport system; (3) and fares can be subsidized for the travelers. The need to pre-book ensures that random strangers cannot go to a participating firm and request a coupon. This model may be used by firms to encourage their employees to commute by public transit, although it has much more applicability to retail and leisure destinations where additional customers translate directly to increases in revenue, and because peak periods may already suffer from congested transit service. Because of the intended use, the ridership increase is likely to occur during off-peak periods as opposed to peak commute periods, resulting in increased efficiencies in the public transport system. It is a situation that can benefit all parties involved. This transaction model is illustrated in Fig. 1, although more sophisticated processes may also be implemented that ensure more secure exchange of travel demand for purchases (e.g. providing the coupon if a customer spends X dollars). These are implementation and design issues that require testing in practice to refine. The purpose of this study is to gain a deeper insight to the proposed transaction model and to answer several policyrelated research questions. First, a marginal cost model is designed to evaluate the consumer welfare potential of the transaction model, which is not just applicable to e-coupons, but also to traditional coupons like in the example earlier. Should a public transport agency allow travel demand to essentially be commoditized and traded with third party private firms? Under what conditions would it make sense to do so? The marginal cost model is used to illustrate how the transaction model can be especially beneficial to DRT systems. An important policy question is how much regulation the transport agency should have on deciding which firms can enter this ‘‘travel demand e-coupon’’ market. Oligopolistic games are constructed between two firms allowed to offer coupons (note that even though the coupon provision is oligopolistic, the firms themselves are assumed to operate within a competitive market), and then for a network of M traveler origins and N destination firms to evaluate this policy.
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Public Transport System Purchase fare, claim coupon
Firms
Generate e-coupon
Transport Check-in Confirm check-in Reimburse fare Fig. 1. Swim lane event diagram of the proposed transaction model.
The remainder of this study is organized as follows. Section 2 is a more comprehensive literature review that focuses on the motivation of this work involving travel information in public transport systems and the evolution of technologies toward this proposed transaction model. Section 3 presents the optimal pricing of an e-coupon for a single firm, with comparisons between fixed route transit and DRT. Section 4 considers oligopolistic games between multiple firms.
2. Motivation The use of smart card data in public transport systems has reached quite a mature point since it first became popular in the 1990s (Pelletier et al., 2011). However, the technology has been used primarily as a data source to better understand travel behavior (Bagchi and White, 2005) or to measure system performance. Related to this research is a need to protect the privacy of users while collecting their travel data and using or sharing it in a public manner (Chen et al., 2012). Ways to use the technology or to introduce new business models in public transport have not been explored to the same extent, much less developing analytical models to evaluate public transport systems operating under such technologies. Several researchers (Oram et al., 1996; Li et al., 2009; Camacho et al., 2013) adopted management frameworks to evaluate the benefits of AFC in introducing new operational strategies or business models, or to investigate these benefits for vendors (Hickman et al., 1998). However, they did not provide any analytical model to evaluate the transport systems. Tirachini (2013) developed one of the few analytical models to evaluate the decision to adopt AFC technology, using multiple regression on transit corridors to show the degree of boarding time savings. He found that benefits of upgrading to AFC increased as the ridership demand increased. Some recent studies have been conducted on information flow within public transport systems in the context of tradeoffs between wait time and planning time for scheduled arrivals (Fosgerau, 2009; de Borger and Fosgerau, 2012). Travelers are assumed to be provided information by the transport agencies, and the optimal quality of information provision is modeled jointly with socially optimal fares. Despite advances in quantifying the value of AFCs and in information provision with a public transport system, there is still a considerable lack of research in business models or revenue management strategies related to adoption of mobile device technologies and the information that they generate. Some exceptions include DRTs designed under the assumption that the technology is already in place, such as the High Coverage Point to Point Transit system (Cortés and Jayakrishnan, 2002; Jung and Jayakrishnan, 2011). In the last few years, new startups in the private sector such as Uber.com and IGGEOS.com have formed to take advantage of the niche market opportunities that the mobile device technology has opened up in urban transport services. These companies and others provide proprietary web-based platforms for booking trips and pricing models for their fares. Systems also exist for collecting large amounts of destination data from online data sources like YELP.com and using that to recommend activities to travelers (Chow and Liu, 2012). Some early progress is being made to cyber-physical systems for public transport, where real time transit data is provided in an interactive manner to mobile technology users (Lau et al., 2011). These examples are evidence that the technology is in place for incorporating mobile technologies and destination information into transport services. This opportunity has not been missed by researchers, as a number of studies have analyzed how travelers can trade ‘‘mobility credits’’ with one another, either for paying tolls or transit fares (Yang and Wang, 2011), parking permits (Zhang et al., 2011), or pollution permits (Nagurney and Dhanda, 2000), among others. These studies focus on trading between travelers for the purpose of allowing a free market to equitably transfer travel costs throughout a population. There is also an opportunity to involve the private sector in trading travel demand. Unlike earlier studies, the purpose of the proposed transaction model is to outsource a transport system’s revenue management to private firms by allowing them to trade mobility with travelers, increase ridership for the transport system, and reduce the burden of travel costs on travelers. New analytical models are presented to evaluate a transit system that operates under such an e-coupon transaction model, further expanding the literature on analytical models for evaluating transport system technologies.
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3. Single firm e-coupons The economics of this transaction model is studied for a single firm issuing e-coupons to identify the requirements for finding an optimal price. To be clear, this single firm is still providing a good or service within a competitive environment. The goods provided by the firm are governed by the competitive market, which are goods-specific. On the other hand, the coupon is being exacted on travel demand by transit, which is a specific derived good. The coupon (and firm) act much like a toll (and toll operator); even though the firm has the sole right to set the toll, travelers can choose to go to that destination via that mode and that time period, or choose another mode like automobile, visit another destination, or not travel at all. These competing forces define the shape of the demand curve in the following section. 3.1. Optimal price for negligible congestion scenario Let us consider a destination firm for which demand is modeled as the following Eq. (1). The function assumes a monotonically decreasing value, and is meant to capture the competitive market present for the travelers: the existence of other modes, other time periods, and other destinations.
q ¼ D0 eag
ð1Þ
where D0 is the maximum demand on a typical day a is an elasticity parameter that defines the steepness of the demand curve g is a generalized cost of travel The average generalized cost may be represented by Eq. (2) for public transport service. For this analysis, automobile mode is ignored for simplicity, and travelers choosing auto mode are assumed to be among those not served by Eq. (1). Furthermore, transaction fees are assumed to be negligible in this electronic-based transaction system (Yang and Wang, 2011; Nie, 2012). Because of the negligible transaction fees, this model can be trivially extended to a multiperiod pricing model that accounts for changes throughout a day. For example, it is possible to consider a capacitated parking facility with random driving visitors as a setting for the firm to update coupon values, although the negligible fees mean this is just a simple switching option that does not require any look-ahead policy (Kulatilaka and Trigeorgis, 2001).
g ¼ bðtt þ ctw þ dt a Þ þ c0 cf
ð2Þ
where b is a value of time parameter c is a premium for wait time over travel time d is a premium for access time over travel time Tt is in-vehicle travel time, a monotonically increasing function of number of riders, q Tw is wait time, a monotonically increasing function of number of riders, q Ta is access time, a monotonically increasing function of number of riders, q c0 is the transit fare cf is e-coupon that the firm provides a traveler The different time variables are there to allow us to evaluate different types of transit services such as DRT. The travel time functions can be calibrated to account for various congestion effects like crowding effects on platforms. To keep the representation simple, we may use T ðqÞ ¼ T t þ cT w þ dT a . As the sole issuer of the e-coupons, the firm is assumed to be maximizing profit and to set the price of the coupons. Assuming that all other business operations remain the same, the net profit P including coupon cost is defined as:
P ¼ q R cf where R is the expected profit per customer visiting the firm. Note that this value is exogenous to the transit travel demand analysis, but is assumed to be determined by a separate competitive market for the goods provide by the firm. In the case where there is congestion effect, i.e. T ðqÞ is an increasing is determined from an equilibrium function, the profit q⁄, derived from the system of two equations g ¼ bT ðq Þ þ c0 cf and q ¼ D0 eag . Since a closed form analytical solution depends on the functional form of T ðqÞ and can nonetheless get very messy for any function besides unrealistic linear ones, we analyze the negligible congestion effect case here, where T = t is constant. Negligible congestion effect is justifiable because on a daily time interval scale, the capacity of a transit service is generally quite large. Furthermore, firms that would use this transaction model are more likely to be social-recreational destinations than workplaces for employees, so travel would more likely occur at non-peak commute times. Third, the transaction model benefits demand responsive services most, which are more competitive against fixed-schedule transit service during off-peak periods where frequencies on fixed-schedule transit are less. There may also be congestion effects at the destination itself (crowding, capacity in number of servers, etc.), but destination congestion is a more complex issue because there exist both negative and positive
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congestion effects. Destinations, particularly social-recreational ones, may benefit from being popular locations with many customers, which would counteract the negative congestion effects. As such, no congestion is assumed for both the travel and the destination. Substituting in Eq. (1) leads to Eq. (3).
P ¼ R cf D0 ea½btþðc0 cf Þ
ð3Þ
0 cf c0 The optimal e-coupon price is obtained from the first order condition:
h i h i h i a btþ c0 cf a btþ c0 cf a btþ c0 cf dP ¼ 0 ¼ aRD0 e D0 e acf D0 e dcf
a ¼ a R 1 a D0 e cf
h
btþ c0 cf
i
Since c0 cf is bounded and finite, the exponent cannot go to zero. It can be removed along with the D0 from the equation, which leads to the optimal price shown in Eq. (4).
cf
¼
8 > < > :
R 1a < 0
0; 1
R a ; 0 R a1 c0
ð4Þ
R 1a > c0
c0 ;
Using the exponential demand functional form, it appears that the optimal coupon price is only sensitive to the revenue and the elasticity parameter, which is quite convenient for analysis without requiring any strong assumptions. The effect of the model on consumer welfare due to transit travel cost can be illustrated for the general congestion cost case with a supply and demand curve as shown in Fig. 2. The improvement in consumer welfare can be measured by the area bounded by the region ABCD. This can be represented by Eq. (5a) for the congested case and Eq. (5b) for the non-congested case, where q1 is the equilibrium number of travelers without an e-coupon and q2 is the equilibrium number of travelers with e-coupons. Eq. (5b) is integrating over the cost axis since the costs are fixed (no congestion), as opposed to Eq. (5a) with congestion effects that require integrating the inverse demand function over the quantity axis and subtracting the total cost.
DSW ¼
Z
q2
ln u ln D0
a
q1
DSW ¼
Z
btþc0
btþ c0 cf
du q2 b T q2 þ c0 þ q1 b T q1 þ c0 cf
ðD0 eaw Þdw
ð5aÞ
ð5bÞ
Fig. 3 shows how the maximum profit may be achieved relative to no coupon, if it exists within the c0 range. This profit is only with respect to the travelers arriving by transit, and is not indicative of the total profit for goods by that firm. The dashed red line represents the profit that would be earned if no coupon is issued. It is possible that a coupon can lead to a net loss compared to having no coupon.
Demand Generalized Travel Cost
Cost of Travel
B A c0
cf* D
C
Number of Travelers Fig. 2. Travel supply-demand curve.
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e-coupon price cf Fig. 3. Profit curve for firm issuing e-coupon.
In some cases, a firm may need to consider an e-coupon but is limited by the maximum capacity of visitors. In those scenarios, the profit maximization in Eq. (3) needs to be accompanied by a capacity constraint, as shown in Eq. (6).
D0 ea½btþðc0 cf Þ K
ð6Þ
where K is the maximum capacity of the firm’s visitors arriving by transit. The constraint can be dealt with by constructing a Lagrangian to obtain Eq. (7).
LP ¼ R cf D0 e
a btþðc0 cf Þ
h
p D0 e
a btþðc0 cf Þ
i
! K
ð7Þ
where p is the Lagrange multiplier for constraint (6). A solution to this problem needs to satisfy the following Karush–Kuhn–Tucker conditions:
h i h i a bðtt þct w Þþ c0 cf a bðt t þct w Þþ c0 cf @L ¼ 0 ¼ aR 1 acf D0 e ap D0 e @cf h
a bðt t þct w Þþ c0 cf
i
p D0 e h
a bðt t þct w Þþ c0 cf
D0 e
! K
¼0
i K
p ; cf 0 3.2. Illustrative example Consider a fixed route transit system accessing a big box retail development with the following parameters (no congestion effect).
b ¼ 15; tt ¼ 0:6; c ¼ 1:25; tw ¼ 0:15; d ¼ 1; t a ¼ 0:1; c0 ¼ 2:5; R ¼ 15; D0 ¼ 500; a ¼ :1 These values indicate a value of time of $15/h, an in-vehicle travel time of 36 min, wait time of 9 min, and access time of 6 min. The revenue per customer is expected to be $15, and the maximum possible demand is 500 travelers. The transit fare is $2.50. Without any coupon, the demand function forecasts a ridership of d = 102.86 travelers taking transit to visit this location. The firm’s daily profit at this setting is 15d = $1542.89. The optimal e-coupon price is max min c0 ; R 1a ¼ max min 2:5; 15 :11 ¼ $2:5. Because the transit fare is only $2.5, the firm cannot provide a greater subsidy to travelers even though the optimal unbounded price should be $5. When fully reimbursing travelers for the fare, the ridership increases up to d = 132.07 travelers to visit the location. The firm’s profit increases to $1650.91, which is an improvement of 7%. Furthermore, the consumer welfare due to increased ridership increases by 500 e:1ð15:8125Þ þ 500 e:1ð13:8125Þ ¼ 227:73. This example illustrates conditions under which both the firm can :1 :1 increase profits while improving ridership and consumer welfare.
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3.3. Benefits for demand responsive transit DRT systems exhibit several qualities that make it ideal for third party firms to adopt e-coupons: (1) they are generally used for non-commute purposes; (2) they generally set higher fares than fixed route transit due to the higher cost of operations; and (3) they operate under closed access systems where users would generally have to book their service beforehand. In the following numerical example, the same parameters from Section 3.2 are modified to illustrate a DRT system, to observe the potential applicability. Consider a DRT system with the following attributes:
b ¼ 15; tt ¼ 0:33; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; ta ¼ 0; c0 ¼ 10; R ¼ 15; D0 ¼ 500; a ¼ :1 The major differences from Section 3.2 are the reduced in-vehicle travel time (19.8 min instead of 36 min), the zero access time, and the higher fare ($10 instead of $2.5). Without a coupon, this service would result in d = 84.64 travelers due to the high fare and despite the improved travel time. The firm’s profit is only $1269.60, which is a less desirable mode for the firm. In this scenario, however, the optimal e-coupon price of $5 can be set. At that price, the ridership demand increases up to 139.54 travelers, or a profit of $1395.41. That is a profit increase of 9.9%. Furthermore, the consumer welfare improves by 549.05, which is higher than the fixed route scenario. Given the right conditions, DRT can be a more ideal setting for applying transit fare e-coupons for firms. 4. Multiple firms, multiple origins How well do the conclusions about the benefit to firm profit and consumer welfare translate when there are multiple identical firms participating in this model and competing for the same travelers? This is an important question, because public transport agencies may implement this relatively unchecked and let the market run its course, or regulate it for specific types of destinations and activities. 4.1. Two-firm oligopoly, single origin game In this game, a population of travelers needs to choose one of two destinations to visit to gain utility represented by the attractiveness of that location. Staying at home is one of the options, where the utility and travel disutility are both set to zero. The destination choice can be modeled as a multinomial logit model, similar to the model presented by Kitamura et al. (1998). Assuming the two firms are identical in every aspect, except for in-vehicle travel time, we obtain the following demand function for firm i in Eq. (8).
di ¼
D0 eUa½bðtit þctw þdta Þþðc0 cif Þ eUa½bðtit þctw þdta Þþðc0 cif Þ þ eUa½bðtjt þctw þdta Þþðc0 cjf Þ þ 1
ð8Þ
where U is the utility, or attractiveness, of the destination firm, and j refers to the other firm. The number of travelers who stay home is determined by Eq. (9).
dhome ¼
D0 eUa½bðt1t þctw þdta Þþðc0 c1f Þ þ eUa½bðt2t þctw þdta Þþðc0 c2f Þ þ 1
ð9Þ
Corresponding to the demand is the profit function for each firm in Eq. (10).
Pi ¼
R cif D0 eUa½bðtit þctw þdta Þþðc0 cif Þ eUa½bðtit þctw þdta Þþðc0 c1f Þ þ eUa½bðtjt þctw þdta Þþðc0 cjf Þ þ 1
ð10Þ
Pi can be represented in a more standard form (for easier manipulation later):
R cif D0 Pi ¼ 1 þ ea½bðtjt tit Þþðcif cjf þ eUþa½bðtit þctw þdta Þþðc0 cif Þ
Since the optimal pricing strategy and subsequent payoff for firm i also depends on the pricing strategy of firm j, it is clear that this is a non-cooperative game. The first order condition for firm i is derived, assuming firm j’s pricing strategy is fixed.
a½bðt jt t it Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ @P i aRD0 e ¼ 2 @cif 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ D0 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ 2 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ ac1f D0 ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ 2 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ
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Since the denominator is finite and greater than zero, it can be removed. Rearranging the remaining terms, we get the following first order condition in Eq. (11).
1 ¼ aR 1 acif
h
e
a bðt jt t it Þþ cif cjf
i
h
þe
Uþa bðt it þct w þdta Þþ c0 cif
i ! ð11Þ
Eq. (11) is firm i’s best response function (BRF), in non-standard form. The optimal price can be obtained using numerical methods like Newton-Raphson. Since the two firms are identical, the other firm should have a symmetric BRF. 4.2. Existence and uniqueness of Nash equilibrium for N-person game According to Rosen (1965), Nash equilibria exist if the BRF for each player is continuous and concave within a bounded space. A sufficient condition for concavity of Eq. (11) is that the second order derivative is negative definite.
h i h i ! a bðt jt t it Þþ cif cjf Uþa bðt it þctw þdta Þþ c0 cif @BRF ¼ a e þe @cif h i h i ! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþ c0 cif jt it jf if e þe a aR 1 acif h i h i ! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþ c0 cif jt it jf if ¼ a2 R 2a a2 cif e þe h i h i! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþðc0 cif Þ @ 2 BRF jt it jf if 2 ¼ a aR 3 acif e þe @cif 2 h i ! a bðt t Þþ c c @ 2 BRF jt it jf if 2 ¼ a aR 2 acif e @cif @cjf Since the exponents are always non-negative, the negative definite condition occurs for the problems where the parameters are such that aR 2 acif < 0. Proposition 1. The N-player e-coupon transit fare pricing game has a unique Nash equilibrium if aR 2 acif < 0. Proof. For uniqueness, Rosen (1965) showed that a BRF that is diagonally strictly concave would result in a unique equilibrium. A sufficient condition for a function to be diagonally strictly concave is that the symmetric matrix of the pseudogradient function is negative definite. The pseudogradient function is defined as follows.
2 g
cf ; r
2
2 c1f
h
a bðt 2t t 1t Þþ c1f c2f
i
h
Uþa bðt 1t þct w þdta Þþðc0 c1f Þ
i! 3
7 6 r 1 a R 2a a e þe 7 6 7 6 h i h i! 7 ¼6 7 6 a bðt t Þþ c c Uþ a b ð t þ c t þdt Þþ c c ð Þ w a 1t 2t 2t 0 5 4 1f 2f 2f e þe r 2 a2 R 2a a2 c2f
If there exists Nash equilibria, then aR 2 acif < 0. The second order derivative of g cf ; r with respect to cf leads to negative definite condition only if aR 3 acif < 0. Since this always occur when there exists Nash equilibria, then the equilibrium is always unique. While this is shown for a 2-player game, the conditions trivially extend to the N-person case, particularly when observing the BRF for the N-person game in Section 4.5. It is also known in the game theory literature that the Nash equilibrium condition for an N-person non-cooperative game is equivalent to those of 2-person game (Fisk, 1984). 4.3. Numerical example: two symmetrically located firms When increasing the number of firms from one to two, the effect on consumer welfare, firm profit, and ridership demand will vary and depend on many different factors. However, this section demonstrates the possibility that going to two firms, under mild assumptions consistent with the single firm case, can lead to negative consequences for the firms at the benefit of the transit agency and the travelers. While this numerical example is not indicative of all cases, it gives policymakers reason to be cautious when implementing these policies. We return to the parameters of the earlier example for fixed route transit, applying these identical conditions for two firms:
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b ¼ 15; tt ¼ 0:6; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; t a ¼ 0:1; c0 ¼ 2:5; R ¼ 15; D0 ¼ 500; a ¼ :1; U ¼ 1 Note in this example both firms are located equally at 0.6 h away from the traveler origin. A relative utility of U = 1 compared to staying at home is considered (which implies a firm revenue of $15 per unit of utility gained per traveler). Because of the utility and destination choice, the problem is defined differently from the monopolistic case so comparisons should not be made between the results. The BRFs for the two firms are derived and graphically shown in Fig. 4. The graph clearly shows the existence of a unique pure Nash equilibrium, located at {$1.145, $1.145}. Since aR 2 acif ¼ 0:6145 < 0 in this case, there equilibrium is unique. The pricing strategies are such that neither firm can unilaterally stray without being worse off in profit. The total profit, or payoff, for each firm is $1927.09. However, the firms’ payoffs when no coupon option is allowed are $1979.79. This means that having the option for e-coupons under competition can lead to worse off situations for the firms (by 2.7%). Nonetheless, the public transport system benefits by increasing ridership from 263.97 travelers to 278.18 travelers, an increase of 5.4%. In that sense, this may be viewed as a tax that the transport system can levy on firms by simply providing the technology and letting the market equilibrate. Without understanding the burden that this can have on all firms in an urban region, it could be a dangerous policy to enact. 4.4. Numerical example: two asymmetrically located firms In this example, the same two firms are now placed in such a manner that firm 1 still incurs an in-vehicle travel time of 0.6 h, but firm 2 is now located at half that travel time (0.3 h). Equivalently, this might be interpreted as differences in fare prices for settings where fare pricing is distance- or zone-based. The other parameters all remain the same as in Section 4.2. The resulting BRFs are now quite different, as shown in Fig. 5. There is still only one unique pure Nash equilibrium, but it has shifted to {$1.528, $0}, an indication of the power that firm 2 has due to its closer proximity to the travelers. Without the coupon option, firm 1 would have a profit of $1721.53 while the closer firm 2 would have a profit of $2699.90. With the equilibrium pricing strategies, the payoff for firm 1 increases to $1735.65 while that of firm 2 decreases to $2601.32. Ridership also changes from {114.77, 179.99} to {128.83, 173.42}, which is an increase for firm 1 at the expense of firm 2. Overall there is a net ridership increase of 7.49, a 2.5% increase. In essence, firm 2 is forced not to set a price, as issuing a coupon would only reduce its overall profit because it would draw a marginal number of new travelers while incurring the fare cost for the much larger proportion of existing customers that would have visited it without the coupon. All other attributes equal, this effect of allowing e-coupons on asymmetrically located firms appears to reduce the location benefit of a firm and force them to be more competitive. However, a policy enacted at this level can also result in unforeseen consequences in land rental rates, which may be disrupted somewhat by the ability of a firm to price out locational disadvantages. Other types of asymmetry obviously exist as well; for example, one type may be one firm having no available parking while a second firm having free parking. Under a scenario where multiple modes (including auto) are considered, the availability of free parking would likely have an effect, and should be investigated in future research. 4.5. Network of N destinations and M origins Like the transition from one firm to two firms, the transition from two to many firms can result in different permutations of consequences to consumer welfare, firm profit, and ridership demand. Even with the simplified analytical framework used in this study, the scenario with multiple firms is so complex that generalizations should not be made. The goal of this section is to adopt an approach and to illustrate one single instance to prove that such a possibility can occur. In this case, the numerical study shows that increasing to four identical firms under consistent assumptions as the 2-firm and 1-firm cases can lead to even greater loss of profit to the firms at the benefit of the transit agency and travelers. This single result is enough evidence to warn policymakers about the risks of implementing this transaction model.
2.5 2 1.5 Firm 1 BRF
1
Firm 2 BRF
0.5 0 0
0.5
1
1.5
2
2.5
Fig. 4. Best response functions for 2-firm oligopoly e-coupon pricing strategies.
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2.5 2 1.5 Firm 1 BRF Firm 2 BRF
1 0.5 0 0
0.5
1
1.5
2
2.5
Fig. 5. Best response functions for 2 firms located asymmetrically from travelers.
For a single firm, the origins of travelers can be segmented into a set of M zones. Then, the profit for the firm would need to be aggregated up as shown in Eq. (12) with the additional r e M indexing. The pricing strategy and transit fare for now assumes no segmentation among different traveler origins.
P ¼ R cf
X
h
i
a bðt rt þct rw þdt ra Þþðc0 cf Þ
Dr0 e
ð12Þ
r2M
Similar to the single origin case in Eq. (4), the optimal e-coupon price can be obtained by finding the solution to Eq. (13).
0¼
X
r cf
ar R 1 a
ar Dr0 e
h
bðt rt þct rw þdt ra Þþ c0 cf
i ð13Þ
r2M
As Eqs. (12) and (13) suggest, the pricing strategies for a firm extend fairly naturally to multiple segmented traveler origins. When this is combined with an N-firm game, the resulting profit function for a firm is shown in Eq. (14), where –i refers to all other players in the game for player i.
Pi ¼
X r2M
1þ
P
i
R cif Dr0 ea½btrit þðcif cif Þ þ eUþa½bðtrit þctrw þdtra Þþðc0 cif Þ
ð14Þ
As shown in Section 4.2, there is a unique equilibrium to this N-firm, M-origin game with destination choice problem. The equilibrium problem can be formulated as a variational inequality (VI). As a set of profit maximization objectives, and for any price h bounded between 0 and c0 for firm i, the VI is represented by Eq. (15).
h i h i !! X a bt þ c c Uþa bðt rit þct rw þdt ra Þþ c0 cif rit if if h cif 0; 8i 2 N aR 1 acif e þe
X r2M
i
Origins M
1
Transit travel me trit (hrs)
Firms N 1
0.3 0.3 0.5
0.4 2
2
0.4 0.3 0.3 0.4 3 0.5
3
0.4 0.3 0.3
4
Fig. 6. Travel times for 4-player e-coupon game with 3-origins and destination choice.
ð15Þ
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Origins M
Transit travel me trit
Firms N 37
1
1
P* = $1,197 P(0) = $1,360
28
31
37 36
2
P* = $1,315 P(0) = $1,495
3
P* = $1,315 P(0) = $1,495
32 2 32 36 37 28 3
31 37
4
P* = $1,197 P(0) = $1,360
Fig. 7. Solution for the 4-player e-coupon game with 3-origins and destination choice.
For general problems, this can be solved using conventional VI solution algorithms (e.g. Nagurney and Ding, 1995; Nagurney and Dhanda, 2000). In this study, we evaluate a simple network extension of the earlier examples by considering four identical firms located from three different customer location segments as shown in Fig. 6. Fig. 6 shows the travel times between each origin-destination pair. Because there are three identical customer segments, the maximum demand is divided equally among them:
b ¼ 15; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; ta ¼ 0:1; c0 ¼ 2:5; R ¼ 15; Dr0 ¼
500 ; a ¼ :1; U ¼ 1 3
It turns out that under this setting, the unique equilibrium pricing strategies for the four firms gravitate toward the maximum allowable coupons of $2.50 each, which can be verified by observation without having to apply a VI solution algorithm. The uniqueness is confirmed since aR 2 acif ¼ 0:75 < 0. The volume of riders and net profits for each firm is shown in Fig. 7. Fig. 7 shows that the profit drops by 12% from the no coupon option for all four firms in this equilibrium. On the other hand, the net ridership goes up from the no coupon option of 380.75 travelers to a sum of 401.96 travelers as shown in disaggregated form for each OD pair. That is an increase of 5.6% in the ridership. By extending the case to more firms that are distributed over different locations on a generic network, the potential negative impact that e-coupons can have for an un-regulated market is made clearer. 5. Concluding remarks A new transaction model is proposed for public transport systems, in light of the technology and social need evident from startup companies in the private sector. The model makes use of the capability of travelers to book transit trips via mobile devices, which in turn allow the transport agency to commoditize the demand and outsource the revenue management to third party private firms. Travelers gain the opportunity to trade that information to third party firms, such as sports stadiums, theme parks, or large shopping centers. The private firms can use that information as leverage for revenue management by issuing electronic coupons to travelers to offset low demand. Transport agencies gain by having higher ridership for more efficient operations; travelers gain through fare subsidies. The model under a monopolistic e-coupon provider setting is shown to be ideal for non-commuting scenarios where transit ridership tends to be low and destination firms are also seeking more visitors. It is also shown to be a potential application for encouraging DRT systems, as those systems feature characteristics geared toward such a transaction model: high demand elasticity; non-commute travel purposes; closed access systems that require pre-booking; and high cost fares that give more room for firms to set optimal coupon prices. When competition comes into play with firms vying for travelers’ demand, it turns out that the e-coupon platform may actually hurt the bottom line of firms due to the competition. However, public transport systems still benefit with higher ridership, so this policy needs to be carefully considered as it can lead to drastic consequences on businesses and real estate value in an urban region. Given the promising results of the model for monopolistic firms and for DRTs, public private partnership opportunities between DRT systems and planned events operated by private sector are recommended. Further study should be conducted on an environment where multiple firms can issue e-coupons to travelers, so that cases can be made on an individual basis where an e-coupon system may be needed. Further research should also be conducted on oligopolies with explicit capacity constraints for each firm, and to consider networks that include automobile mode, road congestion, parking capacity, destination capacity for both auto and transit users, and parking pricing integrated with transit fare e-coupons. Pilot tests can be conducted by transit agencies to empir-
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ically test the public’s acceptance of such a business model and the impact it would play. These pilot tests should evaluate the effect that the model may have on time-of-day distributions and other important factors. Extensions of the model to travelers with heterogeneous values of time and cost factors can be considered. Actual implementation of this policy will require different considerations that pertain to the users. For example, transit systems that use monthly passes may risk having travelers that make trips to destinations solely to accrue credits for travel if the fare is already fixed at a pre-paid amount. To address, the implementation may involve different pre-booking requirements, purchase requirements at the destination, limitations on number of claims, or to more directly account for travel time in the discount value. These issues are similar to those that are faced by other pricing policies like mobility credits, parking rebates, etc., that have been studied in recent years.
Acknowledgments This research was undertaken, in part, thanks to funding from the Canada Research Chairs program. Helpful comments from two anonymous referees are much appreciated.
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Tirachini, A., 2013. Estimation of travel time and the benefits of upgrading the fare payment technology in urban bus services. Transp. Res. Part C 30, 239– 256. Tirachini, A., Hensher, D.A., 2011. Bus congestion, optimal infrastructure investment and the choice of a fare collection system in dedicated bus corridors. Transp. Res. Part B 45 (5), 828–844. Yang, H., Wang, X., 2011. Managing network mobility with tradable credits. Transp. Res. Part B 45 (3), 580–594. Zhang, X., Yang, H., Huang, H.J., 2011. Improving travel efficiency by parking permits distribution and trading. Transp. Res. Part B 45 (7), 1018–1034.
Contents lists available at ScienceDirect
Transportation Research Part A journal homepage: www.elsevier.com/locate/tra
Policy analysis of third party electronic coupons for public transit fares Joseph Y.J. Chow ⇑ Ryerson University, Toronto, ON, Canada
a r t i c l e
i n f o
Article history: Received 16 May 2013 Received in revised form 14 May 2014 Accepted 29 May 2014 Available online 24 June 2014 Keywords: Public transport Automated fare collection Marginal cost theory Revenue management Game theory Electronic coupon
a b s t r a c t Mobile technologies are generating new business models for urban transport systems, as is evident from recent startups cropping up from the private sector. Public transport systems can make more use of mobile technologies than just for measuring system performance, improving boarding times, or for analyzing travel patterns. A new transaction model is proposed for public transport systems where travelers are allowed to pre-book their fares and trade that demand information to private firms. In this public-private partnership model, fare revenue management is outsourced to third party private firms such as big box retail or large planned events (such as sports stadiums and theme parks), who can issue electronic coupons to travelers to subsidize their fares. This e-coupon pricing model is analyzed using marginal cost theory for the transit service and shown to be quite effective for monopolistic coupon rights, particularly for demand responsive transit systems that feature high cost fares, non-commute travel purposes, and a closed access system with existing pre-booking requirements. However, oligopolistic scenarios analyzed using game theory and network economics suggest that public transport agencies need to take extreme care in planning and implementing such a policy. Otherwise, they risk pushing an equivalent tax on private firms or disrupting the urban economy and real estate values while increasing ridership. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Urban sustainability depends on making public transport systems attractive to travelers (Kennedy, 2002; Sinha, 2003). Without high ridership, public transport requires costly subsidies (Parry and Small, 2009) partly because few riders results in lower operating frequency and consequently higher user costs such as wait and access time (Mohring, 1972). However, many transport systems around the world operate with low ridership outside of the peak periods, and in some cases for all periods. This problem is especially endemic in low population density suburban communities in the United States. Of course, there are exceptions where transit ridership is so high compared to the available capacity that congestion at a station or in a vehicle is a recurrent problem (Lam et al., 1999; Hamdouch and Lawphongpanich, 2010). For fixed route and fixed schedule services, low ridership during off-peak periods, combined with demand uncertainty, can lead to lower cost efficiency of a system. Ridership concern is even greater when operating demand responsive transit (DRT) systems (Schofer et al., 2003): paratransit, dial-a-ride, or personal DRT. These systems operate with relatively smaller capacity vehicles compared to buses or rail, and they can spend significant portions of their time running empty after dropping off passengers. ⇑ Tel.: +1 416 979 5000. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.tra.2014.05.015 0965-8564/Ó 2014 Elsevier Ltd. All rights reserved.
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Proper revenue management, which involves dynamic pricing and marketing strategies to maximize revenue, can improve ridership and other system performance measures (Li et al., 2009). As those authors pointed out, the challenge that the public transport industry faces compared to the airline or car rental industries is that it is an open-access system that does not require pre-booking. The result is that travel demand and behavior remain difficult to forecast. In cases where reservations can be made, such as intercity rail, revenue management models are being developed (e.g. Cirillo et al., 2011). However, urban public transport systems at best can implement pricing differentiation strategies—time-based pricing, directional pricing, regional pricing, usage-based pricing, or demand-based pricing (Li et al., 2005)—because of the inherent open access structure. Technology may perhaps change this outlook. Automated fare collection (AFC) systems have enabled many of the pricing strategies presented by Li et al. (2005). Smart card technologies reduce the amount of time it takes to board a transit vehicle, which can ultimately improve operational efficiency (Tirachini and Hensher, 2011; Tirachini, 2013). The technology allows transit system performance measures to be collected (Morency et al., 2007), and for travel patterns to be estimated (Chakirov and Erath, 2011; Nassir et al., 2011; Munizaga and Palma, 2012). With the growing use of mobile devices, further opportunities in fare collection are possible. In Helsinki, Finland, public transport users have been able to pay their fares with their mobile phones since 2001 (Mallat et al., 2008). Böhm et al. (2005) explained the practical advantage of paying fares through mobile devices, which reduces the cost of transit infrastructure for AFC and also presents opportunities for location-based services to link with fare payment. Páez et al. (2011, 2012) saw an opportunity to engage private sector with the transit demand information available from smart cards, and proposed spatial analysis methods to identify local business opportunities or to market to particular demographics. If we consider the near-future scenario where the majority of the population owns mobile devices that can purchase fares offsite from a transit system, what can be done to improve ridership? Besling et al. (2002) introduced the idea of using smart cards to allow payment of electronic coupons. With mobile devices, there is potential for a new form of fare transaction model where the public transport system’s revenue management can be outsourced to third party private firms, as suggested by Páez et al. (2011) in the form of rebates, offers, and/or loyalty points. These firms would issue electronic coupons to travelers to subsidize their fares. Traditional coupons already exist, but only in limited form, for example for intercity bus services to take tourists to casinos. In an urban area, traditional coupons would not work because there is no centralized control; for example, a traveler may just take a paid transit fare to multiple vendors at a destination and ask for rebates if they all participated in the model. This is why this business model is used by intercity destinations like casinos but has not yet found its way to urban destinations. Even existing businesses that currently provide free transportation service to their customers can benefit, because they are investing in the free transportation due to insufficient capacity or demand from other modes like driving. In these cases, the businesses would be transferring the cost to an alternative that may be less costly while increasing transit ridership. In this example of a public-private partnership, the public transport system serves as a platform for fare transactions. Firms that operate large destinations for travelers, such as a sports stadium, a theme park, or big box retail, can issue electronic coupons on the platform. Users are allowed to book their transit fares in advance (pre-book), and in doing so, have the option to claim a coupon if they intend to travel to that destination. When they arrive at the destination and check in to that location, the platform gets informed of completion of the travel transaction, and their trip fare is reimbursed in the amount of the coupon. The advantages of such a system are three-fold: (1) the firms can attract more customers, or may seek customers arriving by other modes due to limited parking availability; (2) ridership goes up for the transport system; (3) and fares can be subsidized for the travelers. The need to pre-book ensures that random strangers cannot go to a participating firm and request a coupon. This model may be used by firms to encourage their employees to commute by public transit, although it has much more applicability to retail and leisure destinations where additional customers translate directly to increases in revenue, and because peak periods may already suffer from congested transit service. Because of the intended use, the ridership increase is likely to occur during off-peak periods as opposed to peak commute periods, resulting in increased efficiencies in the public transport system. It is a situation that can benefit all parties involved. This transaction model is illustrated in Fig. 1, although more sophisticated processes may also be implemented that ensure more secure exchange of travel demand for purchases (e.g. providing the coupon if a customer spends X dollars). These are implementation and design issues that require testing in practice to refine. The purpose of this study is to gain a deeper insight to the proposed transaction model and to answer several policyrelated research questions. First, a marginal cost model is designed to evaluate the consumer welfare potential of the transaction model, which is not just applicable to e-coupons, but also to traditional coupons like in the example earlier. Should a public transport agency allow travel demand to essentially be commoditized and traded with third party private firms? Under what conditions would it make sense to do so? The marginal cost model is used to illustrate how the transaction model can be especially beneficial to DRT systems. An important policy question is how much regulation the transport agency should have on deciding which firms can enter this ‘‘travel demand e-coupon’’ market. Oligopolistic games are constructed between two firms allowed to offer coupons (note that even though the coupon provision is oligopolistic, the firms themselves are assumed to operate within a competitive market), and then for a network of M traveler origins and N destination firms to evaluate this policy.
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Public Transport System Purchase fare, claim coupon
Firms
Generate e-coupon
Transport Check-in Confirm check-in Reimburse fare Fig. 1. Swim lane event diagram of the proposed transaction model.
The remainder of this study is organized as follows. Section 2 is a more comprehensive literature review that focuses on the motivation of this work involving travel information in public transport systems and the evolution of technologies toward this proposed transaction model. Section 3 presents the optimal pricing of an e-coupon for a single firm, with comparisons between fixed route transit and DRT. Section 4 considers oligopolistic games between multiple firms.
2. Motivation The use of smart card data in public transport systems has reached quite a mature point since it first became popular in the 1990s (Pelletier et al., 2011). However, the technology has been used primarily as a data source to better understand travel behavior (Bagchi and White, 2005) or to measure system performance. Related to this research is a need to protect the privacy of users while collecting their travel data and using or sharing it in a public manner (Chen et al., 2012). Ways to use the technology or to introduce new business models in public transport have not been explored to the same extent, much less developing analytical models to evaluate public transport systems operating under such technologies. Several researchers (Oram et al., 1996; Li et al., 2009; Camacho et al., 2013) adopted management frameworks to evaluate the benefits of AFC in introducing new operational strategies or business models, or to investigate these benefits for vendors (Hickman et al., 1998). However, they did not provide any analytical model to evaluate the transport systems. Tirachini (2013) developed one of the few analytical models to evaluate the decision to adopt AFC technology, using multiple regression on transit corridors to show the degree of boarding time savings. He found that benefits of upgrading to AFC increased as the ridership demand increased. Some recent studies have been conducted on information flow within public transport systems in the context of tradeoffs between wait time and planning time for scheduled arrivals (Fosgerau, 2009; de Borger and Fosgerau, 2012). Travelers are assumed to be provided information by the transport agencies, and the optimal quality of information provision is modeled jointly with socially optimal fares. Despite advances in quantifying the value of AFCs and in information provision with a public transport system, there is still a considerable lack of research in business models or revenue management strategies related to adoption of mobile device technologies and the information that they generate. Some exceptions include DRTs designed under the assumption that the technology is already in place, such as the High Coverage Point to Point Transit system (Cortés and Jayakrishnan, 2002; Jung and Jayakrishnan, 2011). In the last few years, new startups in the private sector such as Uber.com and IGGEOS.com have formed to take advantage of the niche market opportunities that the mobile device technology has opened up in urban transport services. These companies and others provide proprietary web-based platforms for booking trips and pricing models for their fares. Systems also exist for collecting large amounts of destination data from online data sources like YELP.com and using that to recommend activities to travelers (Chow and Liu, 2012). Some early progress is being made to cyber-physical systems for public transport, where real time transit data is provided in an interactive manner to mobile technology users (Lau et al., 2011). These examples are evidence that the technology is in place for incorporating mobile technologies and destination information into transport services. This opportunity has not been missed by researchers, as a number of studies have analyzed how travelers can trade ‘‘mobility credits’’ with one another, either for paying tolls or transit fares (Yang and Wang, 2011), parking permits (Zhang et al., 2011), or pollution permits (Nagurney and Dhanda, 2000), among others. These studies focus on trading between travelers for the purpose of allowing a free market to equitably transfer travel costs throughout a population. There is also an opportunity to involve the private sector in trading travel demand. Unlike earlier studies, the purpose of the proposed transaction model is to outsource a transport system’s revenue management to private firms by allowing them to trade mobility with travelers, increase ridership for the transport system, and reduce the burden of travel costs on travelers. New analytical models are presented to evaluate a transit system that operates under such an e-coupon transaction model, further expanding the literature on analytical models for evaluating transport system technologies.
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3. Single firm e-coupons The economics of this transaction model is studied for a single firm issuing e-coupons to identify the requirements for finding an optimal price. To be clear, this single firm is still providing a good or service within a competitive environment. The goods provided by the firm are governed by the competitive market, which are goods-specific. On the other hand, the coupon is being exacted on travel demand by transit, which is a specific derived good. The coupon (and firm) act much like a toll (and toll operator); even though the firm has the sole right to set the toll, travelers can choose to go to that destination via that mode and that time period, or choose another mode like automobile, visit another destination, or not travel at all. These competing forces define the shape of the demand curve in the following section. 3.1. Optimal price for negligible congestion scenario Let us consider a destination firm for which demand is modeled as the following Eq. (1). The function assumes a monotonically decreasing value, and is meant to capture the competitive market present for the travelers: the existence of other modes, other time periods, and other destinations.
q ¼ D0 eag
ð1Þ
where D0 is the maximum demand on a typical day a is an elasticity parameter that defines the steepness of the demand curve g is a generalized cost of travel The average generalized cost may be represented by Eq. (2) for public transport service. For this analysis, automobile mode is ignored for simplicity, and travelers choosing auto mode are assumed to be among those not served by Eq. (1). Furthermore, transaction fees are assumed to be negligible in this electronic-based transaction system (Yang and Wang, 2011; Nie, 2012). Because of the negligible transaction fees, this model can be trivially extended to a multiperiod pricing model that accounts for changes throughout a day. For example, it is possible to consider a capacitated parking facility with random driving visitors as a setting for the firm to update coupon values, although the negligible fees mean this is just a simple switching option that does not require any look-ahead policy (Kulatilaka and Trigeorgis, 2001).
g ¼ bðtt þ ctw þ dt a Þ þ c0 cf
ð2Þ
where b is a value of time parameter c is a premium for wait time over travel time d is a premium for access time over travel time Tt is in-vehicle travel time, a monotonically increasing function of number of riders, q Tw is wait time, a monotonically increasing function of number of riders, q Ta is access time, a monotonically increasing function of number of riders, q c0 is the transit fare cf is e-coupon that the firm provides a traveler The different time variables are there to allow us to evaluate different types of transit services such as DRT. The travel time functions can be calibrated to account for various congestion effects like crowding effects on platforms. To keep the representation simple, we may use T ðqÞ ¼ T t þ cT w þ dT a . As the sole issuer of the e-coupons, the firm is assumed to be maximizing profit and to set the price of the coupons. Assuming that all other business operations remain the same, the net profit P including coupon cost is defined as:
P ¼ q R cf where R is the expected profit per customer visiting the firm. Note that this value is exogenous to the transit travel demand analysis, but is assumed to be determined by a separate competitive market for the goods provide by the firm. In the case where there is congestion effect, i.e. T ðqÞ is an increasing is determined from an equilibrium function, the profit q⁄, derived from the system of two equations g ¼ bT ðq Þ þ c0 cf and q ¼ D0 eag . Since a closed form analytical solution depends on the functional form of T ðqÞ and can nonetheless get very messy for any function besides unrealistic linear ones, we analyze the negligible congestion effect case here, where T = t is constant. Negligible congestion effect is justifiable because on a daily time interval scale, the capacity of a transit service is generally quite large. Furthermore, firms that would use this transaction model are more likely to be social-recreational destinations than workplaces for employees, so travel would more likely occur at non-peak commute times. Third, the transaction model benefits demand responsive services most, which are more competitive against fixed-schedule transit service during off-peak periods where frequencies on fixed-schedule transit are less. There may also be congestion effects at the destination itself (crowding, capacity in number of servers, etc.), but destination congestion is a more complex issue because there exist both negative and positive
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congestion effects. Destinations, particularly social-recreational ones, may benefit from being popular locations with many customers, which would counteract the negative congestion effects. As such, no congestion is assumed for both the travel and the destination. Substituting in Eq. (1) leads to Eq. (3).
P ¼ R cf D0 ea½btþðc0 cf Þ
ð3Þ
0 cf c0 The optimal e-coupon price is obtained from the first order condition:
h i h i h i a btþ c0 cf a btþ c0 cf a btþ c0 cf dP ¼ 0 ¼ aRD0 e D0 e acf D0 e dcf
a ¼ a R 1 a D0 e cf
h
btþ c0 cf
i
Since c0 cf is bounded and finite, the exponent cannot go to zero. It can be removed along with the D0 from the equation, which leads to the optimal price shown in Eq. (4).
cf
¼
8 > < > :
R 1a < 0
0; 1
R a ; 0 R a1 c0
ð4Þ
R 1a > c0
c0 ;
Using the exponential demand functional form, it appears that the optimal coupon price is only sensitive to the revenue and the elasticity parameter, which is quite convenient for analysis without requiring any strong assumptions. The effect of the model on consumer welfare due to transit travel cost can be illustrated for the general congestion cost case with a supply and demand curve as shown in Fig. 2. The improvement in consumer welfare can be measured by the area bounded by the region ABCD. This can be represented by Eq. (5a) for the congested case and Eq. (5b) for the non-congested case, where q1 is the equilibrium number of travelers without an e-coupon and q2 is the equilibrium number of travelers with e-coupons. Eq. (5b) is integrating over the cost axis since the costs are fixed (no congestion), as opposed to Eq. (5a) with congestion effects that require integrating the inverse demand function over the quantity axis and subtracting the total cost.
DSW ¼
Z
q2
ln u ln D0
a
q1
DSW ¼
Z
btþc0
btþ c0 cf
du q2 b T q2 þ c0 þ q1 b T q1 þ c0 cf
ðD0 eaw Þdw
ð5aÞ
ð5bÞ
Fig. 3 shows how the maximum profit may be achieved relative to no coupon, if it exists within the c0 range. This profit is only with respect to the travelers arriving by transit, and is not indicative of the total profit for goods by that firm. The dashed red line represents the profit that would be earned if no coupon is issued. It is possible that a coupon can lead to a net loss compared to having no coupon.
Demand Generalized Travel Cost
Cost of Travel
B A c0
cf* D
C
Number of Travelers Fig. 2. Travel supply-demand curve.
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e-coupon price cf Fig. 3. Profit curve for firm issuing e-coupon.
In some cases, a firm may need to consider an e-coupon but is limited by the maximum capacity of visitors. In those scenarios, the profit maximization in Eq. (3) needs to be accompanied by a capacity constraint, as shown in Eq. (6).
D0 ea½btþðc0 cf Þ K
ð6Þ
where K is the maximum capacity of the firm’s visitors arriving by transit. The constraint can be dealt with by constructing a Lagrangian to obtain Eq. (7).
LP ¼ R cf D0 e
a btþðc0 cf Þ
h
p D0 e
a btþðc0 cf Þ
i
! K
ð7Þ
where p is the Lagrange multiplier for constraint (6). A solution to this problem needs to satisfy the following Karush–Kuhn–Tucker conditions:
h i h i a bðtt þct w Þþ c0 cf a bðt t þct w Þþ c0 cf @L ¼ 0 ¼ aR 1 acf D0 e ap D0 e @cf h
a bðt t þct w Þþ c0 cf
i
p D0 e h
a bðt t þct w Þþ c0 cf
D0 e
! K
¼0
i K
p ; cf 0 3.2. Illustrative example Consider a fixed route transit system accessing a big box retail development with the following parameters (no congestion effect).
b ¼ 15; tt ¼ 0:6; c ¼ 1:25; tw ¼ 0:15; d ¼ 1; t a ¼ 0:1; c0 ¼ 2:5; R ¼ 15; D0 ¼ 500; a ¼ :1 These values indicate a value of time of $15/h, an in-vehicle travel time of 36 min, wait time of 9 min, and access time of 6 min. The revenue per customer is expected to be $15, and the maximum possible demand is 500 travelers. The transit fare is $2.50. Without any coupon, the demand function forecasts a ridership of d = 102.86 travelers taking transit to visit this location. The firm’s daily profit at this setting is 15d = $1542.89. The optimal e-coupon price is max min c0 ; R 1a ¼ max min 2:5; 15 :11 ¼ $2:5. Because the transit fare is only $2.5, the firm cannot provide a greater subsidy to travelers even though the optimal unbounded price should be $5. When fully reimbursing travelers for the fare, the ridership increases up to d = 132.07 travelers to visit the location. The firm’s profit increases to $1650.91, which is an improvement of 7%. Furthermore, the consumer welfare due to increased ridership increases by 500 e:1ð15:8125Þ þ 500 e:1ð13:8125Þ ¼ 227:73. This example illustrates conditions under which both the firm can :1 :1 increase profits while improving ridership and consumer welfare.
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3.3. Benefits for demand responsive transit DRT systems exhibit several qualities that make it ideal for third party firms to adopt e-coupons: (1) they are generally used for non-commute purposes; (2) they generally set higher fares than fixed route transit due to the higher cost of operations; and (3) they operate under closed access systems where users would generally have to book their service beforehand. In the following numerical example, the same parameters from Section 3.2 are modified to illustrate a DRT system, to observe the potential applicability. Consider a DRT system with the following attributes:
b ¼ 15; tt ¼ 0:33; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; ta ¼ 0; c0 ¼ 10; R ¼ 15; D0 ¼ 500; a ¼ :1 The major differences from Section 3.2 are the reduced in-vehicle travel time (19.8 min instead of 36 min), the zero access time, and the higher fare ($10 instead of $2.5). Without a coupon, this service would result in d = 84.64 travelers due to the high fare and despite the improved travel time. The firm’s profit is only $1269.60, which is a less desirable mode for the firm. In this scenario, however, the optimal e-coupon price of $5 can be set. At that price, the ridership demand increases up to 139.54 travelers, or a profit of $1395.41. That is a profit increase of 9.9%. Furthermore, the consumer welfare improves by 549.05, which is higher than the fixed route scenario. Given the right conditions, DRT can be a more ideal setting for applying transit fare e-coupons for firms. 4. Multiple firms, multiple origins How well do the conclusions about the benefit to firm profit and consumer welfare translate when there are multiple identical firms participating in this model and competing for the same travelers? This is an important question, because public transport agencies may implement this relatively unchecked and let the market run its course, or regulate it for specific types of destinations and activities. 4.1. Two-firm oligopoly, single origin game In this game, a population of travelers needs to choose one of two destinations to visit to gain utility represented by the attractiveness of that location. Staying at home is one of the options, where the utility and travel disutility are both set to zero. The destination choice can be modeled as a multinomial logit model, similar to the model presented by Kitamura et al. (1998). Assuming the two firms are identical in every aspect, except for in-vehicle travel time, we obtain the following demand function for firm i in Eq. (8).
di ¼
D0 eUa½bðtit þctw þdta Þþðc0 cif Þ eUa½bðtit þctw þdta Þþðc0 cif Þ þ eUa½bðtjt þctw þdta Þþðc0 cjf Þ þ 1
ð8Þ
where U is the utility, or attractiveness, of the destination firm, and j refers to the other firm. The number of travelers who stay home is determined by Eq. (9).
dhome ¼
D0 eUa½bðt1t þctw þdta Þþðc0 c1f Þ þ eUa½bðt2t þctw þdta Þþðc0 c2f Þ þ 1
ð9Þ
Corresponding to the demand is the profit function for each firm in Eq. (10).
Pi ¼
R cif D0 eUa½bðtit þctw þdta Þþðc0 cif Þ eUa½bðtit þctw þdta Þþðc0 c1f Þ þ eUa½bðtjt þctw þdta Þþðc0 cjf Þ þ 1
ð10Þ
Pi can be represented in a more standard form (for easier manipulation later):
R cif D0 Pi ¼ 1 þ ea½bðtjt tit Þþðcif cjf þ eUþa½bðtit þctw þdta Þþðc0 cif Þ
Since the optimal pricing strategy and subsequent payoff for firm i also depends on the pricing strategy of firm j, it is clear that this is a non-cooperative game. The first order condition for firm i is derived, assuming firm j’s pricing strategy is fixed.
a½bðt jt t it Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ @P i aRD0 e ¼ 2 @cif 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ D0 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ 2 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ ac1f D0 ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ 2 1 þ ea½bðtjt tit Þþðcif cjf Þ þ eUþa½bðtit þctw þdta Þþðc0 cif Þ
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Since the denominator is finite and greater than zero, it can be removed. Rearranging the remaining terms, we get the following first order condition in Eq. (11).
1 ¼ aR 1 acif
h
e
a bðt jt t it Þþ cif cjf
i
h
þe
Uþa bðt it þct w þdta Þþ c0 cif
i ! ð11Þ
Eq. (11) is firm i’s best response function (BRF), in non-standard form. The optimal price can be obtained using numerical methods like Newton-Raphson. Since the two firms are identical, the other firm should have a symmetric BRF. 4.2. Existence and uniqueness of Nash equilibrium for N-person game According to Rosen (1965), Nash equilibria exist if the BRF for each player is continuous and concave within a bounded space. A sufficient condition for concavity of Eq. (11) is that the second order derivative is negative definite.
h i h i ! a bðt jt t it Þþ cif cjf Uþa bðt it þctw þdta Þþ c0 cif @BRF ¼ a e þe @cif h i h i ! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþ c0 cif jt it jf if e þe a aR 1 acif h i h i ! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþ c0 cif jt it jf if ¼ a2 R 2a a2 cif e þe h i h i! a bðt t Þþ c c Uþa bðt it þct w þdt a Þþðc0 cif Þ @ 2 BRF jt it jf if 2 ¼ a aR 3 acif e þe @cif 2 h i ! a bðt t Þþ c c @ 2 BRF jt it jf if 2 ¼ a aR 2 acif e @cif @cjf Since the exponents are always non-negative, the negative definite condition occurs for the problems where the parameters are such that aR 2 acif < 0. Proposition 1. The N-player e-coupon transit fare pricing game has a unique Nash equilibrium if aR 2 acif < 0. Proof. For uniqueness, Rosen (1965) showed that a BRF that is diagonally strictly concave would result in a unique equilibrium. A sufficient condition for a function to be diagonally strictly concave is that the symmetric matrix of the pseudogradient function is negative definite. The pseudogradient function is defined as follows.
2 g
cf ; r
2
2 c1f
h
a bðt 2t t 1t Þþ c1f c2f
i
h
Uþa bðt 1t þct w þdta Þþðc0 c1f Þ
i! 3
7 6 r 1 a R 2a a e þe 7 6 7 6 h i h i! 7 ¼6 7 6 a bðt t Þþ c c Uþ a b ð t þ c t þdt Þþ c c ð Þ w a 1t 2t 2t 0 5 4 1f 2f 2f e þe r 2 a2 R 2a a2 c2f
If there exists Nash equilibria, then aR 2 acif < 0. The second order derivative of g cf ; r with respect to cf leads to negative definite condition only if aR 3 acif < 0. Since this always occur when there exists Nash equilibria, then the equilibrium is always unique. While this is shown for a 2-player game, the conditions trivially extend to the N-person case, particularly when observing the BRF for the N-person game in Section 4.5. It is also known in the game theory literature that the Nash equilibrium condition for an N-person non-cooperative game is equivalent to those of 2-person game (Fisk, 1984). 4.3. Numerical example: two symmetrically located firms When increasing the number of firms from one to two, the effect on consumer welfare, firm profit, and ridership demand will vary and depend on many different factors. However, this section demonstrates the possibility that going to two firms, under mild assumptions consistent with the single firm case, can lead to negative consequences for the firms at the benefit of the transit agency and the travelers. While this numerical example is not indicative of all cases, it gives policymakers reason to be cautious when implementing these policies. We return to the parameters of the earlier example for fixed route transit, applying these identical conditions for two firms:
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b ¼ 15; tt ¼ 0:6; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; t a ¼ 0:1; c0 ¼ 2:5; R ¼ 15; D0 ¼ 500; a ¼ :1; U ¼ 1 Note in this example both firms are located equally at 0.6 h away from the traveler origin. A relative utility of U = 1 compared to staying at home is considered (which implies a firm revenue of $15 per unit of utility gained per traveler). Because of the utility and destination choice, the problem is defined differently from the monopolistic case so comparisons should not be made between the results. The BRFs for the two firms are derived and graphically shown in Fig. 4. The graph clearly shows the existence of a unique pure Nash equilibrium, located at {$1.145, $1.145}. Since aR 2 acif ¼ 0:6145 < 0 in this case, there equilibrium is unique. The pricing strategies are such that neither firm can unilaterally stray without being worse off in profit. The total profit, or payoff, for each firm is $1927.09. However, the firms’ payoffs when no coupon option is allowed are $1979.79. This means that having the option for e-coupons under competition can lead to worse off situations for the firms (by 2.7%). Nonetheless, the public transport system benefits by increasing ridership from 263.97 travelers to 278.18 travelers, an increase of 5.4%. In that sense, this may be viewed as a tax that the transport system can levy on firms by simply providing the technology and letting the market equilibrate. Without understanding the burden that this can have on all firms in an urban region, it could be a dangerous policy to enact. 4.4. Numerical example: two asymmetrically located firms In this example, the same two firms are now placed in such a manner that firm 1 still incurs an in-vehicle travel time of 0.6 h, but firm 2 is now located at half that travel time (0.3 h). Equivalently, this might be interpreted as differences in fare prices for settings where fare pricing is distance- or zone-based. The other parameters all remain the same as in Section 4.2. The resulting BRFs are now quite different, as shown in Fig. 5. There is still only one unique pure Nash equilibrium, but it has shifted to {$1.528, $0}, an indication of the power that firm 2 has due to its closer proximity to the travelers. Without the coupon option, firm 1 would have a profit of $1721.53 while the closer firm 2 would have a profit of $2699.90. With the equilibrium pricing strategies, the payoff for firm 1 increases to $1735.65 while that of firm 2 decreases to $2601.32. Ridership also changes from {114.77, 179.99} to {128.83, 173.42}, which is an increase for firm 1 at the expense of firm 2. Overall there is a net ridership increase of 7.49, a 2.5% increase. In essence, firm 2 is forced not to set a price, as issuing a coupon would only reduce its overall profit because it would draw a marginal number of new travelers while incurring the fare cost for the much larger proportion of existing customers that would have visited it without the coupon. All other attributes equal, this effect of allowing e-coupons on asymmetrically located firms appears to reduce the location benefit of a firm and force them to be more competitive. However, a policy enacted at this level can also result in unforeseen consequences in land rental rates, which may be disrupted somewhat by the ability of a firm to price out locational disadvantages. Other types of asymmetry obviously exist as well; for example, one type may be one firm having no available parking while a second firm having free parking. Under a scenario where multiple modes (including auto) are considered, the availability of free parking would likely have an effect, and should be investigated in future research. 4.5. Network of N destinations and M origins Like the transition from one firm to two firms, the transition from two to many firms can result in different permutations of consequences to consumer welfare, firm profit, and ridership demand. Even with the simplified analytical framework used in this study, the scenario with multiple firms is so complex that generalizations should not be made. The goal of this section is to adopt an approach and to illustrate one single instance to prove that such a possibility can occur. In this case, the numerical study shows that increasing to four identical firms under consistent assumptions as the 2-firm and 1-firm cases can lead to even greater loss of profit to the firms at the benefit of the transit agency and travelers. This single result is enough evidence to warn policymakers about the risks of implementing this transaction model.
2.5 2 1.5 Firm 1 BRF
1
Firm 2 BRF
0.5 0 0
0.5
1
1.5
2
2.5
Fig. 4. Best response functions for 2-firm oligopoly e-coupon pricing strategies.
J.Y.J. Chow / Transportation Research Part A 66 (2014) 238–250
247
2.5 2 1.5 Firm 1 BRF Firm 2 BRF
1 0.5 0 0
0.5
1
1.5
2
2.5
Fig. 5. Best response functions for 2 firms located asymmetrically from travelers.
For a single firm, the origins of travelers can be segmented into a set of M zones. Then, the profit for the firm would need to be aggregated up as shown in Eq. (12) with the additional r e M indexing. The pricing strategy and transit fare for now assumes no segmentation among different traveler origins.
P ¼ R cf
X
h
i
a bðt rt þct rw þdt ra Þþðc0 cf Þ
Dr0 e
ð12Þ
r2M
Similar to the single origin case in Eq. (4), the optimal e-coupon price can be obtained by finding the solution to Eq. (13).
0¼
X
r cf
ar R 1 a
ar Dr0 e
h
bðt rt þct rw þdt ra Þþ c0 cf
i ð13Þ
r2M
As Eqs. (12) and (13) suggest, the pricing strategies for a firm extend fairly naturally to multiple segmented traveler origins. When this is combined with an N-firm game, the resulting profit function for a firm is shown in Eq. (14), where –i refers to all other players in the game for player i.
Pi ¼
X r2M
1þ
P
i
R cif Dr0 ea½btrit þðcif cif Þ þ eUþa½bðtrit þctrw þdtra Þþðc0 cif Þ
ð14Þ
As shown in Section 4.2, there is a unique equilibrium to this N-firm, M-origin game with destination choice problem. The equilibrium problem can be formulated as a variational inequality (VI). As a set of profit maximization objectives, and for any price h bounded between 0 and c0 for firm i, the VI is represented by Eq. (15).
h i h i !! X a bt þ c c Uþa bðt rit þct rw þdt ra Þþ c0 cif rit if if h cif 0; 8i 2 N aR 1 acif e þe
X r2M
i
Origins M
1
Transit travel me trit (hrs)
Firms N 1
0.3 0.3 0.5
0.4 2
2
0.4 0.3 0.3 0.4 3 0.5
3
0.4 0.3 0.3
4
Fig. 6. Travel times for 4-player e-coupon game with 3-origins and destination choice.
ð15Þ
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Origins M
Transit travel me trit
Firms N 37
1
1
P* = $1,197 P(0) = $1,360
28
31
37 36
2
P* = $1,315 P(0) = $1,495
3
P* = $1,315 P(0) = $1,495
32 2 32 36 37 28 3
31 37
4
P* = $1,197 P(0) = $1,360
Fig. 7. Solution for the 4-player e-coupon game with 3-origins and destination choice.
For general problems, this can be solved using conventional VI solution algorithms (e.g. Nagurney and Ding, 1995; Nagurney and Dhanda, 2000). In this study, we evaluate a simple network extension of the earlier examples by considering four identical firms located from three different customer location segments as shown in Fig. 6. Fig. 6 shows the travel times between each origin-destination pair. Because there are three identical customer segments, the maximum demand is divided equally among them:
b ¼ 15; c ¼ 1:25; t w ¼ 0:15; d ¼ 1; ta ¼ 0:1; c0 ¼ 2:5; R ¼ 15; Dr0 ¼
500 ; a ¼ :1; U ¼ 1 3
It turns out that under this setting, the unique equilibrium pricing strategies for the four firms gravitate toward the maximum allowable coupons of $2.50 each, which can be verified by observation without having to apply a VI solution algorithm. The uniqueness is confirmed since aR 2 acif ¼ 0:75 < 0. The volume of riders and net profits for each firm is shown in Fig. 7. Fig. 7 shows that the profit drops by 12% from the no coupon option for all four firms in this equilibrium. On the other hand, the net ridership goes up from the no coupon option of 380.75 travelers to a sum of 401.96 travelers as shown in disaggregated form for each OD pair. That is an increase of 5.6% in the ridership. By extending the case to more firms that are distributed over different locations on a generic network, the potential negative impact that e-coupons can have for an un-regulated market is made clearer. 5. Concluding remarks A new transaction model is proposed for public transport systems, in light of the technology and social need evident from startup companies in the private sector. The model makes use of the capability of travelers to book transit trips via mobile devices, which in turn allow the transport agency to commoditize the demand and outsource the revenue management to third party private firms. Travelers gain the opportunity to trade that information to third party firms, such as sports stadiums, theme parks, or large shopping centers. The private firms can use that information as leverage for revenue management by issuing electronic coupons to travelers to offset low demand. Transport agencies gain by having higher ridership for more efficient operations; travelers gain through fare subsidies. The model under a monopolistic e-coupon provider setting is shown to be ideal for non-commuting scenarios where transit ridership tends to be low and destination firms are also seeking more visitors. It is also shown to be a potential application for encouraging DRT systems, as those systems feature characteristics geared toward such a transaction model: high demand elasticity; non-commute travel purposes; closed access systems that require pre-booking; and high cost fares that give more room for firms to set optimal coupon prices. When competition comes into play with firms vying for travelers’ demand, it turns out that the e-coupon platform may actually hurt the bottom line of firms due to the competition. However, public transport systems still benefit with higher ridership, so this policy needs to be carefully considered as it can lead to drastic consequences on businesses and real estate value in an urban region. Given the promising results of the model for monopolistic firms and for DRTs, public private partnership opportunities between DRT systems and planned events operated by private sector are recommended. Further study should be conducted on an environment where multiple firms can issue e-coupons to travelers, so that cases can be made on an individual basis where an e-coupon system may be needed. Further research should also be conducted on oligopolies with explicit capacity constraints for each firm, and to consider networks that include automobile mode, road congestion, parking capacity, destination capacity for both auto and transit users, and parking pricing integrated with transit fare e-coupons. Pilot tests can be conducted by transit agencies to empir-
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ically test the public’s acceptance of such a business model and the impact it would play. These pilot tests should evaluate the effect that the model may have on time-of-day distributions and other important factors. Extensions of the model to travelers with heterogeneous values of time and cost factors can be considered. Actual implementation of this policy will require different considerations that pertain to the users. For example, transit systems that use monthly passes may risk having travelers that make trips to destinations solely to accrue credits for travel if the fare is already fixed at a pre-paid amount. To address, the implementation may involve different pre-booking requirements, purchase requirements at the destination, limitations on number of claims, or to more directly account for travel time in the discount value. These issues are similar to those that are faced by other pricing policies like mobility credits, parking rebates, etc., that have been studied in recent years.
Acknowledgments This research was undertaken, in part, thanks to funding from the Canada Research Chairs program. Helpful comments from two anonymous referees are much appreciated.
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