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Research in Transportation Economics 42 (2013) 77e86

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Research in Transportation Economics

journal homepage: www.elsevier .com/locate /retrec

Cooperation among freight forwarders: Mode choice and intermodal freighttransport

Naima Saeed*

Department of Economics, Informatics and Social Science, Molde University College, Specialised University in Logistics, 6402 Molde, Norway

a r t i c l e i n f o

Article history:Available online 26 November 2012

Classification codes:R40L91

Keywords:Freight forwardersIntermodal-transportGame theoryBertrand modelCoalition

* Tel.: þ47 (0) 71214234; fax: þ47 (0) 71214100.E-mail address: naima.saeed@himolde.no.

0739-8859/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.retrec.2012.11.005

a b s t r a c t

The objective of this paper is to compare vertical and horizontal cooperation among freight forwarders.The paper analyses three freight forwarders (‘players’) with two different means of transportation. Thefirst two players are truck-operating freight forwarders. The third player is a freight forwarder with itsown ship. For the purposes of analysis, the paper applied a two-stage game. The results revealed that thebest form of cooperation is the one in which the large truck-operating company would establish a coa-lition with the ship-operating company; that is, vertical cooperation. This cooperation would generatebetter payoffs in the form of profit, not only to the members of this coalition, but also to the player thathas not joined the coalition. However, user surplus is negative in all coalitions, which shows that theestablishment of these kinds of cooperation is not beneficial (in terms of prices) for the users of theseservice providers.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Freight forwarders have long played an important role incommerce and the international carriage of goods. Traditionally, thefreight forwarder has been the link between the owner of the goodsand the carrier, and provided forwarding or clearing services. Theforwarderacted as the agent for theownerof the cargo or the carrier.

Researchers have failed to agree on a definition of the interna-tional freight forwarders sector. Most definitions imply that freightforwarders play the role of the intermediary in international trans-port. Common definitions portray International freight forwarders(IFFs) as logistical specialists for export shipments (Cateora &Keaveney, 1987). Other views, however, indicate that IFFs provideboth export and import services (Pope & Thomchick, 1985).

In the recent past, however, freight forwarders have assumedanother role, not only helping the parties get the goods transported,but also ‘undertaking’ to have the goods transported by their ownmeans of transport (truck/train/ship) or making arrangements withother transport providers. In this role, the freight forwarder acts asa principal rather than an agent. The United Nations Conference onTrade and Development (UNCTAD, 1995) has categorised freightforwarders in “ocean-based” Multimodal Transport Operators(MTOs) or Vessel Operating Multimodal Transport Operators

All rights reserved.

(VO-MTOs), and those that do not operate vessels eNon-VesselOperating Multimodal Transport Operators (NVO-MTOs).

Some of the functions included in the freight forwarders’activities are:

� Acting on the customers’ behalf to procure the most suitablemode/combination of transportmodes, be it road, rail, sea or air.However, road, sea and air transport is most commonly used,while very few freight forwarding companies deal with railwaytransport, even casually (Kokkinis, Mihiotis, & Pappis, 2006).

� Undertaking the arrangement of the routing and choice ofmode for the customer, together with any ancillary service suchas customs clearance or packing. This level of involvementintroduces a higher level of expertise, which the shipper maynot always be able to provide.

� Offering stand-alone ancillary services, such as warehousing,customs clearance, packing and port agency.

� Moreover, freight forwarders must work closely with shippersas they must adapt and provide more value-added logisticsactivities in order to respond effectively to the ever-changingneeds of customers’ logistics requirement. This has led freightforwarders to effectively become third-party logistics serviceproviders (3PLs), particularly with regard to internationalfreight logistics services. In order to compete, many 3PLs haveutilised price competition and sales-influenced strategies. Asa result, only arms-length relationships between 3PLs andtrading firms are developed (Banomyong & Supatn, 2011).

Fig. 1. Different combinations of cooperation among freight forwarders. Source:Author.

N. Saeed / Research in Transportation Economics 42 (2013) 77e8678

Many enterprises outsource transportation tasks by entrustingindependent freight forwarding companies with their trans-portation activities. The forwarding company is allowed to choosethemode of fulfilment; that is, it can use its own vehicles to executethe corresponding entrusted tasks (self-fulfilment), or an externalfreight carrier (subcontractor) receives a fee for the request fulfil-ment (subcontracting). The subcontractor receives independentshipment contracts of different types and specifications forcompletion. According to (Chu, 2005) there are two incentives forinvolving a subcontractor. Firstly, when the total demand is greaterthan the overall capacity of owned trucks, logistics managers mayconsider using outside carriers. Secondly, integrating the choice offulfilment mode into transportation planning may bring significantcost savings to the company because better solutions can begenerated in an extended decision space. This extended problem isknown as integrated operational freight carrier planning.

A freight forwarding company’s profit is the difference betweenthe price that the customer is obliged to pay for the requestexecution and the costs of request fulfilment. These costs resulteither from fulfilment by the company’s own transportationcapacity or from the external processing of orders as a consequenceof involving a subcontractor (Krajewska & Kopfer, 2006).

As globalisation proceeds, large international freight forward-ing companies have a competitive advantage over small companiesdue to their wider portfolio of disposable resources and marketpower position. This leaves medium- and small-sized carrierbusinesses with the option of establishing coalitions in order toextend their resource portfolios and reinforce their market posi-tions (Krajewska & Kopfer, 2006). Moreover, the structure of largefreight forwarding companies often assumes autonomously oper-ating subsidiaries that should cooperate in order to maximisebusiness’ overall profit.

The purpose of having freight forwarders cooperate is to findequilibrium between the demanded and the available transportresources within several carrier entities by interchanging customerrequests (Kopfer & Pankratz, 1999).

1.1. Players

In this paper following three players are defined:

1. A freight forwarder with its own means of land transport(trucks). This is assumed to be a large truck-operating company.

2. The second player is a small truck-operating company that alsoworks as a freight forwarder.

3. The third player is a freight forwarder with its ship. This type ofplayer is known in the literature (see UNCTAD, 1995) asa vessel-operating multimodal transport operator (VO-MTO).VO-MTOs are ship owners that have extended their servicesbeyond carrying the cargo from port to port to include carriageover land and even by air. They may or may not own the othermeans of transport, in which case they arrange for these typesof transport by subcontracting with such carriers.

1.2. Different combinations of coalitions

Various combinations of coalitions are possible in this situation(see Fig.1).

1.2.1. Coalition between players 1 and 3 or between players 2 and 3For instance, if player 1 or player 2 cooperated with player 3, this

wouldresult inan intermodal freight transportation situation. This typeof cooperation is considered vertical cooperation because it involvestwo different means of transportation; that is, trucks and ships.

1.2.2. Coalitions between players 1 and 2Similarly, players 1 and 2 could cooperate with each other. This

is considered horizontal cooperation because it involves twoplayers with the same means of transportation; that is, trucks.

1.3. Expected incentives to form coalitions

The following are some of the expected benefits from theformation of coalitions:

� Potentially higher profit due to improved service quality: Aftercollaboration, freight forwarders will gain a competitiveadvantage that will increase the profit margin. Even if pricesincrease, customersmay appreciate the corresponding increasein service quality. Many researchers have found that customersselecting freight forwarders place greater emphasis on factorsother than price, such as travel duration, reliability, and qualityof transportation (Bardi, 1973; Bell, 2000; Gibson, Rutner, &Keller, 2002; Lambert, Lewis, & Stock, 1993; McGinnis, 1979).After collaboration, players will be able to improve the servicequality in terms of travel duration, reliability, etc.

� Economies of scale: Freight forwarders that form a coalitionwillhave large volumes of cargos to transfer and will therefore beable to negotiate better agreements with the carriers, load theirmeans of transport to capacity, and decrease costs. In so doing,they will achieve economies of scale by transferring largequantities per cargo.

� Economies of scope: Having established cooperation, freightforwarders can also provide value-added services to theircustomers, which will yield economies of scope.

� Moreover, one of the disadvantages of sea transport (secondplayer) compared to road transport (first player) is lowfrequency. In order to offer a satisfactory level of frequency andflexibility in service, sea transport needs a certain volume ofcargo ‘critical mass’. The formation of a coalition will help thesea transport to achieve this critical mass.

� Other disadvantages of sea transport (second player) are slowspeed and low flexibility. However, there may be room toimprove these drawbacks by combined transport solutions,using faster modes of transport on part of the journey. This isillustrated by an example of a differentiated set of transportalternatives between Kobe, Japan and Amsterdam. A customercould choose pure sea transport, which would take 28 days butat a very low cost. A faster alternative would be the ‘landbridge’solution of transporting the cargo by train over the USA. Aneven faster alternativewould be a combined air-sea alternative,or an air-only transport alternative.

N. Saeed / Research in Transportation Economics 42 (2013) 77e86 79

� Formation of coalition/coalitions, especially involving player 3,will help to reduce the congestion in roads because cargo willbe shifted from road to sea.

The objective of this paper is to compare vertical and horizontalcooperation among freight forwarders. A two-stage game is appliedfor the purpose of analysis. In the first stage, the three players haveto decide on whether to act singleton or to enter into a coalitionwith any other player (Fig. 1).

The decision at this stage should presumably be based on thepredicted outcome for the second stage. The second stage is heremodelled as a Bertrand game with one outside competitor and thecoalition. Since the first stage decision (when players have to decidewhether to join the coalition or not) depends on the predictedoutcome for the second stage, the problem will be studied bybackward induction. Furthermore, the stability of these suggestedcoalitions will be checked with the help of concepts of ‘‘coalitionalrationality” of the cooperative game.

The rest of the paper is organized as follows: Section 2 presentsa number of research works related to the application of coopera-tive game theory to the freight forwarders’ sector, and the differ-ence between this research and previous research. In Section 3,a model for a Bertrand game for the second stage and its parame-ters are presented. Section 4 constitutes a numerical analysis and isfollowed by a conclusion and policy implications in Section 5.

2. Literature review

Krajewska and Kopfer (2009) presented a model for collabora-tion among independent freight forwarding entities. They arguedthat, in today’s highly competitive transportation branch, freightforwarders reduce their fulfilment costs by exploiting differentexecution modes (self-fulfilment and subcontracting). The freightforwarders use their own vehicles to execute self-fulfilmentrequests and forward subcontracting orders to external freightcarriers. Competitiveness can be further enhanced if the freightforwarders cooperate in the form of coalitions in order to balancetheir request portfolios. Participation in such a coalition providesadditional profit for the entire coalition and for each participant,which reinforces the market position of the partners. Their paperintroduces the integrated operational transport problem, as well asexisting collaboration approaches.

Moreover, themodel proposed by Krajewska and Kopfer (2009) isbased on the combinatorial auction theory, as well as on the opera-tions research game theory. The model’s main strength is that eachparticipant generates no losses as a consequence of the collaborationand has a realistic chance of increasing its profit by participating inthe coalition. The collaboration-advantage indexes have been chosenin such a way that enables all participating coalition members toexpect positive payoff vectors. Therefore, each partner has strongincentives to join and tomaintain the coalition towhich they belong.

Ting (2009) described the logistics service (even freightforwarders with no independent means of transport) as a type ofoligopoly market because a small number of logistics serviceproviders (LSPs) always compete to win a shipping contract. Theyare interdependent in the sense that the profit that each providerearns also depends on the others’ actions. Ting (2009) use a gametheoretic approach including the Cournot, Collusion and Stackel-berg models to study the cooperative and competitive behaviouramong the oligopolistic competitors.

Cantos-Sanchez, Moner-Colonques, Sempere-Monerris, andAlvarez (2010) developed a theoretical model for freight transportthat is characterised by competition between means of transport(the road and maritime sectors), where modes are perceived asdifferentiated products. Competitive behaviour is assumed in the

road freight sector, and there are constant returns to scale. Incontrast, the freight maritime sector is characterised by oligopo-listic behaviour, whereby shipping lines enjoy economies of scale.Themarket equilibrium inwhich the shipping lines behave as profitmaximisers provides a first approximation to the determinants ofmarket shares, profits and user welfare.

Moreover, the results show that maritime freight increases afterthe merger, in cases where the merger entails further economies ofscale. When prices for maritime services increase, which occurswhen the merger only has a strategic effect, road freight transportalso increases. Furthermore, horizontal integration has been foundto be beneficial in private and social terms under certain conditions.In empirical applications, Cantos-Sanchez et al. (2010) employeddata for two freight routes between the hinterland of Valencia andthe hinterlands of Genoa and Antwerp. Their results show that, inall of the examined cases, the shipping lines have strong incentivesto merge. Additionally, a merger (horizontal integration) betweentwo shipping lines in which economies of scale are exploitedfurther generally leads to an increase in social welfare. In mostcases, the merger produces a significant increase in road traffic thatis greater than the reduction in traffic transported by the shippinglines, which leads to an increase in user surplus. Their study hasfound that the social gains depend mainly on the characteristics ofthe market. Then, the social gains obtained with the merger arehigher in those markets where the road and shipping services areless differentiated. If the services are clearly differentiated, then thesocial gains are significantly lower.

Krajewska, Kopfer, Laporte, Ropke, and Zaccour (2008) analysedthe profit margins that resulted from horizontal cooperationamong freight carriers. Thework presented in their paper combinesfeatures of routing and scheduling problems and of cooperativegame theory. The authors assumed that the structure of customerrequests corresponds to that of a pick-up and delivery problemwithtime windows for each freight carrier. The paper then discusses thepossibility of sharing these profit margins fairly among the part-ners. The paper also presents numerical results for real-life andartificial instances. The paper shows that collaboration can yielda considerable cost decrease and that efficient profit allocation ispossible using cooperative game theory.

Theys, Dullaert, and Notteboom (2008) illustrated the potentialof cooperative game theory as a methodological tool with which toanalyse intermodal networks. More specifically, they have used themany solution concepts proposed in the game-theoretic literatureto evaluate whether cooperation in an intermodal project is feasibleand efficient, as well as what would be a fair cost division among theparticipants.

According to Theys et al. (2008), an important assumption that isoften made in applications of cooperative game theory is the sub-additivity of the characteristic function, which implies that no playeris worse off as a result of cooperating and that the grand coalition isthe most efficient cooperation structure. This assumption of sub-additivity will hold for most economic applications. However, asTheys et al. (2008) illustrated, this is not necessarily the case formorerealistic intermodal cooperationprojects. Hence, they concludes that,for real-life applications in intermodal transportation, one must relyon far more advanced game-theoretic solution concepts, whichresults in a significant increase in computational complexity. Hence,practical limitations to the computations in intermodal cost-allocation games seem to exist and should be explored further.

This research is different from the previously mentionedresearch done in the same field in the following aspects. First, innone of the research is the multinomial logit model used to analysethe game outcome by solving a numerical example with the help ofdata. Second, to author’s knowledge, no one has analysed thepossibilities of coalitions between freight forwarders (vertical and

N. Saeed / Research in Transportation Economics 42 (2013) 77e8680

horizontal cooperation) as presented in this paper. Third, in thispaper the Bertrand game in terms of prices is solved but we alsoanalyse the outcome from the perspective of users’ benefits whencoalitions are formed.

3. Model

3.1. The demand for freight forwarders

This paper applies the model developed by the author inprevious work (Saeed & Larsen, 2010) in order to illustrate thecompetition and cooperation among freight forwarders. However,some additional characteristics related to the freight forwardingsector (such as schedule delay, frequency) have also been incor-porated into the model.

The present model treats the competition between freightforwarders as a Bertrand game and also uses the outcome of Ber-trand games to investigate the payoff (profit) to different coalitions.In a competitive situationwith fewplayers and a non-homogeneousproduct, the outcome in terms ofmarket shares and prices can oftenbe treated as the result of a game inwhich each playermaximises itsprofit but with due consideration of the expected reaction of itscompetitors. When a competitor’s actions are confined to settingthe prices of its ownproduct (service), the outcome can bemodelledas the Bertrand equilibrium (Pindyck & Rubinfeld, 2001).

The Bertrand game is a natural choice in this setting. We aredealing with a service industry in which competitors offer servicesthat, from the perspective of individual customers, are similar butnot quite homogeneous. In order to detail the structure of theBertrand game, the demand function faced by each service providermust be made explicit.

3.1.1. Schedule delayAnother important concept, introduced by Small (1982), is the

schedule delay costs for trips. Consumers (users) who want toundertake certain activities during a day will schedule themaccording to their preferences, taking into consideration externalconstraints. Deviating from these scheduling preferences will resultin disutility; that is, schedule delay costs. Schedule delay costs focuson alleviating congested transport networks because they indicatethe costs that travellers attribute to changing their travel behaviour(Bakens, Knockaert, & Verhoef, 2010).

Schedule delays become much more important for users’ deci-sions when any mode of transportation has low frequencies andtimetable information is used to select that mode of transportation.If a mode of transportation has high frequencies, it is believed thatusers do not use timetable information ex ante. In other words, ittakes users some effort to consult timetables, and this effort isnegligible when there is little to gain by it. Therefore, for thosemodes of transportation that have high-frequency services, userswill tend to choose the preferred departure time from the originand accept the uncertainty in terms of waiting time and total traveltime. In our case, trucks have a high frequency and lowwaiting timecompared to ships. The model considers this feature by assigninghigh negative value of alternative specific constants in the utilityfunctions of player 3 (ship-operating company).

In our numerical implementation of the Bertrand model, themarket share of each freight forwarder is determined by anaggregate multinomial logit model, and the demand for all freightforwarders combined is a function of the logsum from the logitmodel. For more details regarding the logit model, see Ben-Akivaand Lerman (1985) and Train (2003). Choice models have alsobeen used in ports and shipping, such as Tiwari, Itoh, and Doi(2003), Nir, Lin, and Liang (2003), Malchow and Kanafani (2004),and Magala (2004).

The use of a logit model presupposes that a ‘utility function’ canbe assigned to each freight forwarder. The utility functions in anaggregate logit model can be interpreted as a measure of theattractiveness of a freight forwarder as perceived by the ‘average’user.

The utility functions of freight forwarders are given asfollows:

Ui ¼ ai þ bðpiÞ (1)

Where Ui is the ‘utility’ of freight forwarder i,

pi is price charged per unit by freight forwarder ib is the co-efficient of price charged by freight forwarders and;ai is the alternative specific constant for freight forwarder i;a1,a2 > a3 due to low waiting time and high frequency oftrucks;

The market share of freight forwarder ‘i’ is given by the logitexpression:

Qi ¼eUiPjeUj

i ¼ freight forwarders (2)

The logsum is defined by:

LS ¼ ln

0@X

j

eUj

1A (3)

Thus, the total aggregate demand (in TEUs) for all the players isgiven by:

X ¼ AeqLS (4)

where A and q are constants and 0 < q < 1,Individual demand for player ‘i’ is given by the equation:

Xi ¼ X$Qi i ¼ freight forwarder (5)

Therefore, the demand faced by a freight forwarder i willdepend on handling prices and schedule delay (which is reflectedin alternative specific constant) for all players. Individual demand iselastic because changes in the price and other attributes of onefreight forwarder will shift the cargo between that freightforwarder and other freight forwarders. There will also be a slighteffect on the total demand via the logsum.

3.2. Revenue/profit for freight forwarders

The operating surplus of the freight forwarder ‘i’ is:

Pi ¼ ðpi � ciÞ$Xi (6)

Where pi is the price per cargo unit paid by the users, ci is themarginal cost per cargo unit.

Whatever the price that other freight forwarders are charging,the freight forwarder i’s profit is maximised when the incrementalprofit from a very small increase in its own price is only zero. Thus,in order to find the best reply for player i, its profit function isdifferentiated with respect to pi and the derivative is set equal tozero. Thus, the Bertrand Nash equilibrium is characterised by thefirst-order conditions:

N. Saeed / Research in Transportation Economics 42 (2013) 77e86 81

vPi

vp¼ 0; i ¼ freight forwarders (7)

i

The profit function, say for freight forwarder 1, is given by:

P1 ¼ ðp1 � c1Þ$X1 (8)

Since X1 ¼ AeqLSQ1 (9)

By substituting the value of X1 in equation (8):

P1 ¼ ðp1 � c1Þ$AeqLSQ1 (10)

P1 ¼ p1$AeqLSQ1 � c1$Ae

qLSQ1 (11)

By taking the derivative of equation (11) and setting it equal to zero:

vP1

vp1¼ AeqLSQ1 þ p1

v�AeqLSQ1

�vp1

� c1v�AeqLSQ1

�vp1

¼ 0 (12)

vP1

vp1¼ AeqLSQ1 þ ðp1 � c1Þ

v�AeqLSQ1

�vp1

¼ 0 (13)

Since X1 ¼ AeqLSQ1Taking the log of the above equation results in:

lnðX1Þ ¼ lnðAÞ þ qLSþ U1 � LS (14)

vlnðX1Þvp1

¼ vX1

vp1$1X1

(15)

Or

vX1

vp1¼ vlnðX1Þ

vp1$X1 (16)

Taking the derivative of equation (14) with respect to p1results in:

vlnðX1Þvp1

¼ qPjeUj

$

v

PjeUj

!

vp1þ vU1

vp1� 1P

jeUj

v

PjeUj

!

vp1(17)

vlnðX1Þvp1

¼ qPjeUj

$eU1ðbÞ þ b� 1PjeUj

$eU1ðbÞ (18)

vlnðX1Þvp1

¼ qbeU1PjeUj

þ b� eU1PjeUj

$b (19)

Since Q1 ¼ eU1=PjeUjSubstituting the value of Q1in the above

equation results in:

vlnðX1Þvp

¼ qbQ1 þ b� bQ1 (20)

1

vlnðX1Þvp1

¼ bðqQ1 þ 1� Q1Þ (21)

Substituting equations (9) and (21) in equation (16) results in:

vX1

vp1¼ AeqLSQ1½bðqQ1 þ 1� Q1� (22)

Substituting equation (22) into equation (13) results in:

vP1

vp1¼ AeqLSQ1 þ ðp1 � c1Þ½bðqQ1 þ 1� Q1Þ�AeqLSQ1 ¼ 0 (23)

AeqLSQ1 þ ðp1 � c1Þ½bðqQ1 þ 1� Q1Þ�AeqLSQ1 ¼ 0 (24)

AeqLSQ1f1þ ðp1 � c1Þ½bðqQ1 þ 1� Q1Þ�g ¼ 0 (25)

Solving the above equation for p1 results in:

p1 ¼ c1 �1

bðqQ1 þ 1� Q1Þ(26)

This is the implicit reaction curve (pricing rule) for player 1. Thereaction function cannot be givenon a closed form in thismodel. Theprices of the other players enter via Q1, see (1) and (2). Similarly, thereaction curves for the other two players can be derived. Solvingthese reaction functions yields the Nash equilibrium in prices.

3.3. Cooperative game with external competitors

As suggested above, the three freight forwarders can establishdifferent combinations of coalitions. In this situation, the profitfunction for each player will be different from equation (6). Forinstance, if all the freight forwarders decided to work under onedecision unit, then the profit function of the coalition (player 1, forexample) would be as follows:

P1 ¼ ½X1ðp1 � c1Þ þ X2ðp2 � c2Þ þ X3ðp3 � c3Þ� (27)

This will give three conditions, one for each price.Again, the Ber-trand Nash equilibrium is characterised by the first-order condi-tions. Therefore, by taking the derivative of equation (27) andsetting it equal to zero, we get the condition:

vP1

vp1¼v�AeqLSQ1

�vp1

ðp1 � c1Þ þ AeqLSQ1 þv�AeqLSQ2

�vp1

ðp2 � c2Þ

þv�AeqLSQ3

�vp1

ðp3 � c3Þ ¼ 0

(28)

From equation (22) we have:

v�AeqLSQ1

�vp1

¼ AeqLSQ1½bðqQ1 þ 1� Q1Þ�

The third (and fourth) terms in equation (28) are the cross-derivatives.

N. Saeed / Research in Transportation Economics 42 (2013) 77e8682

v�AeqLSQ2

�qLS

vp1ðp2 � c2Þ ¼ Ae Q2½bðqQ1 � Q1Þ�ðp2 � c2Þ (29)

Similarly,

v�AeqLSQ3

�vp1

ðp3 � c3Þ ¼ AeqLSQ3½bðqQ1 � Q1Þ�ðp3 � c3Þ (30)

Substituting equations (22), (29) and (30) in equation (28)results in:

vP1

vp1¼AeqLSQ1½bðqQ1 þ 1� Q1Þ�ðp1 � c1Þ þ AeqLSQ1

þ AeqLSQ2½bðqQ1 � Q1Þ�ðp2 � c2Þ þ AeqLSQ3½bðqQ1 � Q1Þ�� ðp3 � c3Þ ¼ 0

(31)Now: AeqLSQ1 cancels out, leaving

½bðqQ1 þ 1� Q1Þ�ðp1 � c1Þ þ 1þ Q2½bðq� 1Þ�ðp2 � c2Þþ Q3½bðq� 1Þ�ðp3 � c3Þ ¼ 0

(32)

This is the reaction curve for player 1 when all three playershave formed a coalition. Similarly, reaction curves for other twoplayers can be derived.

4. Numerical analysis

4.1. Route: from Oslo to Rotterdam

4.1.1. By seaFor example, the Unifeeder service line offers a container feeder

service from Oslo to Rotterdam, twice a week. The Unifeeder vesseldeparts Oslo on Thursday and reaches Rotterdam on Monday. Itdeparts Rotterdam on Friday and reaches Oslo on Monday.1

Therefore, it takes three or four days to reach from Oslo to Rotter-dam via sea. The capacity of feeder vessels is between 700 and 750TEUs.

4.1.2. By roadTravel distance between Oslo and Rotterdam is approxi-

mately 960 km.2 A road vehicle maintaining an average speed of50 km/h would take approximately 19 h to travel from Oslo toRotterdam.

A model consisting of equations (1), (2), (6), (26) and (32) (foreach player) and 4 is solved using an equation solver. In otherwords, solving the equilibrium of the Bertrand game provides thepricing rule set by the players, which will yield the Nash equilib-rium. However, before this we need to make certain assumptionsabout the values for parameters a, b, marginal costs and capacity offreight forwarders.

4.2. Assumptions about the parameters of the model

Tables 1 and 2 provide information about the input parametersused in the model. Due to the unavailability of data, a brief litera-ture review is conducted that is similar in many ways to the currentcase, in order to establish a base for the assumption aboutparameters.

1 See http://www.unifeeder.com/C125702600609F2D/0/DD65A320D08D0680C125708300548F1C?opendocument.

2 See http://www.distance-calculator.co.uk/distances-for-oslo-to-rotterdam.htm.

4.2.1. Assumed value for bb is the co-efficient of price or cost for customers. In other words,

this is the coefficient of price of choices faced by decision makers.Polydoropoulou and Litinas (2007) developed models including

a multinomial logit model with dependent variable choice amongdifferent types of shipping lines and airlines. Their result showsthat the parameter of travel cost of ships is negative and significant.An increase of 1 Euro in shipping costs will result in a utilityreduction of 0.0516.

In research conducted by Cantillo, Heydecker, and de DiosOrtuzar (2006), this value is around �0.070 as a coefficient ofcost, as an attribute for three choices: taxi, bus and metro. Theestimated values for mainline deviation costs (based on deviationfrom main navigation course for trans-shipment port) and feedercosts (costs of feeder transport stack-to-stack between feederregion and trans-shipment port), are �0.077 and �0.030, respec-tively, by Veldman and Rachman (2008).

Based on these values, the value for the price parameter in thismodel is assumed to be �0.050.

4.2.2. Assumed value for aIn general terms, equation (1) can be written by dividing utility

into two additive parts. For instance, for two alternatives (A and B),the utilities can be written as follows:

UAn ¼ VAn þ εAn and UBn ¼ VBn þ εBn where n ¼ 1;.N:

(1a)

Where N is the number of decision makers (or users), VAn&VBn arethe systematic (or representative) components of the utility of Aand B, and εAn&εBn are the random parts and are called thedisturbance (or random components). The parameter a is thealternative-specific constant and reflects the mean ofεBn � εAn; thatis, the difference between the utilities of alternatives A and Bwhen‘all other things are equal’. The values of the alternative-specificconstant for players 1 and 3 are chosen arbitrarily. The non-negative values for players 1 and 2 are set due to the low waitingtime and high frequency of trucks. The high negative value forplayer 3 reflects schedule delays and the inflexible service offeredby the ship-operating company.

4.2.3. Assumed value for costCommercial trucking firms have costs that depend upon

a number of factors, including the types of commodities hauled, thelength of hauls, the types of equipment used, the proportion oftruckload (TL) or less-than-truckload (LTL) traffic, and the regionsthey serve (McMullen, 1987). In addition, policies that restrict theroutes andweights of commercial vehicle traffic can have an impacton a firm’s operating costs (Levinson, Corbett, & Hashami, 2004).

Notteboom, Delhaye, and Vanherle (2010) calculated the cost forroad haulage (in Euro per km) for four regions in Europe: (a) Ben-elux countries, France and Germany, (b) Eastern Germany andPoland, (c) the United Kingdom and (d) the Baltic States and Russia.The calculated costs are 1.75, 1.84, 1.37 and 1.05 Euro per km,respectively.

In this case, 1.7 euro or $2 per km are selected to calculate thetotal cost for a distance of 960 km ¼ 2*960 ¼ $1920. Moreover,according to Notteboom et al. (2010), fuel costs account for 20e25percent of the total cost. On this basis, $400 (20 percent of $1920) isconsidered as a truck’s fuel consumption cost in this case.

The ship’s fuel consumption’s cost is calculated using theNetwork for Transport and Environment model (NTM), which wasdeveloped by Cooper and Gustafsson (2004a, 2004b). For a vesselwith amedium-speed diesel engine run on residual oil at a speed of17.5 knots with a capacity of 700 TEUs, the NTM model gives fuel

Table 3Case A: Bertrand equilibrium (when all players are independent).

Table 1General parameters of demand.

Level of demand (A) Logsum parameter (q) Price parameter (l)

200,000 0.010 �0.050

Table 2Freight forwarders’ specific parameters.

Player 1(big truck-operating company)

Player 2(small truck-operating company)

Player 3(ship operator)

Alt.spec. constant(ai)

0.9 0 �16

Marginal cost in $(ci)

$400 $400 $80

Capacity (CAPi) 3000 TEU 1000 TEU 73,000 TEU

N. Saeed / Research in Transportation Economics 42 (2013) 77e86 83

consumption of 0.08 tons per nautical mile. Moreover, an engineworkload of 80 percent is assumed in order to calculate fuelconsumption cost.

Distance from Rotterdam to Oslo ¼ 552 nautical miles3 or1000 km.

Fuel (bunker) price ¼ $700 per ton.4

Total fuel consumption for a one-way trip ¼ 0.08*1000 ¼ 80tons.

Total fuel cost ¼ 80*700 ¼ $56,000.

Fuel cost per TEUs ¼ 56,000/700 ¼ $80.

4.2.4. Assumed value for qA change in the price and other attributes (e.g., schedule delay,

differences in frequency of services, etc.) of one player will shift thetraffic from the other players to that player. It will not affect thetotal demand to a great degree but it will affect the market share ofall players. That is why the value for q is quite low; i.e., 0.01.

4.2.5. CapacityTurnaround time of a vessel in days TTV ¼ 7 days.Frequency of scheduled vessel calls per week fv ¼ 2.Capacity of vessel ¼ X* (in TEUs) ¼ 700 TEUs.Annual capacity (one way) ¼ 2*52*700 ¼ 72,800TEUs.

Player 1 Player 2 Player3

Equilibrium Price US$/TEU 440 430 110Market share% 44 28 28Profit (in millions of US$) 2.6 1.2 1.2Total demand in 1000s TEUs 163.5Logsum 20

Table 4Case B: Bertrand equilibrium (when players 1 & 3 are cooperating).

Player 1 Player 2 Player 3

Equilibrium Price US$/TEU 450 430 130Market share 30 37 33Profit (in millions of US$) 2.6 1.9 2.9Total demand in 1000s of TEUs 162.8Logsum 20.6

Table 5Case C: Bertrand equilibrium (when players 1 & 2 are cooperating).

Player 1 Player 2 Player 3

Equilibrium Price US$/TEU 450 450 112Market share 46 15 39Profit (in millions of US$) 3.8 1.2 2.0Total demand in 1000s of TEUs 162.6Logsum 20.6

Table 6Case D: Bertrand equilibrium (when players 2 & 3 are cooperating).

Player 1 Player 2 Player 3

Equilibrium Price US$/TEU 435 440 120

4.3. Bertrand solutions

In the first case, when all players are working independently,Nash equilibrium prices are higher for players 1 and 2 than forplayer 3 (see Table 3). These are reasonable results because player 3(the ship) is a cheap means of transportation. However, despite thehigh price, player 1 captures the largest market share. This reflectsusers’ preference to trucks over ship to carry their cargo, eventhough ships are cheaper. This could be due to the fact that trucksoffer a flexible, door-to-door service with low waiting time. Forexample, as information about the case study shows, travel timefrom Oslo to Rotterdam by road is approximately one day, whiletravel by ship takes three to four days.

In case B, players 1 and 3 established a coalition that resulted ina duopoly situation. Results are presented in Table 4. As expected,the Nash equilibrium prices of players who have joined a coalitionare higher than in case A. As a result of these higher prices, themarket shares of players 1 have declined. Although the Nashequilibrium price of player 3 is also higher compared to theprevious case, it still offers a cheaper and better service aftercooperating with player 1. As a result, its market share hasincreased. Moreover, player 2, which is an outsider in this situation,is able to capture a higher market share due to the comparativelylow price offered by this player.

Similarly, in case C, the Nash equilibrium prices of all players arehigh compared to a situation in which all players are workingindependently. However, there is a drastic decrease in the marketshare of player 2 (small-truck operating company) due to newhigher price after forming a coalition with player 1. Player 1’smarket share has increased slightly despite charging a higher price;this is due to the provision of better service after collaborating withplayer 2. Finally, player 3 managed to capture a significantly highermarket share due to its lower price. Results are presented in Table 5.

In case D, when players 2 and 3 are cooperating, the overallresults are similar to the previous case. That is, player 2’s marketshare decreases and those of players 1 and 3 increase. (see Table 6).

Market share 46 14 39Profit (in millions of US$) 2.8 1.0 2.7Total demand in 1000s of TEUs 163.4Logsum 20.18

3 See http://www.cruiseportrotterdam.com/.4 See http://www.bunkerworld.com/prices/ accessed 7th April 2012.

Table 7Profit of players for different combinations of coalitions (in millions of US$).

Profit (in millions of US$) Player 1 Player 2 Player 3 Combinedprofit of allplayers

Case A: All playersare independent

2.6 1.2 1.2 5.0

Case B: (1 þ 3) and Player2 is independent

2.6 1.9 2.9 7.4

Case C: (1 þ 2) and Player3 is independent

3.8 1.2 2.0 7

Case D: (2 þ 3) and Player1 is independent

2.8 1.0 2.7 6.5

Table 8Joint profits of players that have formed a coalition (in millions of US$).

Joint profit after coalition Joint profit before coalition

Players 1 & 3 5.5 3.8Players 1 & 2 5.0 3.8Players 2 & 3 3.7 2.4

N. Saeed / Research in Transportation Economics 42 (2013) 77e8684

4.4. Analysis of the stability of the coalitions

If all players in a game decide to work together, this raises thequestion of how to divide the total profit. The literature has dis-cussed several different answers to this question (see Curiel, 1997;Friedman, 1977; Peleg & Sudholter, 2003; Straffin, 1993; Suijs,2000), the most prominent of which are ‘core’ and ‘Shapleyvalue’. The present paper uses the concept of core to analyse thesituation. Core, proposed by Gillies (1953), is a generalisation ofEdgworth’s ‘contract curve’ and consists of those payoff vectors thatare, in a specific sense, acceptable to all players (Friedman, 1977).

The core rests upon the idea of an ‘imputation’. An imputationsatisfies both ‘individual rationality’ and ‘collective rationality’(Shubik, 1968). The formal definitions of these terms, as given bySong and Panayides (2002), are as follows:

Let U be an ne person game in characteristic function formwithplayersP ¼ ðp1; p2; ::::pnÞ. An ne tuple ðx1; x2; ::::xnÞ of real numbersis said to be an imputation if both of the following conditions hold:

1. Individual rationality:

xi � UðpiÞ i ¼ 1;2.n (33)

The above equation indicates that each agent is only willing toparticipate in the coalition if it pays him at least as much as he canobtain on his own.

2. Collective rationality:

Xni¼1

xi ¼ UðPÞ (34)

Equation (34) states that the sumof payoffs of a group ofn-playersis equal to the value that is guaranteed by the characteristic function.

Any payoff vector that satisfies equations (33) and (34) isdeemed to be an imputation. The imputation can be thought of asa possible social arrangement that satisfies minimal conditions ofrationality. Presumably, any ultimate arrangement will be drawnfrom the set of imputations. However, one drawback of sets ofimputations could itself be quite large. Therefore, ‘coalition ratio-nality’ can be argued to be a natural extension of the conditions ofindividual and collective rationality. Coalition rationality requiresthat the security level of every coalition defined by characteristicfunction be satisfied, formally:

Xpi˛C

xi � UðCÞ for all C in P (35)

where C denotes all possible coalitions formed by a sub-set of then players. For example, C may stand for the coalitionðp1; p2Þ;or ðp1; p2; p3Þ.

The core is made up of the set of imputations that satisfies theconditions of the coalition rationality. The rationale behind condition(35) is as follows. Suppose that a coalition, C, forms and attempts todivide the value assigned to C by the characteristic function. Further,suppose that a sub-groupofC, sayC1, is offeredapayoff less thanwhatC1 is worth according to the characteristic function. In this case, C1would not accept the offer, since it can do better without theremaining members of C. Thus, in order for C1 to remain in the coa-lition it should receive at least as much as UðC1Þ. If this argument isextended to all possible conditions, then the condition of coalitionrationality is required (Song & Panayides, 2002).

In order to analyse the stability of the coalitions, Tables 7 and 8show both the individual profit and the joint profit of all threeplayers in all cases. The results show that the joint profits of all

players are high in each coalition. This satisfies the condition ofcoalition rationality; that is, equation (35).

Moreover, the individual profits for players who have joinedcoalitions in cases B and C are either equal or greater than in case A.In case D, however, the individual profit of player 2 is lower than itis in case A. This situation apparently violates equation (33) (indi-vidual rationality). However, the presence of higher joint profit inthis coalition suggests that the distribution of profits among playerscould easily increase the individual profit of player 2, while stillkeeping its partner (player 3), in a better-off situation.

The results show that it is more profitable for player 1 to establisha coalition with player 2 than with player 3 because its individualprofit would be higher. However, the joint profit (5.5) of establishinga coalition with player 3 is higher than doing so with player 2.

However, it is better for player 2 (a small truck-operatingcompany) to establish a coalition with player 1 (a large truck-operating company) than with player 3 (a ship-operatingcompany). This is because both the individual and joint profits ofestablishing a coalition with player 1 are higher than a situation inwhich player 2 forms a coalition with player 3. It is interesting tonote that player 2 receives the highest profit (1.9) when players 1and 3 establish a coalition. Therefore, the formation of a coalitionbetween players 1 and 3 is not only beneficial for these players, butalso generates higher profit for an outsider that is not a part of thiscooperation (player 2).

4.5. Users’ surplus

In addition to profit, which is the payoff for freight forwarders,the situation can be analysed from the users’ perspective. The ‘ruleof the half’ is used to estimate the users’ benefits. In this method,a change in users’ surplus is estimated as being changes in thegeneralised costs multiplied by the average demand before andafter the formation of a coalition, as shown in equation (36):

US ¼ 12ðGCi � GC0Þ$ðXi þ X0Þ (36)

where US ¼ users’ surplus; GC0 ¼ generalised costs before coalitioni (i ¼ B, C, D, E).

GCi¼ generalisedcostsafter formationofacoalition i (i¼B,C,D,E).X0 ¼ demand before formation of a coalition i (i ¼ B, C, D, E).Xi ¼ demand after formation of a coalition i (i ¼ B, C, D, E).

Table 9Users’ surplus for all the coalitions (in thousands of US$).

Coalitions Users’ surplus

Case B: (1 þ 3) and Player 2 is independent �1958Case C: (1 þ 2) and Player 3 is independent �1957Case D: (2 þ 3) and Player 1 is independent �588

N. Saeed / Research in Transportation Economics 42 (2013) 77e86 85

However, this analysis contains changes in the generalised costs,both for truck and ship users. Accordingly, an alternative method ofestimating the user’s surplus has been applied, based on the wellknown property of the logit model. As noted by De la Barra (1989),amongst others, changes in the logsum of the logit model areconceptually equivalent to the traditional user’s surplus indicatorshown in (36). Therefore, (36) can be written as follows in equation(37):

US ¼ 12ðXi þ X0Þ $

1bðLSi � LS0Þ (37)

where LS0 ¼ logsum of the logit model before formation of a coa-lition i (i ¼ B, C, D, E).

LS1 ¼ logsum after formation of a coalition i(i ¼ B, C, D, E).b ¼ the model parameter for user’s cost.

Table 9 presents the calculated users’ surplus in all three coali-tions. In all coalitions, the users’ surplus is negative. Therefore, theformation of any kind of coalition among freight forwarders is notbeneficial for users.

5. Conclusion and policy implication

This paper has analysed four cases for three freight forwarderswith two different means of transportation. In the first case, allplayers work independently and the numerical analysis obtainedby solving the Bertrand model reveals that the Nash equilibriumprices are higher for players 1 and 2 e freight forwarders with theirown trucks. However, despite the high price, player 1 captures thelargest market share. This reflects users’ preference to trucks overship to carry their cargo, even though ships are cheaper. This couldbe due to the fact that trucks offer a door to door and flexibleservice with low waiting time. Moreover, shippers that followa ‘just in time’ (JIT) strategy would prefer trucks over ships despitethe higher cost because a truck will transfer their cargo wheneverthere would be a demand, with their flexible and door-to-doorservices. This would result in a decline in the inventory compo-nent of the overall cost of logistics due to faster and just-in-timedelivery of cargo. However, transport costs will increase due tothe selection of expensive and better service.

However, the frequency of ships is lower and waiting time ishigh, which is why this player, despite its low price, could notcapture as muchmarket share as captured the large truck operatingcompany. Moreover, although player 2 is also a freight forwardingcompany with its own truck, it is a small company that simplycannot offer services with the same high frequency as a large truck-operating company.

The next three cases discussed different combination of coali-tions among these players. A two-stage game was applied for thepurpose of analysis. In the first stage, the three players had todecidewhether to act alone or to enter into a coalitionwith anotherplayer. The decision at this stage should presumably be based onthe predicted outcome for the second stage. Here, the second stageis modelled as a Bertrand game, with one competitor (who has notjoined the coalition) and the coalition. The numerical results revealthat all three kinds of coalitions generate higher profits for the

members of the coalitions, as well as for the competitors in eachcase. The reason for the high profit is the high Nash equilibriumprices that players are able to charge from their users due to thecreation of a duopoly after the establishment of a coalition amongany two players.

Although all combination of coalitions result in higher profit forthe players involved, the combined profit of the members of coa-lition, as well as competitors, is highest in a situation in whichplayers 1 and 3 cooperate and offer intermodal services to theirusers. Due to market power and improved quality of service, theseplayers are able to charge higher prices. The quality of servicewould improve in different aspects in this case. Firstly, havingcooperated with the large truck operating company, player 3 canincrease the frequency of its services and, as a result, provideflexible services to its customer. Secondly, these two big players canjointly offer different value-added services to their customers. Inother words, the first and second points reveal that both playerscan utilise the benefits of economies of scale and economies ofscope. Thirdly, trucks can be used to cover short-distance deliveryof services. This would help decrease congestion in the road sector.Longer distance can be covered by cheap and environmentallyfriendly modes of transport; that is, ships with higher frequency.

Therefore, according to these findings, it is more beneficial toestablish a vertical cooperation between a large truck operator anda ship operator to offer intermodal services than to establisha horizontal cooperation between two players. This is becausehorizontal cooperation among large and small truck operatingcompany would result only in the provision of more “flexible”services. Vertical cooperation, on the other hand, can improveservice quality in a variety of ways, as explained above.

Moreover, establishing vertical cooperation among a smalltrucking company and a ship operator is also not as beneficial as thepreviously mentioned vertical cooperation. This is mainly due tothe fact that cooperation between a vessel operating company anda small truck operating company would not increase the volume ofcargo to a great degree, which can be utilised to increase thefrequency of a vessel. However, this cooperation would be benefi-cial for a vessel-operating company to decrease its road access costto and from port.

However, calculations of users’ surplus show that these kinds ofcoalitions are not beneficial for users because they generatea negative payoff for them, which reflects the high prices they willhave to pay to the service providers. However, there is a possibilitythat users will ignore the increase in price when they receiveimproved and good quality services after the formation of a coali-tion among players.

Acknowledgements

This work was supported by the ERA-Net project “Customer andAgent Initiated Intermodal Transport Chains” (CA-CHAINS), fundedby the Norwegian and Swedish Research Councils. The author isgrateful to Professor Odd I. Larsen for his valuable comments on anearly draft of this paper, and also appreciates the comments ofanonymous referees.

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