Managing Relational Exchanges
Gila E. Fruchter
Bar-Ilan University
Simon Pierre Sigué
Athabasca University
The authors propose an analytic model that deals with
both behavioral considerations between exchange partners and the determination of relational marketing efforts
over time. On the basis of the behavioral marketing literature, they consider three main factors that drive the levels
of relational commitments between two exchange partners: the trust/distrust component, the opportunism component, and the relational marketing effort of the seller.
Incorporating these factors in a well-known model used in
applied mathematics for “love dynamics,” the authors claim
that the issue of managing relational exchanges is an optimal control problem. Their analysis shows that the seller’s
optimal policy for determining relational marketing effort
over time is either time-invariant or time-variant, depending on whether or not the exchange partners are conservative and the structural and contextual environment of the
relationship remains unchanged over time.
Keywords: relational exchange; commitment; trust; opportunism; optimal control; relational marketing effort
During the past decade, the study of relationship marketing and customer relationship management has attracted the attention of several marketing scholars (e.g.,
Berry 1995; Garbarino and Johnson 1999; Morgan and
Hunt 1994; Sheth and Parvatiyar 1995a; Verhoef 2003).
Increasingly, it is believed that successful and lasting relational exchanges are those in which partners go beyond
short-term transactional benefits and incorporate behavioral factors such as trust and commitment (e.g., Dwyer,
Schurr, and Oh 1987; Gundlach, Achrol, and Mentzer
1995; Sirdeshmukh, Singh, and Sabol 2002). This belief
has pervaded marketing thought such that many scholars,
especially in Europe, are calling for a paradigm shift in
marketing (e.g., Grönroos 1994; Gummesson 1997).
From the seller’s perspective, the challenge presented
by the emerging paradigm of relationship marketing is to
determine a sequence of marketing decisions and behavior
capable of establishing, developing, and maintaining successful relationships with buyers (e.g., Morgan and Hunt
1994). For many scholars, it is no longer possible to focus
on marketing mix as the only set of strategic marketing
variables (e.g., Grönroos 1994). Given improved technologies, resources, and skills, competitors are increasingly
able to meet the quality of any offer in the market. One of
the critical consequences of this trend has been an amplified focus on pricing and sales promotion to attract customers in the short term, which, unfortunately, increases
customers’ sensibility to prices and decreases their loyalty
to brands.
The fundamental idea of relationship marketing is to go
beyond short-term transactional marketing actions and to
build loyalty to brands and sellers. To accomplish this,
The authors thank the participants of the INFORMS 2003 Marketing Science Conference for the feedback on an earlier draft of the article. The comments provided by Roland Rust as well as two anonymous Journal of Service Research reviewers are greatly appreciated.
Finally, the second author thanks the School of Business, Athabasca University for support of the research and Janice Thiessen for her
useful comments. Correspondence concerning this article should be addressed to Gila E. Fruchter, Graduate School of Business Administration, Bar-Ilan University, Ramat-Gan 52900, Israel; fax: +972 (3) 535-3182; e-mail: [email protected].
Journal of Service Research, Volume 7, No. 2, November 2004 142-154
DOI: 10.1177/1094670504268421
© 2004 Sage Publications
Fruchter, Sigué / RELATIONAL EXCHANGES 143
sellers must design marketing programs such that loyal
and committed customers receive more value than disloyal
customers. There are numerous benefits for sellers in pursuing such a paradigm, including increased access to markets, generating repeat purchases, creating 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; Panda
2003; Saren and Tzokas 1998).
Despite the intense interest in customer relationship
management, the growing body of relationship marketing
and customer relationship management literature still
faces several challenges. For example, the critical issue of
resource allocation for building and maintaining successful relational exchanges has not been fully examined.
Rather, several studies have investigated the link between
behavioral antecedents and outcomes of relational exchanges (e.g., Andaleeb 1996; Hunt and Morgan 1994;
Sirdeshmukh, Singh, and Sabol 2002). On the other hand,
researchers have also studied the effectiveness of relational marketing efforts such as direct mail, tangible rewards, and preferential treatment, as well as customers’
relationship perceptions on more operational management
constructs, including customer retention rate and customer share (e.g., De Wulf, Odekerken-Schröder, and
Iacobucci 2001; Verhoef 2003). Although these studies
have generated significant knowledge on the effectiveness
of various relational marketing efforts, their methodological approach, generally based on survey and aggregated
panel data from customers, does not explicitly address the
seller’s decision-making process.
Other relevant methodological approaches available in
the transactional marketing literature that can cope with
the dyadic or/and dynamic nature of relational exchanges
have not been extensively used. For instance, the field of
analytic modeling has been surprisingly timid in addressing relational issues. The first known exception is the recent book chapter by Sigué and Elloumi (2002). The
authors of this chapter use a system of differential equations to describe how relational commitments are established and maintained. They build a bridge between
relationship marketing and a well-known modeling approach used in applied mathematics to describe love dynamics between two individuals (e.g., Feichtinger,
Jørgensen, and Novak 1999; Rinaldi 1998a, 1998b;
Rinaldi and Gragnani 1998). The model of love dynamics
takes three aspects of love into account: the forgetting process, the pleasure of being loved, and the reaction to the appeal of the partner. Sigué and Elloumi’s model assumes
that relational commitments between two exchange partners are driven by trust, opportunistic behavior, and the
partners’ appeal. However, the model remains descriptive
and does not indicate how marketing decisions are made in
order to establish and maintain relational exchanges.
Although a complete marketing program may well include both transactional and relational marketing (see
Coviello et al. 2002; Hultman and Shaw 2003), in this article, we deliberately focus on relational marketing actions.
We propose, for the first time, an analytic model dealing
with both behavioral considerations between exchange
partners and the determination of relational marketing efforts. Our model goes beyond the descriptive dynamics of
Sigué and Elloumi and prescribes an optimal way of determining relational marketing efforts while sellers aim at
maximizing their discounted utility. It is our thesis that the
problem of establishing and maintaining long-run relational exchanges is an optimal control problem in which
the ultimate goal of the seller is to maximize her
intertemporal utility.1 We consider that the seller’s relational utility stems from the commitments of the two exchange partners, which are built by three main components: (a) the trust/distrust component, which is the
willingness/reluctance of a party to rely on the trustworthiness of the other; (b) the opportunism component, to capture a partner’s own forgetfulness or failure to remember
previous commitments over time; and (c) the seller’s relational marketing efforts, which can be either an economic
reward or other social activities creating social and psychological benefits for the buyer. Unlike the behavioral literature of customer relationship management that has
studied the effectiveness of various relational marketing
instruments, our normative approach assumes that the
seller is the decision maker and has direct control over her
relational marketing efforts (e.g., De Wulf, OdekerkenSchröder, and Iacobucci 2001; Verhoef 2003).
Our main finding supports the view that the seller’s relational marketing effort should increase (decrease) with
any increase (decrease) over time of trust between the two
partners, the effectiveness of the relational marketing program on the partners’ commitments, and of the partners’
contributions to the seller’s relational benefits. On the
other hand, it should decrease (increase) with any increase
(decrease) over time of opportunistic propensities and distrust of the two partners. Our model advocates the use of
real-time relational marketing programs in the context of
relational exchanges involving personal interactions, continuous changes in the structural and contextual relational
environment, and a variety of relational marketing instruments, as it is often the case in the service industry. But it
also applies to conservative partners involved in a stable
relationship in which the parameters affecting the dynamics of their commitment do not change over time, as in the
case of several reward-based loyalty programs in consumer markets.
The rest of this article is organized as follows. First, we
discuss relational commitment and its driving factors.
1. Hereafter, the seller is a woman and the buyer is a man.
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JOURNAL OF SERVICE RESEARCH / November 2004
Second, we present our model and determine its optimal
policy. Third, we consider some typical behavioral situations encountered in relational exchanges. In the last section, we conclude and discuss our findings.
BUILDING A RELATIONAL COMMITMENT
One of the most critical concepts of relationship marketing is relational commitment. Many scholars share this
view (e.g., Garbarino and Johnson 1999; Gundlach,
Achrol and Mentzer 1995; Morgan and Hunt 1994). For
example, Morgan and Hunt (1994) considered relational
commitment as one of the two key mediating variables of
relationship marketing. Gundlach, Achrol, and Mentzer
(1995) viewed commitment as an essential ingredient of
successful long-term relationships. With a few empirical
exceptions, the relationship marketing literature recognizes the existence of positive relationships between commitment among partners and many favorable constructs
that create relational value, such as trust, cooperation, acquiescence, loyalty, functional conflict, communication,
and satisfaction (De Wulf, Odekerken-Schröder, and
Iacobucci 2001; Grayson and Ambler 1999; Moorman,
Zaltman, and Deshpandé 1992; Verhoef 2003). Relational
commitment is generally considered as a behavioral outcome of fruitful interactions between exchange partners
(Dwyer, Schurr, and Oh 1987; Geyskens, Steenkamp, and
Kumar 1999).
Following Morgan and Hunt (1994), we assume that relational commitment is an exchange partner’s belief that
an ongoing relationship with another is sufficiently important as to deserve maximum efforts to maintain it. Committed partners are those who are able to make short-term
sacrifices to realize long-term benefits. Therefore, the current and future success of relational exchanges may be
evaluated through the partners’ relational commitments.
As a forward-looking concept, commitment implies the
presence and consistency over time of both the attachment
and the willingness to maintain a relationship. Obviously,
the willingness to continue a relationship stems from the
social and economic benefits that each partner accumulates from it (Dwyer, Schurr, and Oh 1987; Gassenheimer,
Houston, and Davis 1998). Although this conceptualization seems very comprehensible, it is not clear how
partners should effectively build and maintain relational commitments among them or what kind of inputs exchange partners should use to reach relational
commitment.
Drawing on the framework of political economy (see
Gassenheimer, Houston, and Davis 1998; Stern and Reve
1980) and the work of Gundlach, Achrol and Mentzer
(1995), we claim that both economic and social drivers
lead to relational commitments. Successful long-term relationships make use of both drivers. According to
Gassenheimer, Houston, and Davis (1998), the economic
driver can be explained using transactional cost analysis
(Williamson 1983). Transactional cost analysis stresses
transactional efficiency and the cost of existing relationships. The economic driver of commitment corresponds to
what Gundlach, Achrol, and Mentzer (1995) called an instrumental view of commitment. In this case, commitment
is a calculative act in which committed parties want to improve their own economic benefits through reducing
transaction costs and to limit relational opportunism
through specific investments. Our work borrows from this
view and addresses relational investments and the
opportunism of exchange partners.
We define relational investments as marketing efforts
or investments undertaken by an exchange partner to create and maintain relational commitments with another
partner. The relationship literature distinguishes among
three levels of relationship marketing activities, including
economic incentives, marketing tactics with social attributes, and structural marketing solutions to customer problems (see Berry 1995). The relationship marketing theory
postulates a positive relationship between relational marketing investments and commitment. For example, De
Wulf, Odekerken-Schröder, and Iacobucci (2001) investigated the impact of perceived relationship investment on
relationship quality, including relational commitment, and
found a positive path from the first to the latter. Note that
relational marketing efforts are different from traditional
or transactional marketing efforts, which can generate
sales at a given period but have very little impact on the
level of relational commitments.
We define opportunism as an exchange partner’s propensity to reduce his or her instantaneous level of commitment at any time, as his or her previous level of
commitment is high. We assume that opportunism is supported by a partner’s forgetfulness and unwillingness to
respect commitments over time, which create inconsistency between previous commitments and the level of
commitment at a specific time. This inconsistency is misleading for the other exchange partner who is more likely
to take previous commitment as a warrant for present and
future commitments. Our conceptualization of opportunism is consistent with the concept of passive opportunism
(see Wathne and Heide 2000). Opportunistic partners,
purposely or not, adopt behavior contrary to the principle
of maintaining a long-term relational exchange. Here, we
consider that they are characterized by neglectful or selfish
failure to remember their commitments over time. The impact of opportunism on the relational commitment is
known to be negative (Gundlach, Achrol, and Mentzer
1995; Rokkan, Heide, and Wathne 2003).
Fruchter, Sigué / RELATIONAL EXCHANGES 145
The social driver of relational commitment comes from
social exchange theory, which argues that parties evaluate
relationships within a behavioral context (Gassenheimer,
Houston, and Davis 1998). In this case, commitment is
perceived as an attitudinal outcome, which can be described in terms of psychological attachment, identification, and value congruence (Gundlach, Achrol, and
Mentzer 1995). This attitudinal view of commitment has
been predominant in the marketing literature (e.g., Doney
and Cannon 1997; Garbarino and Johnson 1999;
Sirdeshmukh, Singh, and Sabol 2002). It associates commitment with prominent behavioral constructs such as satisfaction and trust. In a recent meta-analysis, Geyskens,
Steenkamp, and Kumar (1999) found that the positive relationship between trust and commitment is unanimous.
Therefore, in a relationship where there is mutual trust, it is
more likely that partners hold higher levels of commitment. Conversely, mutual distrust can prevent parties from
committing to a relationship. We assume that trust (distrust) is a significant input to building long-term relational
commitments. We define trust/distrust as the willingness/
reluctance of a party to rely on the trustworthiness of the
other in building up its own commitment. This definition is
consistent with other definitions in the literature focusing
on cognitive and behavioral perspectives of trust (e.g.,
Andaleeb 1996; Anderson and Narus 1990).
Finally, we treat economic and social drivers as additive
and separable forces that contribute to relational commitment. This conceptualization allows compensation between the two types of drivers. Lack of trust may be
balanced by relational marketing investment and still lead
to higher relational commitments. At the same time, trust
may help to overcome some economic and social investment deficiencies to higher relational commitments.
THE MODEL
The Dynamics of Commitment
We consider a seller who wants to build a long-term relational exchange with a buyer. Let xs = xs(t) and xb = xb (t)
be state variables that, respectively, measure the levels of
commitment in the relational exchange of the seller and
the buyer at time t. The seller’s commitment translates to
the willingness of the seller to stay in the relationship with
the buyer, which, in turn, leads to relational marketing investments, or the improvement of the relational value offered to the buyer. The buyer’s commitment leads to
loyalty or discernible repeat purchasing or buying behavior, facilitates communication, and generates positive
word of mouth (see Morgan and Hunt 1994; Verhoef
2003). There is a reciprocal relational indifference when
the values of xb and xs are zero. This will appear when the
partners have no interest in staying in a relational exchange. Otherwise, if the two partners are in a relational
exchange, their respective commitment is positive. Thus,
we assume
xi ≥ 0, i ∈ {s, b}.
(1)
We use two premises to model relational commitment.
One is that the relational commitment between the seller
and the buyer is unbalanced. The other is that the seller
manages the establishment of the relational exchange with
the buyer. These two premises are related and are common
in many applications of relationship marketing in consumer markets (see Blattberg and Deighton 1991; De
Wulf, Odekerken-Schröder, and Iacobucci 2001; Gruen
1995; O’Malley and Tynan 2000). The first premise
claims that the seller has more interest in establishing and
maintaining a long-term relational commitment than the
buyer. As a consequence, the second premise gives an active role to the seller in the relational exchange, whereas
the buyer plays a reactive role. Stated differently, the seller
is the person who offers something of value to the buyer or
undertakes some idiosyncratic investments for the relationship. This second premise is implicit in the growing
literature of customer relationship management (see Berry
1995; Parvatiyar and Sheth 2001; Sheth and Parvatiyar
1995a).
Let u = u(t) be a control variable that represents the
seller’s relationship marketing efforts at time t. The variable u(t) can be any relationship marketing activity fitting
into Berry’s (1995) first two levels of relationship marketing. According to Berry (1995), the first level relies on
economic incentives or offers tangible rewards over time
to develop and maintain relationships. The second level of
relationship marketing focuses on social aspects of a relationship and offers social and psychological benefits to
customers (see Panda 2003). We assume that whether the
seller’s marketing effort, u(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 marketing
effort is modeled as an input for building up the
commitment of the buyer as well as a bonding mechanism
for the seller herself.
Assume that the levels of commitment of the two
exchange partners evolve according to the following
dynamics:
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JOURNAL OF SERVICE RESEARCH / November 2004
x i = −β i x i + θ i x j + α i u, x i ( 0) = 0,
(2)
i ≠ j and i, j ∈{s, b},
where αi = αi (t) > 0, βi = βi (t) > 0, θ = θi (tD) are timevariant and bounded functions in the interval 0 t ≤ ∞.
The specification in (2) assumes that the change in partner
i’s level of relational commitment can be considered as an
additive separable function of three terms. The first
term, –βi xi, represents the opportunistic behavior of partner i, where βi (called the opportunistic propensity coefficient), measures the honest forgetfulness and neglectful or
selfish failure to remember commitments of partner i over
time. The opportunistic propensity coefficient depends on
the partner’s own personality, value system, and care, as
well as on the structural and contextual environment of the
exchange. For example, a relational marketing program
occurring in a context where 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). Also,
disproportionate structural investments between the two
partners can lead to higher opportunistic propensity from
the less involved partner (Gundlach, Achrol, and Mentzer
1995). Although such structural investments can also be
considered as relationship marketing (Level 3 of relationship marketing in Berry’s classification), we consider
here that they are exogenous and indirectly affect the
commitment of the partners through their opportunistic
propensity.
The second term, θi x j, is a reaction function of partner i
to partner j’s commitment. Parameter θi captures partner
i’s level of trust/distrust over time. 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 exogenous factors to the
model influence the level of trust/distrust between the two
exchange partners. The literature identifies several antecedents of trust, including relationship termination costs,
shared values, communication, and opportunistic behavior that can influence the trust/distrust between the two
partners (e.g., Geyskens, Steenkamp, and Kumar 1999;
Morgan and Hunt 1994). According to our model specification, a trusting partner will increase his or her instantaneous level of commitment as the commitment of his or
her partner increases. This stems from the application of
the principle of reciprocity that fosters positive relational
exchange (Bagozzi 1995; De Wulf, Odekerken-Schröder,
and Iacobucci 2001). Conversely, a distrusting partner will
decrease his or her instantaneous level of commitment as
the commitment of his or her partner increases. For the
first case, the partner’s commitment is desired; for the latter, it is not welcomed. In the latter case, many researchers
have recognized the existence of scenarios in which the
seller wishes for a long-term relationship, whereas the
buyer does not (see Barnes 1994; Berry 1995; Sheth and
Parvatiyar 1995b).
The third term, αiu, represents the impact of the seller’s
relational marketing effort on her own and the buyer’s levels of commitment at time t. The parameter αi represents
the effectiveness of the seller’s relational marketing effort
on partner i’s commitment. In a similar specification,
Sigué and Elloumi (2002) called the third term the intrinsic exchange benefit and considered it as a subjective concept capturing the appeal of partner i to partner j. In
addition, they assumed time-invariant parameters and did
not treat the appeal as an outcome of purposeful marketing
decisions. 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 the level
of interest of the buyer to the seller’s relational marketing
effort over time. 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
over time. 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.
We assume in (2) that, at the starting point, the two relational partners’ levels of commitment are zero. This assumption allows us to determine what level of marketing
effort is needed to start a relational exchange.
Note that our assumption of time-variable parameters
in (2) means that, at any time of the relationship, every exchange partner actively screens available data to determine the current values of opportunistic propensity, trust/
distrust, and the effectiveness of the seller’s relational marketing efforts in building relational commitments. This
specification includes, of course, the particular case of
time-invariant parameters in (2) that may occur if the exchange partners do not change their opportunistic propensity, trust/distrust, and interest for the seller’s relationship
marketing program. We refer to these types of relational
partners as conservative partners. Conservative partners
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 evidence on their partner’s trustworthiness, opportunistic propensity, and response to
Fruchter, Sigué / RELATIONAL EXCHANGES 147
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 it is often the case for
onetime transactions such as buying a house (Parvatiyar
and Sheth 2001).
The Seller’s Problem
Our goal in this study is to investigate how a seller can
manage (establish and maintain) a long-lasting relationship with the buyer. Specifically, assuming the impact of
relational marketing effort, u, depends on her economic
and psychological effort, our objective is to determine how
the seller should choose u in order to maximize her utility
from the relational commitment over time.
We have two assumptions here. First, we suppose that
relational benefits may go beyond sales and profit and incorporate several other dimensions for the seller. 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 relational benefits (objectives) in terms of
financial goals, marketing goals, strategic goals, operational goals, and organizational goals. We specify the
seller’s relational benefits as a function of both relational
commitments, ƒ(xb, xs). Note ƒ(xb, xs) is a function that
transforms the two partners’ commitments into relational
benefits for the seller. Second, as mentioned, 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
involved from forgone alternatives. We assume these costs
can be translated to a single unit (e.g., monetary terms) and
represented as follows: C = C(u).
Considering the above assumptions, and the dynamics
of both partners’ relational commitments, the generic
problem of how the seller can establish and maintain a
long-lasting relationship with the buyer over a planning
period can be stated formally by the following optimal
control problem:
 Max ∞ e − rt ( f ( x , x ) − C(u)) dt
s
b
∫0
u


s. t.

 x b = −β b x b + θ b x s + α b u, x b ( 0) = 0 .
 x = −β x + θ x + α u, x ( 0) = 0
s s
s b
s
s
 s
x b ≥ 0 and x s ≥ 0


(3)
In problem (3), 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. Higher values of r
mean that the seller is shortsighted and discounts heavily
future relational utility, which may be the attainment of
any combination of financial goals, marketing goals, strategic goals, operational goals, and organizational goals
through a relational exchange with a buyer.
For simplicity we assume that the relationship benefits
function ƒ is a linear combination of both relational commitments, that is,
ƒ(xb, xs) = cb x b + csxs,
(4)
where cb = cb (t) and cs = cs (t) are nonnegative time-variant
parameters denoting, respectively, the contribution of
each partner’s commitment into the seller’s relational benefits. Note that the linear separable function specification
in (4) does not account for situations where the joint effect
of the two partners’ commitments increases or decreases
the seller’s relational benefits. Although such a general
specification is possible by adding a third multiplicative
term involving the two commitments into the right-hand
side of (4), it adds nontrivial mathematical intricacies to
the problem.
The utility function in (4) can be used, for example, in
finding an optimal relational marketing policy that maximizes the profit earned from a customer over the entire
period of a relational exchange. This is similar to maximizing the lifetime value of the customer, which can be defined as the profit generated from an individual customer
over time (see Berger, Weinberg, and Hanna 2003; Gupta
and Lehmann 2003; Jain and Singh 2002). In this context,
the parameters cb and cs of the seller’s relational benefits in
(4) could respectively be considered as the conversion rate
of the buyer’s commitment to gross margin and the efficiency gain (e.g., transaction cost reduction) generated
due to the seller’s own commitment.
As is common in the marketing literature, the impact of
marketing efforts has the property of decreasing returns.
The study of Hibbard et al. (2001) also supports this property in the context of relational marketing activities. With
this in mind, again for simplicity, we consider the following specification for seller’s relational marketing effort
costs:
C = C(u) =
1 2
u .
2
(5)
The cost function C(u) does not take into account other
marketing cost (advertising, for example) that the seller
will support in the absence of a relational marketing program. For simplicity, we assume these costs are zero if
they do not change when the seller introduces her relational marketing program. Otherwise, in the case where
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JOURNAL OF SERVICE RESEARCH / November 2004
the relational marketing program helps reduce the other
marketing costs, as has been claimed in the literature, we
consider that it generates a gain of efficiency, which is
taken into account in (4) through the positive contribution
of the seller’s commitment into the seller’s relational benefits (see Kalwani and Narayandas 1995).
OPTIMAL POLICY
To solve problem (3) by considering (4) and (5), we use
dynamic optimization techniques (e.g., Kamien and
Schwartz 1991). We conclude with the following results.
Theorem 1 (optimal policy): Consider the relational benefits optimization problem (3)-(5). Then, the optimal relational marketing effort (spending) to
establish and maintain a relational commitment between the seller and the buyer is time-variant and
nonzero if and only if the seller and buyer commitments are positive (nonzero). In case of positive
commitments, the magnitude of this relational marketing effort depends nonlinearly on several factors,
including the contribution of each partner’s commitment into the seller’s relational benefits, the opportunistic propensity and the trust/distrust coefficients
of the two partners, the seller’s preference for future
utility, and the response of each partner to the relational marketing effort or investment. Formally, it
has the following structure:
C * (t) =
1 *
(u (t)) 2 =
2
(6)
2
α b (t)[ c b (t)( r + β s (t)) + θ s (t) c s (t)]


+ α s (t)[ c s (t)( r + β b (t)) + θ b (t) c b (t)]
1
.

2  (β b (t) + r)(β s (t) + r) − θ b (t)θ s (t)




0 ≤ t ≤ ∞.
Proof: See appendix.
The optimal decision rule in (6) is very appealing and
requires that the seller should make real-time relational
marketing decisions based on the current values of the
model parameters. Practically, this means that, at any time
t, the seller should assess the state of the relationship between herself and the buyer and adjust her relational marketing effort in view of that assessment. The optimal
decision rule in (6) reveals that the seller’s investment in
relationship marketing at any time t should be high if the
two exchange partners mutually maintain high levels of
trust and value this type of investment in building and
maintaining their commitment. In addition, the seller
should allocate heavy resources to building and maintaining relational commitments if she is farsighted and receives bigger contributions to her relational benefits from
the buyer’s and her own commitments. As expected, in a
context characterized by high opportunistic propensities
or distrust either from the seller herself or from the buyer,
the seller should allocate minor resources to relational
marketing efforts.
The special form of the optimal control rule (6) leads to
the following important result.
Theorem 2: Consider the relational benefits optimization
problem (3)-(5). Then the optimal relational marketing effort (spending) that establishes and maintains
relational commitments between the seller and the
buyer is constant over time if and only if the opportunistic propensities, the trust/distrust coefficients
of the two partners, the response of each partner to
the relational marketing effort, and the contribution
of each partner’s commitment into the seller’s
relational benefits, are all time-invariant.
Proof: See appendix.
As stated earlier, the case of time-invariant parameters
described in Theorem 2 is more likely to occur when the
structural and contextual environment of the relationship
remains unchanged and the two exchange partners are
conservative. In such a context, establishing and maintaining a relational commitment with the buyer requires the
same level of marketing effort for the seller at any time.
Several loyalty programs in consumer markets that, according to some scholars, create commitment to incentives
(marketing effort) rather than commitment to the seller fall
into this category (e.g., Barnes 1994).
Note that substituting (6) into (2) leads to a nonhomogeneous system of differential equations with time-variant
coefficients that can be solved analytically to obtain the
optimal commitment trajectories, xb(t) and xs(t) (see Boyce
and Diprima 1986, p. 387).
Considering the optimal policy (6), we obtain the following results.
Proposition 1: The seller’s relational marketing effort increases (decreases) with an increase (decrease) over
time of trust between the two partners, the effectiveness of the relational marketing program on the partners’ commitments, and the partner’s contributions
to the seller’s relational benefits. On the other hand,
it decreases (increases) with an increase (decrease)
over time of opportunistic propensities of the two
partners.
Proof: See appendix.
Fruchter, Sigué / RELATIONAL EXCHANGES 149
Although we have treated trust/distrust, opportunity propensity, the effectiveness of the seller’s relational marketing, and the relational benefit contributions as exogenous
factors to our model, Proposition 1 reveals that in case they
change over time, the seller’s relational marketing efforts
will necessarily change to reflect the current situation. To
improve the seller’s relational benefits over time, other actions different from relational marketing efforts studied in
our model should be planned to increase trust, the effectiveness of the seller’s relational marketing effort, and the
relational benefit contributions of the two exchange partners, as well as to decrease opportunistic propensities and
distrust over time.
TYPICAL BEHAVIORAL SITUATIONS
We can get better insights into the optimal policy by examining special cases that reflect typical behavioral situations encountered in the marketing literature.
Trust/Distrust Effects
We first focus on the effects of the two partners’ trust/
distrust on their relational commitment. For this purpose,
let us examine some hypothetical cases by assuming that
both partners experience equal opportunistic propensities,
value identically the seller’s marketing effort in building
their commitment, and that their contributions to the
seller’s relational benefits are the same over time. In other
words, we have the following relationships between the
parameters of our model:
β b (t) = β s (t) (opportunistic propensity coefficients)  (7)

α b (t) = α s (t) (effectiveness of marketing efforts)  .
c b (t) = c s (t) (commitment contribution coefficients)
Keeping all other parameters symmetric as in (7), we want
to analyze three trust scenarios: mutual trust over time
(θb(t) = θs(t) > 0), trust-distrust over time (Sign [θbθs] = –1),
when the seller is the trusting partner, whereas the buyer is
the distrusting partner, thus θb(t) < 0 and θs(t) > 0 and finally asymmetric-trust over time (with the seller holding a
higher level of trust, θs(t) > θb(t) > 0).
Considering Theorem 1, we have the following results
for these scenarios.
Proposition 2 (trust effects): Assume (7). Then over time:
a. The levels of commitment of both the buyer and
seller in a mutual trust scenario are equal.
b. The seller’s marketing effort in a trust-distrust scenario is lower than the marketing effort for mutual trust.
In the long run (steady state):
c. The levels of commitment of a trust-distrust scenario are lower than the levels of commitment of
a mutual trust scenario.
d. In a trust-distrust scenario, the level of commitment
of the seller is higher than that of the buyer.
e. If the seller trusts the buyer more, then the level of
commitment of the seller is higher than that of the
buyer.
Proof: See appendix.
Proposition 2 highlights several important effects of trust
on the levels of commitment and on the seller’s marketing
effort. In item (a), mutual and symmetric trusting partners
holding positive expectations of their partner’s commitment develop equal levels of commitment over time. In the
longer term, however, the levels of commitment of mutually symmetric trusting partners prevail over those of trustdistrusting partners (item c). This result can be explained
by the fact that the seller in a mutually symmetric trusting
scenario invests more in relational marketing than in the
opposite situation (item b). From item (b), it can also be
said that the lack of reciprocity between the two exchange
partners prevents the seller from allocating heavy resources to relational marketing programs (Bagozzi 1995).
From items (d) and (e), whether with a trust-distrust scenario or a mutual asymmetric trust scenario, the more
trusting party, here the seller, maintains a higher level of
commitment than the less trusting, the buyer.
Opportunism Effects
Now let us focus on the opportunistic propensity of the
partners. To this end, we assume that both partners experience the same level of trust, value identically the seller’s
marketing effort in building their commitment, and that
the two partners’ contributions to the seller’s relational
benefits are the same. In other words, we have the following relationships between the model parameters:
θ b (t) = θ s (t) ( trust / distrust coefficients)
(8)

α b (t) = α s (t) (effectiveness of marketing efforts)  .
c b (t) = c s (t) (commitment contribution coefficients)
We analyze a scenario when the buyer (seller) is more
opportunistic than the seller (buyer), that is, βb(t) > βs(t)
(βs(t) > βb(t)). Considering (8) and again Theorem 1, we
have the following results.
Proposition 3 (opportunistic behavior effects): Assume
(8). Then in the long run (steady state), if the buyer is
more (less) opportunistic than the seller, then the
level of commitment of the buyer is lower (higher)
than that of the seller.
150
JOURNAL OF SERVICE RESEARCH / November 2004
Proof: See appendix.
The effects of opportunistic behavior on the levels of commitment of the two partners are straightforward. The partner with the higher opportunistic propensity commits less
than the other. This result is consistent with the relationship marketing literature, which considers opportunistic
behavior as a detrimental factor for commitment.
CONCLUSION AND DISCUSSION
This research studied how a seller can manage an optimal intertemporal marketing program that maintains
long-term relational commitments with a buyer and maximizes utility. Our main message is that the problem of
establishing and maintaining relational exchange can be
studied using the methodology of optimal control. This
approach is possible in those applications of relationship
marketing in consumer markets in which the seller designs a marketing program to gain the commitment of the
buyer. It may also be possible in the service industry and
some business-to-business exchanges where the seller
undertakes investments for the relationship and the buyer
does not.
Contributions
Building on a well-known modeling approach used in
applied mathematics for love dynamics and on the behavioral marketing literature, we developed an analytic model
of two-partner relational commitments. We postulated that
the success of relational exchanges could be measured
through the partners’ commitments, which are the source
of relational benefits. Our model specification assumes
that the partners’ relational commitments are driven by the
trust/distrust component, the opportunism component,
and the seller’s relational marketing effort. In this context,
we wish to show how the seller should determine her optimal marketing effort to build and maintain fruitful relational commitments with a buyer. This research extends
the emerging paradigm of relationship marketing and customer relationship management, which has focused on relational behavior and the study of the effectiveness of
relational marketing instruments with little attention to
decision making or has indirectly addressed decisionmaking issues without the formal approach of optimal
control (e.g., Berry 1995; De Wulf, Odekerken-Schröder,
and Iacobucci 2001; Dwyer, Schurr, and Oh 1987;
Hibbard et al. 2001; Morgan and Hunt 1994; Sigué and
Elloumi 2002; Verhoef 2003).
Our main finding supports the view that an optimal
control rule for building and maintaining long-term relational commitments that maximize the seller’s discounted
utility consists of a time-variant relational marketing program. At any time, the seller’s relational marketing effort
depends nonlinearly on the current value of several parameters, including the contribution of each partner’s commitment to the seller’s relational benefits, the opportunistic
propensity and trust/distrust coefficients of the two partners, the seller’s preference for future utility, and the effectiveness of the seller’s relational marketing effort in
building her own and the buyer’s commitments. In particular, the seller’s relational marketing effort increases (decreases) with an increase (decrease) over time of the trust
between the two partners, the effectiveness of the relational marketing program on the partners’ commitments,
and the partners’ contributions to the seller’s relational
benefits. On the other hand, it decreases (increases) with
an increase (decrease) over time of opportunistic propensities and distrust of the two partners.
We believe that this type of real-time relational marketing program applies to relational exchanges involving
more personal interactions, continuous changes in the
structural and contextual relational environment, and a variety of relational marketing instruments, as in the context
of the service industry. These require that the seller constantly listen and scrutinize the requirements and behavior
of customers and adjust her relational marketing activities
as a result. Our findings also apply to what we have called
conservative partners or partners involved in a stable relationship where the parameters affecting the dynamics of
their commitment do not change over time. It is our belief
that this is the case in several reward-based loyalty programs in consumer markets in which the main driver of a
consumer’s commitment is the reward itself (Barnes
1994). On the other hand, the seller’s relational marketing
is standard for many consumers and does not need a continuous adjustment to the situation of a particular consumer (De Wulf, Odekerken-Schröder, and Iacobucci
2001).
Since the work by Moorman, Zaltman, and Deshpandé
(1992), followed by the replication of Grayson and Ambler (1999), the effectiveness of long-term relationship
marketing over time has been questioned. Recently, Hibbard et al. (2001) concluded that although relational commitment and other components of relationship marketing
continue to have a positive effect on the performance of
exchange partners, this positive effect diminishes over
time. Hibbard and colleagues (2001) then suggested that
managers should recognize that there is a downside to using relational marketing strategy and consequently, identify the true costs of the inputs necessary for maintaining
successful and mutually beneficial relational exchanges.
Our generic model supports this view and demonstrates
that the determination of an optimal relational marketing
program over time should be based on a continuous costbenefit analysis. In addition, it should also integrate rele-
Fruchter, Sigué / RELATIONAL EXCHANGES 151
vant evaluation over time of the partners’ opportunism,
trust/distrust, and response to the marketing efforts that
have been proved to be critical in the relationship marketing literature (e.g., Dwyer, Schurr, and Oh 1987;
Gundlach, Achrol, and Mentzer 1995; Morgan and Hunt
1994). As a matter of fact, our analysis of typical behavioral situations in Propositions 2 and 3 support the relationship marketing theory that trust and opportunistic
behavior are respectively beneficial and detrimental both
for the seller’s relational marketing effort and the two
partners’ relational commitments.
Last, our model offers a general framework for understanding and managing relational exchanges. For example, an increase of relational commitment over time may
not be useful for the seller if, at the same time, either her
own commitment contribution or the contribution of the
buyer’s commitment to her relational benefit decreases
significantly over time. According to Kalwani and
Narayandas (1995), this is more likely to occur if, in the
longer term, the buyer becomes more sensible to the economic value of the seller’s offer and strives to share equitably relational benefits or serving the buyer becomes very
costly for the seller. On the other hand, heavy investments
in relationship marketing efforts may be useless if they
provide no significant value to the buyer to justify his commitment or, at the same time, occur in the context of opportunistic behavior and distrust, especially from the buyer.
As a consequence, our findings support that the seller
should continuously assess the effectiveness of her relationship marketing programs. As recent studies have
shown, not all relational marketing instruments are effective in building relational commitment with all consumers
(De Wulf, Odekerken-Schröder, and Iacobucci 2001;
Verhoef 2003). The use of ineffective instruments should
not lead to the questioning of the theory of relationship
marketing. Also, even with effective instruments that fit
into the first two levels of relationship marketing according to Berry’s (1995) classification, we believe that the
seller may need additional actions either to reduce opportunistic behavior or to increase/decrease trust/distrust.
Therefore, assessing the effectiveness of relational marketing efforts on the buyer’s commitment should also pay
attention to the structural and contextual environment of
the relationship. The importance of the structural and contextual environment of relationships is well recognized in
the literature. For example, a study by Wathne, Biong, and
Heide (2001) downplays the role of interpersonal relationships—second level of relationship marketing in Berry’s
(1995) classification—in the context of business-tobusiness services, and shows that switching barriers and
traditional marketing variables (price and product
breadth) play a significant role in the buyer’s choice of a
supplier. The authors then conclude that “a customer’s role
as friend may assume less importance in the presence of
explicit competitive offers” (Wathne, Biong, and Heide
2001, p. 62). The same thing can easily be said for
relational marketing programs based on some economic
rewards.
Limitations and Future Research
We deliberately made our theoretical approach simple
in order to allow for analytic insights. Some of our assumptions can be relaxed. First, we have assumed a linear
additive separable function for the seller’s relational benefit. This assumption allows a degenerate feedback solution, which does not depend on the relational commitments. Although more advanced specifications of the
seller’s relational benefit function should be considered
for future extensions, in many cases, however, their tractability might be a cumbersome task. Second, our current
model assumes an unbalanced relationship between the
two exchange partners wherein the seller is the only party
investing in the relational exchange. We acknowledge that
this unbalance could be either in the buyer’s favor when a
product is being sold (e.g., Kalwani and Naraynadas 1995)
or in the seller’s favor when a service is being sold (e.g.,
Kumar 1999). Also, in many business-to-business cases
this assumption does not hold. Both the seller and the
buyer often invest in the relational exchange to enhance
their mutual commitments. Third, our model does not take
competition into account. In the real world, competitors
often duplicate relational marketing programs to reduce
their competitive power. Relational marketing programs
such as recommended here could then be ineffective in the
face of so-called me-too relational marketing programs.
Third, even using our approach, it seems worthwhile to attempt to modify the commitment dynamics to generate
more complex relational marketing programs. The authors
are actively working in this direction.
APPENDIX
Proof of Theorem 1
Consider the optimal control problem (3) with the assumption in (1). The current-value Hamiltonian is given by
H(xb, xs, u, λb, λs) = ƒ(xb, xs) – C(u)
+ λb(–βxb + θb xs + αb u) + λs(–βs xs + θs xb + αs u)
+ µb xb + µs xs,
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, re(continued)
152
JOURNAL OF SERVICE RESEARCH / November 2004
APPENDIX (continued)
spectively, 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
cb ( t )(r + β s ( t )) + θ s ( t )c s ( t )
.
− (β b ( t ) + tr )(β s ( t ) + r ) + θ b ( t )θ s ( t )
(A8b)
Substituting (A8a-A8b) into (A5) leads to (6).
If xb = xs = 0, then from (2) we obtain u = 0. On the other hand,
if u = 0, the system (2) becomes a homogeneous system of differential equations with constant coefficients. Thus, if the initial solution is zero, so are the solutions, that is, xb = 0 and xs = 0. 䊐
The necessary optimality condition is given by
∂H
= − C ′( u) + λ b α b + λ sα s = 0;
∂u
λ b ( t) = −
(A1)
Proof of Theorem 2
∂H
= rλ b − fx b + β b λ b − θ s λ s − µ b
λ b = rλ b −
∂x b
(A2)
This follows directly from the nature of the formula in (6). If,
and only if, all the time-variant functions that compose the formula (6) will become time-invariant, then u will become timeinvariant.
䊐
∂H
= rλ s − fx s − θ b λ b + β s λ s − µ s
λ s = rλ s −
∂x s
(A3)
The adjoint equations are the following:
Proof of Proposition 1
cb (β s + r ) + c sθ s
,
(β b + r )(β s + r ) − θ b θ s
c s (β b + r ) + cb θ b
∂u / ∂α s =
(β s + r )(β b + r ) − θ b θ s
∂u / ∂α b =
and the boundary conditions are
lim λ b e − rt = 0 and lim λ s e − rt = 0.
t→ ∞
The proposition follows by taking the derivative of u with the
respective variable:
t→ ∞
(A4)
Considering (5) and (A1), the optimal marketing effort satisfies
(A5)
u = λbαb + λsαs.
The relation in (A5) means that the optimal marketing effort to
establish and maintain mutual commitment between the two
partners is a linear combination of the net benefit (damage) of increasing by one unit the levels of commitment of the seller and of
the buyer, and the reactiveness of both partners to the seller’s
marketing effort.
If xb > 0 and xs > 0, then substituting (4) into (A2)-(A4)
leads to
λ b = (r + β b )λ b − θ s λ s − cb ,
lim λ b e − rt = 0
t→ ∞
[α b (β s + r ) + α sθ b ][ cb (β s + r ) + c sθ s ]
,
[(β b + r )(β s + r ) − θ b θ s ]2
[α (β + r ) + α b θ s ][ c s (β b + r ) + cb θ b ]
∂u / ∂β s = − s b
[(β b + r )(β s + r ) − θ b θ s ]2
∂u / ∂β b = −
[α s (β b + r ) + α b θ s ][ cb (β s + r ) + c sθ s ]
,
[(β b + r )(β s + r ) − θ b θ s ]2
[α (β + r ) + α sθ b ][ c s (β b + r ) + cb θ b ]
∂u / ∂θ s = b s
[(β b + r )(β s + r ) − θ b θ s ]2
∂u / ∂θ b =
(A6)
α b (β s + r ) + α sβ b
,
(β b + r )(β s + r ) − θ b θ s
α s (β b + r ) + α b θ s
.
∂u / ∂c s =
(β s + r )(β b + r ) − θ b θ s
∂u / ∂cb =
λ s = − θ b λ b + (r + β s )λ s − c s ,
lim λ s e − rt = 0.
t→ ∞
(A7)
The special boundary condition in (A6) and (A7) and the assumption that the coefficients are all bounded functions in 0 ≤ t ≤
∞, we conclude with the solution
λ s ( t) = −
and
c s ( t )(r + β b ( t )) + θ b ( t )cb ( t )
− (β b ( t ) + r )(β s ( t ) + r ) + θ b ( t ) θ s ( t )
(A8a)
䊐
Proof of Proposition 2
(a) This follows directly from the symmetry of the assumptions, the equations in (2) and the result in (6).
(b) This follows by substituting the conditions (1) and (2) into
(6) and comparing the results.
(c) In the long run, it is easy to see that
(continued)
Fruchter, Sigué / RELATIONAL EXCHANGES 153
APPENDIX (continued)
xb =
(α b β s + α s θ b )u*
and
β bβ s − θbθs
xs =
(A9)
(α s β b + α b θ s )u*
.
β bβ s − θbθs
Substituting the conditions θb < 0, θs > 0 into the expression of
(A9), it is easy to see that this leads to lower values than if we substitute the condition θb = θs > 0.
(d) This follows directly from (A9), if θs > 0 and θb < 0, then
x b < x s.
(e) If the seller is more confident than the buyer, then θs > θb.
The proposition follows by substituting θs > θb in (A9) and
comparing the results.
䊐
Proof of Proposition 3
This follows directly from the assumptions and considering
䊐
the ratio xb/xs in (A9).
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Gila E. Fruchter is a senior lecturer of marketing in 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, 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, the
Journal of Service Research, the Journal of Optimization Theory
and Application, the Journal of Economic, Dynamics and Control, the 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 serves as a referee for leading marketing
academic journals, among them Marketing Science and
Management Science.
Simon Pierre Sigué, Ph.D., HEC Montréal, is an assistant professor at Athabasca University, Canada, and honorary associate
professor in 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 articles, some of which have earned international
awards.