Transactions vs. Relationships:
What Should the Company Emphasize?
Gila E. Fruchter
Bar-Ilan University
Simon P. Sigué
Athabasca University
The relevance of transactional and relational marketing
variables in relational exchanges is now well established
in the marketing literature. However, the knowledge about
their relative effectiveness and their optimal mix over time
remains very sparse. An analytical model is proposed to
help determine optimal decision rules for transactional
and relational marketing efforts. Some of the main results
are as follows: (a) If the seller benefits from the interaction between the transactional marketing effort and
buyer’s commitment, then the seller’s optimal decision
rules change over time and depend on the level of the partners’ commitment. (b) Otherwise, the seller’s optimal decision rules for the two types of marketing are constant
over time. (c) The seller should allocate more resources to
relational marketing at the beginning of a relational exchange and, later on, should allocate more resources to
transactional marketing.
Keywords: relational exchange; commitment; trust; opportunism; optimal control; relational marketing effort; transactional marketing effort
The growing emphasis on relationship marketing in the
marketing literature may lead to the belief that traditional
marketing mix variables play a secondary role or no role at
all in relational exchanges. In fact, some marketing scholars have minimized the role of traditional marketing vari-
ables by arguing that they represent only a partial picture
of economic exchanges (e.g., Grönroos 1991, 1994;
Gummesson 1997). Building and maintaining close and
strong relationships with buyers seems to be a key concept
in the new marketing paradigm (e.g., Berry 1995;
Grönroos 1994; Parvatiyar and Sheth 2001; Sheth and
Parvatiyar 1995).
Although this argument is strongly shared in the marketing literature, intuition, evidence in the marketplace,
and recent empirical research suggest that traditional marketing variables still play a significant role in the way firms
conduct their businesses (Coviello et al. 2002; Hultman
and Shaw 2003). The question, then, is why marketing
practitioners still invest in traditional marketing variables
when developing close relationships with their buyers.
The economic sociology literature, which has claimed
that economic transactions are embedded in social relationships, provides a theoretical explanation for the double
consideration of traditional marketing variables and relationship marketing variables (Granovetter 1985; Wathne,
Biong, and Heide 2001). Two of the seven principles of
embeddedness listed by Hunt and Arnett (2003) can be
used to justify the simultaneous use of transactional and
relational marketing efforts. The first principle claims that
human action should not be oversocialized. This principle
advises on the danger of ignoring the importance of the intrinsic economic value of an exchange to the exclusive
benefit of its social advantages. The second principle
The authors thank Ashutosh Prasad, the editor, and three anonymous reviewers for valuable suggestions and Vince Ambrock for copyediting assistance. The second author acknowledges the support of a grant from Athabasca University. The usual disclaimer applies.
Journal of Service Research, Volume 8, No. 1, August 2005 18-36
DOI: 10.1177/1094670505276629
© 2005 Sage Publications
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 19
states that the concrete social relations of economic actors
have the capacity to either inhibit or enhance the likelihood
of attaining desirable economic outcomes. This principle
stresses the impact of social relations on the economic outcome of an exchange relationship. The virtue of relationship marketing lies in the fact that some relationship properties enhance desired economic outcomes, both for the
buyer and the seller.
Although the relevance of transactional and relational
marketing variables seems obvious, knowledge about the
conditions of their use is still sparse. Recognizing that both
relational and transactional marketing variables involve
investments of various kinds, Wathne, Biong, and Heide
(2001) have argued that knowledge about their relative effectiveness represents an important input in a firm’s resource allocation decisions. The challenge for academics
and managers, then, is to make sound predictions on the effectiveness of the two types of marketing activities for different products, customers, and market conditions. It is our
belief that formal analytical research approaches can offer
a promising alternative for addressing this challenge.
Prior analytical research in marketing has been limited
to exploring how sellers determine some of their transactional marketing variables, typically pricing and advertising (e.g., Danaher 2002; Fruchter 1999; Jørgensen,
Sigué, and Zaccour 2000). On the other side, the relationship marketing literature has been mainly behavioral, investigating causal relationships between certain important concepts such as dependence, trust, opportunism,
commitment, and satisfaction (e.g., Andaleed 1996;
Doney and Cannon 1997; Garbarino and Johnson 1999;
Geyskens, Steenkamp, and Kumar 1999; Morgan and
Hunt 1994; Sirdeshmukh, Singh, and Sabol 2002). Other
empirical studies have investigated the effectiveness of relationship marketing activities on different behavioral loyalty measures, without devoting any attention to resource
allocation (e.g., De Wulf, Odekerken-Schröder, and
Iacobucci 2001; Verhoef 2003). Several conjectures on the
effects of transactional and relational marketing have also
been made (e.g., Berry 1995; Cahill 1998; Coviello et al.
2002; Grönroos 1991; Saren and Tzokas 1998). At the
same time, a few works have empirically examined the simultaneous use of transactional and relational marketing
(e.g., Coviello et al. 2002; Hultman and Shaw 2003). On
the contrary, to the best of our knowledge, there is no analytical work that addresses the simultaneous determination of transactional and relational marketing efforts.
This article is the first analytical attempt at studying the
simultaneous determination of transactional and relational
marketing efforts and anticipates making two contributions to the marketing literature. The first is to formally integrate social interactions and transactional marketing activities in the formulation of the seller’s utility. Building on
the economic sociology literature, we claim that the
seller’s utility, which is a mapping function of the buyer’s
utility, stems from two sources. The first source of utility is
the transactional benefit delivered to the buyer, which is a
result of different investments in transactional marketing
variables. It can also be considered as the intrinsic value
proposition made to the buyer. In the absence of any interpersonal relationship, the buyer only looks at this transactional value proposition in making a buying decision.
The second source of utility is the interpersonal component of an exchange, which is captured in this study
through the modeling of the commitment of the two partners. Our point of view is that the level of commitment of
the exchange partners adds to the seller’s total utility. This
argument is consistent with the second criterion of embeddedness presented above. The utility derived from relational commitments is manifested in access to new markets, generation of repeat purchases, creation of exit
barriers, positive word of mouth, and information sharing
(see Anderson 1998; Berry 1995; Dwyer, Schurr, and Oh
1987; Hennig-Thurau, Gwinner, and Gremler 2002; Saren
and Tzokas 1998).
In addition, we consider that the two sources of utility
not only are additive but also interact to enhance or moderate the seller’s total utility. For example, the fact that the
seller makes a relatively low-value proposition may be
compensated by the two partners’ commitments in the relationship, but it also depends on the magnitude of the buyer’s
commitment and the seller’s own value proposition.
The second contribution of this article is to formally
show the value of undertaking transactional marketing in a
relational exchange. Such an undertaking has major theoretical and strategic implications. Theoretically, although
the thesis of economic transaction embeddedness in social
relationships has influenced recent developments in marketing literature, its conceptualization has been vague
(Wathne, Biong, and Heide 2001). Our article addresses
this shortcoming and highlights the importance of transactional and relational marketing in the seller’s overall
utility. We show the relative strategic effectiveness of
transactional and relational marketing throughout the life
cycle of a relational exchange. In particular, we answer the
following questions: Should transactional and relational
marketing be given the same weight from the start of a relationship to the end? If not, how should the mix of these
two types of marketing activities evolve over time? Although the idea of a relationship life cycle is well established in the literature, its strategic implications have not
been fully investigated (see Backhaus 1999).
To reach our objectives, we extend the model of
Fruchter and Sigué (2004) to include the mix of relational
and transactional marketing efforts and use dynamic optimization techniques to derive optimal policies.
The remainder of the article is arranged as follows.
First, we review some previous related works. Second, we
20
JOURNAL OF SERVICE RESEARCH / August 2005
present our model. Third, we derive the seller’s optimal
policy and discuss some of its consequences. Fourth, we
present numerical illustrations that provide insight into the
impact on marketing decisions and relational commitment
of trust, opportunism, and contributions from transactional marketing and relational commitment to the seller’s utility. The last section concludes our article and discusses
managerial implications and limitations.
RELATED LITERATURE
Formal decision-making literature in marketing has
been mainly focused on marketing mix variables. Its main
subject of inquiry has been to find an optimal way of determining individual variables, or a combination of marketing mix variables, that are likely to maximize the seller’s
current or discounted profits in various conditions of market, competition, and demand (for a review, see Blattberg
and Neslin 1993; Moorthy 1993; Rao 1993). The marketing science literature borrows from the microeconomic literature and, in many cases, uses operations research techniques, including dynamic programming, optimal control,
static nonlinear optimization, and static and dynamic
games. Generally, this literature assumes that the seller can
have a significant short-term and long-term impact on demand, which is expressed as a reaction function of buyers
to a seller’s manipulation of marketing mix variables.
However, although the marketing science literature often recognizes that some marketing mix variables may
have a carryover effect (e.g., Chintagunta and Jain 1992;
Jørgensen, Sigué, and Zaccour 2000), this application has
been doubly criticized for being short-term oriented and
for overemphasizing economic aspects of an exchange to
the detriment of social interactions (e.g., Grönroos 1994;
Webster 1992). Indeed, social interactions between sellers
and buyers have been surprisingly ignored in the formulation of sellers’ payoff functions. Game theory literature in
economics has recognized this problem and investigated
the repeat-purchase contract-enforcement mechanism as a
way of motivating sellers to honor their promises to buyers
(e.g., Klein and Leffler 1981; Shapiro 1983). Although
this literature uses concepts such as reputation and cheating, it does not explicitly deal with critical behavioral variables such as trust and commitment between two exchange partners. Recently, however, Sigué and Elloumi
(2002) proposed the first analytical model dealing with social interactions between a buyer and a seller. Borrowing
from the modeling of love dynamics in applied mathematics (see Feichtinger, Jørgensen, and Novak 1999; Rinaldi
1998a, 1998b; Rinaldi and Gragnani 1998), these authors
use a system of two differential equations to describe the
dynamics of relational commitments between two ex-
change partners. (The use of the metaphor of marriage and
love affairs in relationship marketing is not new. See, for
example, Dwyer, Schurr, and Oh (1987); Gummesson
(2002); Morgan and Hunt (1994); O’Malley and Tynan
(2000).) Their model has the merit of showing formally
how factors such as trust, opportunism, and the economic
appeal of the partners affect the dynamics of relational
commitment. Unfortunately, this model remains descriptive and prescribes no rule for designing a successful marketing program over time.
Fruchter and Sigué (2004) make a step forward in integrating social interactions in the formal design of marketing strategies. They recognize that some marketing activities, called relational marketing efforts, can be undertaken
to build and maintain relational commitment. Then, the
problem of the seller is not limited to the maximization of
profit as usually assumed but extends to the maximization
of utility stemming from the relational commitment of the
exchange partners. The model proposed does not take into
account the seller’s transactional marketing efforts.
We concur here that the seller’s problem is well conceptualized through the maximization of utility. Extending
Fruchter and Sigué’s (2004) work, we propose a generalized concept of utility, which integrates the following
sources of utility: the seller’s transactional marketing effort, the commitment of the two partners, and the interaction between the seller’s transactional marketing and the
buyer’s commitment. Our research is based on the premise
that the real problem in business today is not which marketing approach to choose but how to combine both transactional and relational marketing to improve the effectiveness of marketing (Coviello et al. 2002).
THE MODEL
The Dynamics of Commitment
We consider a seller who wants to build a long-term relational exchange with a buyer. Let xs(t) be a state variable
that measures the level of commitment of the seller in the
relational exchange with the buyer at time t. By seller’s
commitment, we mean the willingness of the seller to stay
in the relationship with the buyer, which leads to relational
marketing investments or the improvement of the value offered to the buyer. Let xb(t) be another state variable that
measures the level of commitment of the buyer in the relational exchange with the seller at time t. By buyer’s commitment, we mean customer loyalty, perceived as discernible repeat purchasing or buying behavior, positive word
of mouth, and information sharing. There is a reciprocal
indifference when the values of xb(t) and xs(t) are zero.
This will appear when the partners have no interest in be-
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 21
ing committed to each other at time t. Otherwise, if the two
partners are in a relational exchange, their respective commitment is positive. Thus, we assume
xi(t) ≥ 0,
i ∈ {s, b}.
(1a)
Let us assume that the seller manages the establishment
and the maintenance of the relational exchange with the
buyer. Although this assumption may seem implicitly restrictive, it is very common in many applications of relationship marketing in consumer markets (see Blattberg
and Deighton 1991; Gruen 1995; O’Malley and Tynan
2000). As a consequence, we accord an active role to the
seller in the relational exchange, whereas the buyer plays a
passive, or a reactive, role. Stated differently, the seller is
the person who offers an economic reward and/or a social
or psychological benefit to the buyer. This assumption is
implicit in the growing literature of customer relationship
management (see Berry 1995; Parvatiyar and Sheth 2001;
Sheth and Parvatiyar 1995).
Let u1(t) be a control variable that represents the seller’s
relationship marketing efforts at time t. The variable u1(t)
can be any relationship marketing activity from the first
two levels of relationship marketing in Berry’s (1995)
classification. According to Berry, the first level of relationship marketing relies on economic incentives or offers
tangible rewards over time to develop and maintain relationships (e.g., frequency marketing programs). The second level of relationship marketing focuses on social aspects of a relationship and offers social and psychological
benefits to customers (e.g., special treatment programs
and club marketing programs). We assume that whether
the seller’s marketing effort, u1(t), creates economic value
or social and psychological benefits for the buyer, it increases the seller’s own commitment to the relationship.
This specification is consistent with Gundlach, Achrol,
and Mentzer’s (1995) view that commitment possesses an
input or instrumental component. The seller’s relational
marketing effort is modeled as a purposeful commitment
input that serves to build up the commitment of the buyer
as well as provide a bonding mechanism for the seller
herself or himself.
The levels of commitment of the two exchange partners
evolve according to the following dynamics:
x i = − β i x i + θ i x j + α i u1 ,
xi (0) = 0, i ≠ j
and i, j ∈ {s, b}.
(1b)
The specification in (1b) assumes that partner i’s level of
change of the relational commitment is an additive separable function of three terms.
The first term, –βi xi , is the opportunism factor of partner i, in which βi is a positive parameter representing the
forgetfulness and selfishness of partner i. Our definition of
opportunism is a particular case of what Wathne and Heide
(2000) call passive opportunism. The rationale is that people with short memories, purposely or not, harm their partners, who logically expect them to recall their previous
commitments. They also do not commit themselves for
long periods because their interest in the relationship
evaporates rapidly. βi is called the propensity to opportunism and can take smaller values when there are exogenous
factors that make it harder for partner i to behave selfishly,
such as moral considerations, and the structural and contextual environment of the relationship, which includes
the availability of competitive alternatives, specific investments, and binding agreements. For example, a relational
marketing program occurring in a context in which both
parties share strong norms of solidarity is likely to evolve
with low opportunistic propensities from both sides
(Gundlach, Achrol, and Mentzer 1995; Rokkan, Heide,
and Wathne 2003). On the other hand, disproportionate
structural investments between the two partners can lead
to higher opportunistic propensity from the less involved
partner (Gundlach, Achrol, and Mentzer 1995). In Berry’s
(1995) classification, some structural investment can be
considered as the third level of relationship marketing. As
it is difficult to separate these types of activities from the
product itself, studies that investigate the effects of relationship marketing often do not take them into account
(see De Wulf, Odekerken-Schröder, and Iacobucci 2001;
Verhoef 2003). Following this line, however, we assume
that their presence may increase or decrease the partners’
propensities to opportunism.
The second term, θixj, is the trust/distrust factor, which
is a reaction function of partner i to partner j’s commitment. A positive θi means that partner i trusts partner j and
relies on partner j’s trustworthiness. A negative θi indicates that partner i distrusts partner j and does not rely on
partner j’s trustworthiness. Finally, partner i is trust-indifferent to partner j when θi = 0. Our specification assumes
that the commitment of one partner enhances the commitment of the other. It stems from the application of the principle of reciprocity that fosters positive relational exchange (Bagozzi 1995; De Wulf, Odekerken-Schröder,
and Iacobucci 2001).
The third term, αi u1, denotes the impact of the seller’s
relational marketing efforts on the change of her or his
own or the buyer’s level of commitment at time t. The parameter αi is positive and represents changes in the response of partner i to the seller’s relational marketing efforts. In our specification, αb could be considered as the
effectiveness of the seller’s marketing effort in building
and maintaining the buyer’s commitment or level of inter-
22
JOURNAL OF SERVICE RESEARCH / August 2005
est in the seller’s relational marketing effort. There is empirical evidence that αb changes with the nature of the
seller’s relationship marketing activities and the buyer’s
characteristics (see De Wulf, Odekerken-Schröder, and
Iacobucci 2001; Verhoef 2003). On the other side, αs indicates the effectiveness of the relational marketing effort on
the seller’s own commitment. Several factors may influence this effectiveness, including the value of the buyer
and the cost of designing and implementing the program.
Therefore, we postulate that a relational marketing program that has a high value for the seller and meets the
interest of the buyer will generate higher levels of commitment from both sides.
Finally, we assume in (1b) that the levels of commitment of the two partners at the beginning of the relationship are zero. This assumption allows us to determine what
level of marketing effort is needed to start a relational exchange. We also consider time-invariant parameters in
(1b), in which the exchange partners do not change their
opportunistic propensity, trust, and interest in the seller’s
relationship marketing program. Consequently, our model
applies exclusively to exchange partners who favor relational stability and are more likely to remain committed as
long as the initial conditions that led to their original commitment do not change. Prior to their commitment, they
have hearsay or factual evidence on their partner’s trustworthiness, opportunistic propensity, and response to relational investments on which they rely during the time their
relational exchange lasts (see Palmer 2000). This is particularly true because trust about a partner may be built
through market intelligence, as is often the case for onetime transactions such as buying a house (Parvatiyar and
Sheth 2001).
marketing efforts here as they do not directly affect the dynamics of the commitment of the partners but enhance the
value proposition of the seller’s at time t. Examples of
transactional marketing activities are, among others, coupons, premiums, rebates, bonus packs, and price-offs. As
per the definition of sales promotion, transactional marketing includes all activities that offer an extra value to the
buyer with the primary objective of creating an immediate
sale. It is worth mentioning that neither our definition of
transactional marketing nor that of relational marketing
includes standard marketing efforts that are indispensable
for any exchange to occur between the buyer and the seller.
Without any loss, they are normalized here to zero.
Let f be the seller’s relational benefit. We assume that
the two partners’ commitments and the seller’s transactional marketing affect the seller’s relational benefit;
thus, f = f (u2, xb, xs). This assumption stems from the economic sociology literature, which recognizes that partners
derive utility from the intrinsic economic value of the object of exchange and their social interactions (see Hunt and
Arnett 2003; Wathne, Biong, and Heide 2001).
The seller supports costs for undertaking relational
marketing efforts with a buyer that, according to Hibbard
et al. (2001), encompass economic, psychological, and
opportunity costs arising from forgone alternatives. We
assume that these costs, as well as the cost of transactional
marketing, can be translated to a single unit (e.g., monetary terms) and represented as follows: C = C(u1, u2).
The objective of the seller is to find an optimal allocation rule for her or his marketing resources to maximize
her or his discounted utility over a planning period. Consider the dynamics of both partners’ relational commitments. Then, the seller’s problem becomes an optimal
control problem formalized as follows:
The Seller’s Problem
The seller’s problem is how she or he can manage (establish and maintain) a long-lasting relationship with the
buyer and maximize her or his utility. We assume that relational benefits of the seller may go beyond sales and profit
and incorporate several other dimensions. As a matter of
fact, this is consistent with the view of Parvatiyar and
Sheth (2001) that, although the overall purpose of a relational marketing program is to increase marketing productivity and enhance mutual value for the partners, the seller
can specify her or his relational benefits (objectives) in
terms of financial goals, marketing goals, strategic goals,
operational goals, and organizational goals.
The seller may also want to exclusively enhance her or
his current economic appeal at time t. Let u2(t) be a second
control variable that represents this type of the seller’s
short-term impact marketing activities at time t. Shortterm impact marketing activities are called transactional
 Max ∞ e − rt ( f (u , x , x ) − C(u , u ) )dt
s
b
2
1
2
 u 1 , u 2 ∫0
s. t.


 x b = −β b x b + θ b x s + α b u1 , x b ( 0) = 0

 x s − β s x s + θ s x b + α s u1 , x s ( 0) = 0
(2)
given (1a). In (2), r denotes the seller’s constant and positive discount rate, which can also be considered as the
seller’s rate of time preference for future utility.
For simplicity, we assume the following specification:
f (u 2 , x b , x s ) = c T u 2 + c b x b + c s x s + c C u 2 x b ,
(3)
where cT, cb, cs, and cC are nonnegative parameters denoting, respectively, the contribution of the transactional marketing effort, the buyer’s and seller’s commitment, and the
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 23
cross-effect of the transactional marketing effort and the
buyer’s commitment to the seller’s overall benefit. Given
the generic nature of our model, the contribution parameters can take different interpretations, depending on the relational marketing program being analyzed. For example,
suppose that the objective of the seller’s relational marketing program is to optimize her or his profit. The parameters cT , cb, cs, and cC may take, respectively, the following
interpretations: the effectiveness of transactional marketing, the effectiveness of the buyer’s commitment, the internal efficiency gain generated from the seller’s commitment, and the cross-effectiveness of transactional
marketing and the buyer’s commitment on the seller’s
gross margin.
Note the first three components on the right-hand side
of (3) are additive separable to take into account the impact
of each of them on the seller’s relational benefits. This
specification also allows us to deal with several types of
products in the product continuum proposed by Grönroos
(1994) and with several types of buyers. This means that
for some products, such as consumer packaged goods, cT
may be very high compared to cb and cs; for other products,
such as industrial goods and services, cb and cs may play a
greater role. The last component on the right-hand side of
(3) denotes the cross-effect of the transactional marketing
effort and the buyer’s commitment. This component accounts for the interaction that may exist between the intrinsic economic value of the seller’s offer and the buyer’s
commitment to their relational exchange. It means that
transactional marketing efforts can be more effective if the
buyer is already committed to the seller.
It is important to highlight that by incorporating the
seller’s commitment into her or his utility function, we are
able to take into account the efficiency gain that the seller
may generate from maintaining a relational exchange with
the buyer (see Kalwani and Narayandas 1995). On the
other hand, not all relational marketing programs generate
efficiency gain. Therefore, in some cases, it may happen
that, cs = 0. In the specific case of a seller only interested in
the profit that she or he may generate directly from the
buyer over time, the seller’s problem, as stated in (2), will
be reduced to maximizing the lifetime value of the buyer
(see Berger, Weinberg, and Hanna 2003; Fruchter and
Sigué 2004; Gupta and Lehmann 2003; Jain and Singh
2002).
Finally, a common theme in the marketing literature is
that the cost of marketing efforts is a property of increasing
returns (i.e., it is a convex function). (Differently said, the
marketing effort, or the size of the vector [u1, u2], has the
property of decreasing return of the cost, C.) With this in
mind, again for simplicity, we consider the following specification for the cost of the marketing efforts:
1
1
C = C(u1 , u 2 ) = u12 + u 22 .
2
2
(4)
OPTIMAL POLICY
We use dynamic optimization techniques (see, e.g.,
Kamien and Schwartz 1991) to solve the seller’s problem
in (2), in which f and C take their respective expression in
(3) and (4). We conclude with the following analytical
results.
Theorem 1 (optimal decision rules). The utility optimization problem (2)-(4), given (1a), has an optimal timeinvariant feedback solution1 for the seller’s relationship
marketing efforts, u1* , and transactional marketing efforts,
u*2 . The seller’s relationship marketing effort is nonzero if,
and only if, the seller and buyer commitments are positive
(nonzero). Furthermore, the decision rules are linear functions of relational commitments. Formally,
 x b  
u1* = [α b α s ]  A  + b
 x s  
(5)
u*2 = c T + c C x b .
(6)
and
 a 11 a 12 
Matrix A = 
 satisfies the following Riccati algea 21 a 22 
braic equation:
 βb
− A
 −θ s
−θ b   r + β b −θ s 
A
 −
β s   −θ b r + β s 
 α
−c
α bα s 
 A− 
+ A
2
 0
α s α b α s 
2
b
2
C
(7)
0
 = 0,
0
and vector b satisfies
 b1 
b= 
b2 
( r + β b ) −θ s 
 α 2 α bα s 

= 
 − A b
(r + β s ) 
α s α b α 2s  
 −θ b
−1
(8)
c b + c C c T 

.
 cs

1. A time-invariant feedback solution is a state-dependent decision rule
(in our case, decision rules are a function of the state variables xb and xs).
24
JOURNAL OF SERVICE RESEARCH / August 2005
Proof. See Appendix A.
The optimal policy of resource allocation in (5) and (6)
displays two explicit analytical decision rules for relational and transactional marketing. Specifically, u1* , the
seller’s optimal decision rule for relational marketing efforts at any instant, is a linear function of the current level
of the partners’ relational commitments, u1* ( x s , x b ),
whereas u*2 , the seller’s optimal rule for transactional marketing efforts at any instant, depends linearly only on the
buyer’s current level of commitment, u*2 ( x b ).
The rule for transactional marketing effort u*2 , in addition to the linear dependence on the buyer’s commitment,
depends directly on the contribution made by the transactional marketing effort, the cross-effect of the transactional marketing effort, and the buyer’s commitment to
the seller’s overall benefit. This result means that to determine her or his optimal transactional marketing effort at
time t, the seller need only look at the level of commitment
of the seller, the contribution stemming from transactional
marketing, and the cross-effect of the transactional marketing effort and the buyer’s commitment. Interestingly,
when there is a cross-effect between the seller’s transactional marketing effort and the buyer’s commitment, the
seller should increase (decrease) her or his transactional
marketing effort as the buyer’s commitment increases
(decreases).2
It is worth mentioning, however, that the feedback
transactional marketing effort does not depend directly on
the partners’ trust/distrust and opportunism, the seller’s
rate of time preference for future utility, and the other
model parameters, but it depends indirectly through the
buyer’s commitment (see Appendix B).
The dependence of u1* on the model parameters is complex and determined through matrix A and vector b (see
Appendixes A and C). As it appears (see Appendix C), the
decision rule u1* depends directly, in addition to the two
partners’ current level of relational commitments, on all
parameters of the model, including the trust/distrust and
opportunism parameters of the two partners, the seller’s
rate of time preference for future utility, and the contribution of the transactional marketing effort and the crosseffect of the transactional marketing effort and the buyer’s
commitment to the seller’s overall benefit.
Considering Theorem 1, we obtain the following result.
Corollary 1 (marketing efforts without cross-effect).
The seller’s optimal relationship and transactional marketing efforts are constant over time and do not depend on the
level of commitment of the two partners (seller and buyer)
if, and only if, the contribution of the cross-effect of
transactional marketing efforts and the buyer’s commit2. To see this, we take the derivative of u2* in (6) with respect to time;
thus, u2* = c C xb .
ment to the seller’s overall benefits is zero. Formally, in
this case,
( r + β b ) −θ s  
u = [α b α s ] 

( r + β s ) 
 −θ b
*
1
=
−1
c b 
 
c s 
(9)
α b [ cb ( r + β s ) + θ s cs ] + α s [ cs ( r + β b ) + θ b cb ]
(β b + r)(β s + r) − θ b θ s
and
u*2 = c T .
(10)
Proof. See Appendix D.
The results in Corollary 1 apply for a case where the
seller’s overall benefit from the relational exchange in (3)
is limited to only the three first components on the righthand side. The constant optimal decision rules for transactional and relational marketing efforts mean that the
seller need not take into account either the time or the current levels of both partners’ commitment to determine her
or his marketing efforts. Moreover, for the transactional
marketing effort, the seller’s concern should be limited exclusively to the effectiveness of the transactional marketing effort to her or his overall benefit. Conversely, to determine her or his optimal relational marketing effort, the
seller would have to consider the trust/distrust and opportunism of the two partners, the seller’s time preference for
future utility, and the contribution of the commitment of
the two partners to the seller’s overall benefit.
For the specific case of a seller interested in the lifetime
value of the buyer, the seller’s relational marketing effort
will increase with the increase of the effectiveness of the
commitment of the two partners on the seller’s gross margin. This implies that the seller should invest more in relational marketing effort if her or his relational marketing
program can generate more internal efficiency gain and
the effectiveness of the buyer’s commitment on the seller’s
gross margin is high. The seller’s relational marketing effort increases with the two partners’trust parameters, but it
decreases with the two partners’ opportunism and distrust
parameters. Practically, these findings mean that an exchange occurring in a structural and contextual environment that does not favor opportunistic behavior among
partners or involving two trusting partners should be supported by extensive investments in relational marketing
programs.
The results in (9) and (10) also show that if transactional marketing efforts make no contribution to the
seller’s utility, cT = 0, the seller should allocate all of her or
his marketing resources to relational marketing activities.
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 25
The relational marketing effort should be kept constant
over time, without any dependence on the partners’ commitments (Fruchter and Sigué 2004). Combining these results with Theorem 1, we can better understand the effect
of transactional efforts. The relational marketing effort
acts as a closed-loop strategy (feedback) of the partners’
commitments only if the seller adds transactional efforts
that contribute directly and interact with the buyer’s commitment to her or his utility.
Next, we compare the allocation of marketing resources
between the two types of marketing efforts.
Corollary 2 (allocation of transactional and relational
marketing). Assume
α b 
[α b α s ] b ≥ c T and c T2 + 2c C c T ≥ b T  
α s 
(11a)


α
T


1 − r[α b α s ]D −1 AD −1  b  [α b α s ]b,

α s 
where
  −β b θ b  α b 

D = 
 +  [α b α s ] A .
  θ s −β s  α s 

(11b)
Then, at the beginning, the seller should allocate more resources to relational marketing. In the long run (steady
3
state ), she or he should allocate more marketing resources
to transactional marketing.
Proof. See Appendix E.
Corollary 2 determines when the optimal relational marketing effort should be either higher or lower than the optimal transactional marketing effort. It appears that the issue
of whether to allocate more resources to relational marketing or transactional marketing at the earlier stages and at
the later stages of a relationship critically depends on all
the parameters comprising the dynamics of the relational
exchange and the seller’s utility function. This result suggests that the allocation of marketing resources between
relational and transactional efforts should ultimately take
into account the preferences of the buyer and the properties of the relational exchange between the two partners.
To provide more insight on the impact of these properties, a set of illustrative examples using our analytical results is provided in a subsequent section.
3. At steady state, the set of differential equations in (2) becomes
xb = xs = 0.
NUMERICAL ILLUSTRATIONS
Using the analytical results obtained in the previous
section, we consider numerical examples to better evaluate and understand the impact of some parameters. More
exactly, we focus on analyzing trust, opportunism, and
the different contributions to the seller’s overall benefit of
the seller’s decisions and the two partners’ relational
commitment.
Trust Effects
We set the model parameters to the values given below
and change the values of the trust parameters to examine
how trust affects the seller’s decisions and the two partners’ relational commitment. In setting the parameters, we
assume partial symmetric partners who hold the same propensity to opportunism and respond identically to relational marketing efforts, as well as a balanced utility
function in which transactional marketing and the partners’ commitment have the same contribution to the
seller’s overall benefit.
βb = βs = 4
αb = αs = 1
Propensity to opportunism
Responses to relational marketing
efforts
cb = cs = cT = cC = 1 Contribution to seller’s overall
benefit
r = 0.1
Discount rate
Table 1 provides examples of three cases: The seller and
the buyer hold the same level of trust (Case 1), the seller is
more trusting than the buyer (Case 2), and the buyer is
more trusting than the seller (Case 3). Case 1 is considered
a benchmark for complete symmetric partners characterized by mutual desire to commit to a long-term relationship (Sigué and Elloumi 2002).
The superscripts denote the number of the case in Table 1. The partners’ commitments and the seller’s marketing efforts compare as follows:
x 1s > x s2 > x s3 , x 1b > x b3 > x b2 ,
(12)
u1i > u i3 > u i2
(13)
i = {1, 2}.
As indicated in (12), the two partners’ commitment decreases with a decrease of trust either on their own side or
on the other partner’s. The decrease of a partner’s commitment is, however, more obvious when accompanied by a
decrease in trust in the other partner. The two partners
maintain the same level of commitment if they hold the
same level of trust (complete symmetry). As expected, the
more trusting partner is also the more committed.
26
JOURNAL OF SERVICE RESEARCH / August 2005
TABLE 1
Optimal Decision Rules, Commitments, and the Time Trajectories for Trust Effects
Optimal Decision Rules and Commitments
Case 1: θb = θs = 2
u1* = 1.63083 + 0.194003 x b + .066443 x s
u2* = 1 + x b
x b* ( t ) = x s* ( t ) =.9375(1 − e −1 .74 t )
Commitments and Marketing Efforts Time Trajectories
1.8
0.6
1.7
1.6
0.4
x s* ( t ) = x b* ( t )
0.2
0.5
Case 2: θb = 1
θs = 2
.
+ 0.15368 x b + 0.02286 x s
u1* = 117378
u2* = 1 + x b
−16
x b* ( t ) = −.03 e −5 .4 t −.42 e 2 .43 t + .45 e 8 .88 .10 t
−5 . 4 t
−243 t
8 . 88 . 10 −16 t
*
x s ( t ) = .04 e
−.58 e
+ .54 e
We set the model parameters to the values given below
and change the values of the propensity to opportunism to
examine how partners’opportunism affects the seller’s decisions and the two partners’ relational commitment. This
setup assumes partial symmetric partners who mutually
trust each other at the same level and respond identically to
relational marketing efforts, as well as a balanced utility
function in which transactional marketing and the part-
0.5
2
1
1.5
u2* ( t )
1.3
0.3
0.2
x s* ( t )
x b* ( t )
1
1.5
2
2.5
3
u1* ( t )
0.5
1.6
0.5
1
1.5
2
2.5
3
u2* ( t )
1.5
0.4
1.4
x s* ( t )
0.3
0.2
1.2
1.1
0.6
1.3
x b* ( t )
0.5
Opportunism Effects
1.5
1.4
0.1
The seller diminishes both her or his relational and
transactional marketing efforts when the two partners
maintain mutual low levels of trust. The diminution of the
seller’s transactional and relational marketing efforts is
more pronounced when the trust of the buyer is lower than
when the seller does not sufficiently trust the buyer (13).
Interestingly, depending on the two partners’ trust, the
seller’s emphasis on both transactional and relational marketing changes over time. Although it is advisable for the
seller to invest more in relational marketing at the earlier
stages, over time, the seller should increase at a greater
speed her or his investment in transactional marketing, especially when she or he sufficiently trusts the buyer. At the
steady state or even before, particularly when the buyer
does not trust the seller, the seller should allocate more
marketing resources to transactional activities than to relational activities.
u2* ( t )
1.4
0.4
0.5
u1* = 12847
.
+ 0.1735 x b + 0.0559 x s
u2* = 1 + x b
x b* ( t ) = −.043 e −5 .44 t −.65 e −2 .33 t + .61
x s* ( t ) = −.033 e −5 .44 t −.47 e −2 .33 t + .51
1
1.5
0.5
0.1
Case 3: θb = 2
θs = 1
u1* ( t )
1.9
0.8
u1* ( t )
1.2
1.1
1
1.5
2
0.5
1
1.5
2
ners’ commitment have the same contribution to the
seller’s overall benefit.
θb = θs = 1
αb = αs = 1
cb = cs = cT = cC = 1
r = 0.1
Trust parameters
Responses to relational marketing
efforts
Contribution to seller’s overall
benefit
Discount rate
In Table 2, we provide three examples: The two partners
have the same propensity to opportunism (Case 1), the
buyer tends to be more opportunistic than the seller
(Case 2), and the seller has a propensity for being more opportunistic than the buyer (Case 3). Again, Case 1 is a
benchmark of complete symmetric partners.
The superscripts denote the number of the case in Table 2. The partners’ commitment and the seller’s marketing efforts compare as follows:
x 1s > x s2 > x s3 , x 1b > x b3 > x b2 ,
(14)
u1i > u i3 > u i2
(15)
i = {1, 2}.
The two partners’ commitment decreases with an increase in their own or the other partner’s propensity to opportunism (14). The decrease of a partner’s commitment
is, however, more prominent when accompanied by an in-
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 27
TABLE 2
Optimal Decision Rules, Commitments, and the Time Trajectories for Opportunism Effects
Optimal Decision Rules and Commitments
Case 1: βb = βs = 2
u1* = 8.1047 + 0.5132 x b + .02166 x s
u2* = 1 + x b
x b* ( t ) = x s* ( t ) = 30 e − .27 t ( −1 + e 27 t )
Commitments and Marketing Efforts Time Trajectories
u1* ( t )
30
30
25
25
20
20
15
15
10
10
x s* ( t ) = x b* ( t )
5
5
Case 2: βb = 4 > βs = 2
u1* = 1.62992 + 0.157352 x b + .0371322 x s
u2* = 1 + x b
. + 0.085 e −4 .35 t − 1.369 e −1 .46 t
x b* ( t ) = 129
*
x s ( t ) = 0.77 − 0.175 e −4 .35 t − 0.596 e −1 .46 t
10
15
5
20
10
15
20
*
1
u ( t)
x s* ( t )
1.4
u2* ( t )
5
1.8
1.2
1.7
1
1.6
0.8
1.5
0.6
x ( t)
0.4
u2* ( t )
1.4
*
b
1.3
1.2
0.2
1.1
1
2
3
4
5
1
0.5
Case 3: βb = 2 < βs = 4
u1* = 2 .38768 + 0.358856 x b + .0676007 x s
u2* = 1 + x b
x b* ( t ) = 0.089 e −4 .45 t − 2 .475 e −1 .1445 t + 2 .39
x s* ( t ) = − 0.234 e −4 .45 t − 1198
. e −1 .1445 t + 1.43
3.5
2
3
1.5
2.5
*
( t)
x 12
1
x s* ( t )
0.5
crease in their own propensity to opportunism. This finding follows from our specification of commitment in (1b),
which assumes a direct influence of a partner’s opportunism on his or her own commitment and an indirect influence on the other partner’s commitment through the trust
factor. Not surprisingly, we found that the partner with the
higher propensity to opportunism is also the less committed of the two. The seller diminishes both her or his relational and transactional marketing efforts when her or his
propensity to opportunism or the buyer’s increases. An increase in the propensity to opportunism in the buyer has a
more damaging impact on the seller’s marketing investments than an increase of the same proportion in the
seller’s propensity to opportunism (15).
We found also that at the earlier stages, the seller should
maintain a higher level of relational marketing, independent of the propensities to opportunism of the two partners.
The investment in transactional marketing should, however, increase more rapidly over time and might overtake
relational marketing at the steady state, especially when
the buyer’s propensity to opportunism is low. This result
suggests that in a relationship where the buyer is very opportunistic, it can be useful for the seller to maintain a
higher level of relational marketing activities (compared to
transactional marketing activities) at the steady state,
which are more likely to build and maintain a higher level
of commitment. Another alternative is to change the
2
3
4
2
2.5
3
u1* ( t )
u2* ( t )
2
1.5
1
1
1.5
2
3
4
5
5
buyer’s propensity to opportunism through a variety of
contractual and managerial mechanisms.
Contribution to the Seller’s Benefit Effects
We set the model parameters to the values given below
and change the values of the different contributions to the
seller’s benefit to examine how they affect the decisions of
the seller and the two partners’ relational commitment.
This setup assumes complete symmetric partners who
hold the same propensity to opportunism, mutually trust
each other at the same level, and respond identically to
relational marketing efforts.
θb = θs = 1
αb = αs = 1
βb = βs = 1
r = 0.1
Trust parameters
Responses to relational marketing efforts
Opportunism coefficients
Discount rate
Table 3 gives two illustrations. The first assumes that
transactional marketing activities have a higher contribution to the seller’s utility (Case 1), and the second assumes
the commitment of the two partners contributes more than
transactional marketing to the seller’s utility (Case 2).
We observe that the seller invests in both relational and
transactional marketing, according to their contributions
to her or his utility. In a context where transactional mar-
28
JOURNAL OF SERVICE RESEARCH / August 2005
TABLE 3
Optimal Decision Rules, Commitments, and the
Time Trajectories for Different Contributions to the Utility
Optimal Decision Rules and Commitments
Case 1: cb = cs = cC = 1
cT = 4
u1* = 2 .0468 + .14734 x b + .02126 x s
u2* = 4 + x b
x b* ( t ) = x s* ( t ) = .723 e −2 .83 t (1 − e 2 .83 t )
Commitments and Marketing Efforts Time Trajectories
0.7
4.5
4
0.6
0.5
*
s
3.5
*
b
x ( t) = x ( t)
3
u2* ( t )
*
1
u ( t)
0.4
2.5
0.5
Case 2: cb = cs = cC = 2
cT = 1
u1* = 2 .55024 + .64565 x b + .1016 x s
u2* = 1 + 2 x b
.
x b* ( t ) = x s* ( t ) = 113208
e −2 .253 t ( −1 + e 2 .2533 t )
1
1.5
2
2.5
3
0.5
1
1.5
2
2.5
3.4
1
3.2
0.8
3
0.6
2.8
x s* ( t ) = x b* ( t )
0.4
2.6
u2* ( t )
u1* ( t )
2.4
0.2
2.2
0.5
keting activities are more effective than relational marketing activities (Case 1) over the entire time horizon, the
seller will allocate more resources to transactional marketing than to relational marketing. The reverse is also true;
that is, relational marketing activities receive more resources if the commitment of the two partners brings more
utility to the seller (Case 2). However, the seller’s marketing investments in Case 2 increase significantly over time,
whereas they tend to be relatively constant over time in
Case 1. As the contribution of the two partners’ commitment to the seller’s utility increases, they both commit
more to the relationship. This could be explained by the
fact that the seller invests heavily in relational marketing,
which has a positive impact on the two partners’ relational
commitments. An indirect consequence of investment in
relational marketing is the increase in transactional marketing activities through the buyer’s commitment.
CONCLUSIONS AND DISCUSSION
In this article, we have proposed an analytical model
that allows the formal examination of how a seller should
design an intertemporal marketing program that includes
transactional and relational activities, to maximize her or
his discounted utility. The model provides original answers and asks some intriguing questions of the current relationship marketing literature, such as the following: Are
transactional and relational marketing substitutes for each
other, or are they complementary? What should be the
optimal mix of transactional and relational marketing
activities over time in a relational exchange? The model
proposed applies exclusively to cases in which the seller
1
1.5
2
2.5
3
0.5
1
1.5
2
2.5
3
invests to establish and maintain relational commitments, and the buyer only reacts to the seller’s marketing
programs.
Contributions
The emerging paradigm of relationship marketing
raises many challenging questions for marketing managers and scholars that, unfortunately, cannot be fully answered by any single research approach or any single article. We hope, however, to have shown here that analytical
modeling, which is traditionally associated with transactional marketing, can be broadened to integrate relational marketing activities and social interactions for the
enrichment of the relationship marketing literature. The
main findings of our analytical model follow.
In a context where the transactional marketing effort
and the buyer’s commitment exclusively contribute in isolation to the seller’s utility, the seller should implement
time- and commitment-independent transactional and relational marketing programs. Thus, the seller’s concern
should be exclusively limited to the effectiveness of transactional marketing efforts (such as sales promotion) on her
or his overall benefit or gross margin. Conversely, the
seller’s optimal relational marketing efforts, such as frequency marketing programs and club marketing programs, should be extensive if they generate internal efficiency gains for the seller and the effectiveness of the
buyer’s commitment on the gross margin is high. As expected, our findings also suggest that an exchange occurring in a structural and contextual environment that does
not favor opportunistic behavior among partners and involving two partners who maintain a significant level of
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 29
trust for each other should be supported by large investments in relational marketing programs. These findings
build an important bridge between the behavioral research
stream, which has investigated opportunism, trust, and
commitment in relational exchanges with little attention
on decision making (e.g., Dwyer, Shurr, and Oh 1987;
Gundlach, Achrol, and Mentzer 1995; Morgan and Hunt
1994), and scholars who have been concerned by the effects of relational marketing activities (e.g., Berry 1995;
Webster 1992). They indicate that the assessment of the
opportunity of using relational marketing activities should
not be limited to customer potential profitability, as some
have advocated, but also expand to factors that may
enhance or lessen the commitment of exchange partners,
such as trust and opportunism.
The transactional marketing effort and the buyer’s
commitment are likely to contribute separately to the
seller’s utility when the intrinsic economic value of the
seller’s offer does not have any direct impact on the
buyer’s commitment. Some club marketing programs or
other relational marketing programs that offer exclusively
social and psychological benefits may fall into this category. The Harley Owners Group, sponsored by HarleyDavidson, is one of the oldest club marketing programs
aimed primarily at providing club members with a variety
of social and psychological benefits. Recently, Martell
launched its Martell Elite Club in Hong Kong to offer “a
forum for like-minded citizens of the world who have set
benchmarks in their fields, and who carry a profound admiration of the finer things in life” (see White 2004). The
benefits for club members are primarily social and psychological. Obviously, although the commitment of these
two clubs’ members is important to secure future sales for
Harley Davidson and Martell, there is no reason to believe
that it would allow them to increase their short-term sales
in response to their transactional marketing activities. This
is because the pleasure of being a member of the club for a
buyer could be separated from the pleasure of making a
good deal in a given period. Strategically, our findings suggest that without interaction between transactional marketing and the buyer’s commitment, it is optimal for the
seller to avoid resting on relational commitments and to
design a balanced, steady marketing program involving
both transactional and relational marketing from the beginning to the end of the relationship.
For scenarios in which the transactional marketing effort and the buyer’s commitment contribute jointly to the
seller’s utility, we have found that the seller’s decisions at
any time on both transactional and relational marketing
follow a feedback decision rule. Frequency marketing programs that reward customers who buy frequently or in
large quantities are typical examples of cases in which the
effect of transactional marketing activities is combined
with the relationship marketing program to generate more
utility to the seller. Basically, this means that committed
buyers may react more favorably to short-term transactional marketing activities as they also increase their
long-term reward. In such a context, besides the parameters listed in the case in which there is no joint contribution, the seller’s decisions also involve the buyer’s commitment for transactional marketing and the commitment
of the two partners for relational marketing. The rules for
determining relational and transactional marketing efforts
display a very interesting property. The first is a linear
function of the commitments of the two partners, whereas
the second is a positive linear function of the buyer’s commitment. This latter rule is a formal proof that, under certain conditions, transactional and relational marketing are
complementary, as relational marketing affects the buyer’s
commitment positively. In contrast with the current belief
that committed buyers may be less sensitive to economic
value variations, our findings support the idea that the
more buyers are committed, the more sellers may have to
improve their intrinsic economic proposition over time
with activities such as sales promotion. Strategically, this
implies that the buyer’s commitment should not be taken
for granted. Instead, the seller must keep investing in
transactional marketing to offer greater value propositions to committed buyers. This finding is consistent with
Kalwani and Narayandas’s (1995) argument that in longterm relationships, buyers may become more sensitive to
the economic value of sellers’ offers and strive to share
relational benefits equitably. Indeed, Backhaus (1999)
reports that in the health care industry, long-term customers react more to events affecting the quality of services
than new customers do.
The allocation of marketing resources between transactional and relational marketing is not limited to the type
of product and the profitability of the buyer, as is often
claimed in the literature (see Coviello et al. 2002;
Grönroos 1994), but also depends on several other factors,
including the contextual and structural environment of the
relational exchange and the reactions of the two partners to
the seller’s relational marketing activities.
The strategic implications of the numerical analysis of
some relational properties are summarized in Table 4.
Consider a structural and contextual environment in
which the propensity to opportunism of the buyer is either
low or high and the buyer holds a low or high level of trust
in the seller’s commitment. We provide a sample of indicators that may favor low- or high-opportunism behavior as
well as low or high level of trust (see Doney and Cannon
1997; Wathne and Heide 2000). The design of an optimal
mix of transactional and relational marketing efforts
should take into account the buyer’s level of trust for the
seller and the scope of his or her propensity to opportun-
30
JOURNAL OF SERVICE RESEARCH / August 2005
TABLE 4
Strategic Actions According to the Buyer’s Trust and Opportunism
Buyer’s Propensity to Opportunism
Some indicators
Transactional
marketing
Relational
marketing
Actions on
parameters
Low
High
Specific investments
Binding agreements
Lack of specific investments
Lack of binding agreements
Monopoly
Share strong norms
of solidarity
Increase steadily up
to the steady state
Increase gradually
for a longer period
of time
Buyer’s Trust in the Seller’s Commitment
Low
High
Competitive alternatives
Divergent norms
Negative rating from third parties
Negative customer service
experience
Negative testimonials
Weak company recommendation
Positive rating from third parties
Positive customer service
experience
Positive testimonials
Strong company reputation
Increase abruptly at
the earlier stages
Increase gradually for a
shorter period of time
Increase abruptly at the
earlier stages
Increase gradually for a
shorter period of time
Increase steadily up to the
steady state
Increase gradually for a
longer period of time
ism. In general, it is advantageous to invest more in relational marketing at the earlier stages of the relationship
and, depending on the buyer’s trust and propensity to opportunism, to rapidly or gradually increase transactional
and relational marketing over time up to the steady state
(maturity) of the relationship.
On the other hand, the seller can take actions exogenous to our model to change the buyer’s trust and opportunism parameters, as indicated in Table 4. In particular,
the level of trust can be enhanced, whereas the propensity
to opportunism can be reduced. Such exogenous actions
could be long-term formal contracts or binding agreements, structural investments that create additional exit
barriers likely to limit the buyer’s propensity to opportunism, or any activity that can help to provide the buyer with
a positive service experience and strengthen the reputation
of the seller.
Finally, the numerical analysis also shows that the contributions of transactional and relational marketing to the
seller’s overall benefit play a significant role. In a context
where transactional marketing activities are more effective
than relational marketing activities, over the entire time
horizon, the seller allocates more resources to transactional marketing than to relational marketing. The reverse is also true (i.e., relational marketing activities receive more resources if the commitment of the two
partners brings more utility to the seller). As the seller’s
utility is a mapping function of the buyer’s utility, our finding supports the notion that the seller should follow a basic
requirement of the marketing concept—the satisfaction of
customers’ needs should drive her or his marketing
programs.
Limitations and Future Research
Some of our modeling assumptions can be relaxed to
address more complex situations, as in the following three
examples. First, we assume that the dynamics of the relational exchange between a buyer and a seller are not influenced by competition. This assumption is restrictive as
there is evidence that buyers often consider alternative
propositions in their choice of suppliers. An obvious extension of our model should be able to show how the existence of competitive offers affects the seller’s optimal relational and transactional marketing decisions and the
dynamics of commitment between partners.
Second, we assume an asymmetric relational exchange
in which only the seller invests in the two partners’ relational commitment. Although this case is common in
consumer markets, it does not fit with many business-tobusiness applications of relationship marketing. A possible extension of our model should examine, in a context of
a differential game, how the seller and the buyer invest in
their relational commitment to reach equilibrium.
Third, although relational marketing programs can easily be implemented for individual buyers, many transactional marketing programs are designed to meet the
needs of multiple buyers. In this context, the seller faces a
more difficult situation than our present setup, in which
she or he designs a complete marketing program for a single buyer. Extending our model to a seller dealing with
two buyers would be more realistic to cope with such a
challenge.
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 31
APPENDIX A
Proof of Theorem 1
Consider the optimal control problem (2) with the assumption in (1a). The current-value Hamiltonian is given by
H(xb, xs, u1, u2, λb, λs) = f(u2, xb, xs)-C(u1, u2) + λb(–βbxb + θbxs + αbu1) + λs(–βsxs + θsxb + αsu1) + µbxb + µsxs,
where λb and λs are the adjoint variables, or, in our context, the net benefit (or damage) of increasing the level of relational commitment of
the buyer to the seller and of the seller to the buyer, respectively, by one additional unit. µb and µs are adjoint variables associated with the
constraints on xb and xs, taking the values
≥ 0 x i ( t ) = 0
µi 
, i ∈ {s, b}.
= 0 x i ( t ) > 0
The necessary optimality conditions are given by
∂H
= − ∂C / ∂u1 + λ b α b + λ sα s = 0,
∂u1
(A1.1)
∂H
= ∂f / ∂u2 − ∂C / ∂u2 = 0.
∂u2
(A1.2)
The adjoint equations are the following:
∂H
= rλ b − fx b + β b λ b − θ s λ s − µ b ,
λ b = rλ b −
∂x b
(A2)
∂H
= rλ s − fx s + β s λ s − θ s λ s − µ s ,
λ s = rλ s −
∂x s
(A3)
lim λ b e − rt = 0 and lim λ s e − rt = 0.
(A4)
and the boundary conditions are
t→ ∞
t→ ∞
Considering (3), (4), (A1.1), and (A1.2), the optimal relationship and transactional marketing efforts satisfy
u1 = λ b α b + λ sα s ,
(A5.1)
u2 = cT + cC x b .
(A5.2)
If xb > 0 and xs > 0, then considering (3), (A5.2), (A2)-(A4), and the differential equations in (2), we obtain
 xb   −β b
  
x s   θ s
λ  = − c 2
 b  C
λ s   0
θb
α 2b
−β s α b α s
0
r + βb
0
−θ b
0
α bα s   x b  

  

2
0
α s  x s  

+
,

−θ s  λ b  − cb − cC cT 

  

r + β s  λ s   − c s
 xb (0) = 0 


 x s (0) = 0 
lim λ e − rt = 0  .

 t→ ∞ b
lim λ s e − rt = 0 

 t→ ∞
(A6)
Assume that
λ b 
x b 
  = A   + b,
λ s 
x s 
(A7)
32
JOURNAL OF SERVICE RESEARCH / August 2005
where
a11 a12 
A=
 and
a21 a22 
b1 
b =  .
b2 
(A8)
Substituting (A7) into (A6) yields
 α 2b α b α s 
 α b2 α b α s 
 β b −θ b   x b 

 A − 
    + A 
A 
2
 −θ s β s   x s 
α sα b α 2s 
α sα b α s 
r + β b −θ s 
 − cC2
 A + 
b = 
 0
 −θ b r + β s 
−θ s 
0  x b  (r + β b )
cb + cC cT 
    + 
b−
.
(r + β s )
cs
0  x s   −θ b


(A9)
Considering (A9), we obtain that A satisfies the following Riccati algebraic equation:
 α 2b α b α s 
 − cC2
 β b −θ b  r + β b −θ s 
 A − 
−A 
 −
 A + A 
 −θ s β s   −θ b r + β s 
α sα b α 2s 
 0
0
 = 0 ,
0
(A10)
and b satisfies
−1
(r + β b )
−θ s 
 α 2b α b α s   cb + cC cT 
  
 − A 
b = 
.
(r + β s )
cs
α sα b α 2s   
 −θ b

(A11)
Considering (A5.1), (A5.2), and (A7), we now conclude with our theorem.
If xb = xs = 0, then from (1b), we obtain u1 = 0. On the other hand, if u1 = 0, again from (1b), we obtain xb = xs = 0.
APPENDIX B
The Buyer’s Commitment xb
Depends on All the Parameters
To see how the buyer’s commitment xb depends on all the parameters, one can substitute the values of u1* from (5) into the set of differential equations in (2) and solve the resulting set of linear differential equations:
x b ( 0 ) = 0 
xb 
x b   α b2 α b α s 
 b, 
D
=
,
 
  + 
2 
x s ( 0 ) = 0 
x s 
x s  α b α s α s 
(B1)
where b is as in (8) and
  −β b
D =  
 θs
θ b  α b 

 +   [α b α s ] A ,
−β s  α s 

(B2)
for xb(t) and xs(t). Thus, the solutions will depend on all parameters of the model.
APPENDIX C
Matrix A
Matrix A in Riccati equation (7) is symmetric; that is, a12 = a21 (to see this, we transpose equation (7)). To find the elements of the matrix (i.e., a11, a22, a12), we need to solve the following system of three nonlinear algebraic equations:
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 33

−2 a11 (β b + .5r ) + 2 a12θ s + ( a11α b + a12α s )2 + cC2 = 0

−2 a22 (β s + .5r ) + 2 a12θ b + ( a22α s + a12α b )2 = 0


2
2
a11 (θ b + a12α b + a22α b α s ) − a12 (β b + β s + r − a12α b α s ) + a22 (θ s + a12α s ) = 0.
(C1)
Using a symbolic software (e.g., Mathematica; Wolfram 1993), one can easily solve this system analytically. Finding a11, a12, and a22, the
explicit solution for u1* is
u1* = ( a11α b + a12α s )x b + ( a12α b + a22α s )x s + α b b1 + α s b2 ,
(C2)
where
b1 =
b2 =
( cb + cC cT )( − a12α b α s − a22α 2s + β s + r ) + c s ( a11α b α s + a12α 2s + θ s )
,
γ
( cb + cC cT )( a12α b 2 + a22α b α s + θ b ) + c s ( − a11α b 2 − a12α b α s + β b + r )
,
γ
(C3)
and
γ = ( − a11α 2b − a12α b α s + β b + r )( − a12α b α s − a22α 2s + β s + r ) − ( a12α b2 + a22α b α s + θ b )( a11α b α s + a12α 2s + θ s ).
(C4)
APPENDIX D
Proof of Corollary 1
If cC = 0 (the cross-effect of transactional marketing efforts and the buyer’s commitment to the seller’s overall benefit), then considering (6), we obtain
u2* = cT .
(D1)
Moreover, if cC = 0, a solution of the Riccati equation (see (7)) is A = 0. Substituting A = 0 in u1* (see (5)), we obtain
−1
−θ s   cb  α b [ cb (r + β s ) + θ s c s ] + α s [ c s (r + β b ) + θ b cb ]
(r + β b
.
   =
u = [α b α s ] b = [α b α s ] 
(β b + r )(β s + r ) − θ b θ s
(r + β s )  c s 
 −θ b
*
1
(D2)
Inversely, if u1* and u2* are constant over time, it is necessary that cC = 0.
APPENDIX E
Proof of Corollary 2
In the first step, we compareu1* withu*2 (see (5) and (6)) at xb = xs = 0 to obtainu1* ( 0) = [α b α s ] b ≥ c T = u*2 ( 0). In the second step, we compare u1*2 and u*22 (see again (5) and (6)) at steady state. Let
α b 
α =  .
α s 
4
At steady state, the optimal relational commitment takes the value given by
(E1)
34
JOURNAL OF SERVICE RESEARCH / August 2005
x b 
α b 
x =   = − D −1   [α b α s ]b,
x s 
α s 
(E2)
−αα T b = D x,
(E3)
or
where b and D are as in (8) and (B2). Using the notation in (E1) and (E2), we obtain
(u*22 − u1*2 )| ss = u*22 − b T αα T b − x T Aαα T Ax − b T αα T Ax − x T Aαα T b.
Thus,
(u*22 − u1*2 )| ss = u*22 − b T αα T b + x T ( − Aαα T A + D T A + AD) x .
Considering the definition of D in (B2), the Riccati equation in (7) becomes
 − c 2 0
AD + D T A − Aαα T A = rA +  C  .
 0 0
(E4)
Thus,
(u*22 − u1*2 )| ss = u*22 − b T αα T b + r( x T Ax ) − c C2 x b2 .
Considering (5) and (6), we have
(u*22 − u1*2 )| ss ( c T2 + 2c T c C x b − b T αα T b + r( x T Ax ).
From (E3), x = –D–1ααTb, thus u*2 | ss ≥ u1* | ss if, and only if,
T
c T2 + 2c C c T ≥ b T α(1 − r α T D −1 AD −1 α) α T b.
4. The steady state is asymptotically stable if matrix D is negative definite, which means that the principal minors are alternating in sign starting with
the negative. For example, in the special case when there is no cross-effect between transactional marketing and the buyer’s commitment (i.e., cC = 0 and
thus A = 0), D is negative definite if the combined effect of the two partners’propensities to opportunism are higher than the combined effect of their trust parameters (βbβs > θbθs).
Fruchter, Sigué / TRANSACTIONS VS. RELATIONSHIPS 35
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Gila E. Fruchter is a senior lecturer of marketing at the School of
Business Administration at Bar-Ilan University, Israel. She
earned all her degrees in mathematics from the Technion, Israel
Institute of Technology. She held visiting positions in marketing
at Washington University in St. Louis, MIT Sloan School of
Management, University of California at Berkeley, and Hong
Kong University of Science and Technology. Her current research focuses on dynamic competitive marketing strategy, service marketing, and relationship marketing. Her recent articles
have appeared in Management Science, Marketing Science,
Journal of Service Research, Journal of Optimization Theory
and Application, Journal of Economic Dynamics and Control,
European Journal of Operational Research, Optimal Control
Applications and Methods, and International Game Theory Review. She is a member of the editorial board of Review of Marketing Science, and she serves as a referee for leading marketing
academic journals, among them Marketing Science and
Management Science.
Simon P. Sigué, Ph.D., HEC Montréal, is an associate professor
of marketing at Athabasca University, Canada, and honorary associate professor at the School of Business, Universidad de Los
Andes, Colombia. He conducts research in areas of franchising,
marketing channel coordination, relationship marketing, and international marketing. He has authored a significant number of
books and scientific papers, some of which have earned
international awards.