Managing Relational Exchanges

Transcription

1 Managing Relational Exchange Gila E. Fruchter Bar-Ilan Univerity Simon Pierre Sigué Athaaca Univerity The author propoe an analytic model that deal with oth ehavioral conideration etween exchange partner and the determination of relational marketing effort over time. On the ai of the ehavioral marketing literature, they conider three main factor that drive the level of relational commitment etween two exchange partner: the trut/ditrut component, the opportunim component, and the relational marketing effort of the eller. Incorporating thee factor in a well-known model ued in applied mathematic for love dynamic, the author claim that the iue of managing relational exchange i an optimal control prolem. Their analyi how that the eller optimal policy for determining relational marketing effort over time i either time-invariant or time-variant, depending on whether or not the exchange partner are conervative and the tructural and contextual environment of the relationhip remain unchanged over time. Keyword: relational exchange; commitment; trut; opportunim; optimal control; relational marketing effort During the pat decade, the tudy of relationhip marketing and cutomer relationhip management ha attracted the attention of everal marketing cholar (e.g., Berry 1995; Gararino and Johnon 1999; Morgan and Hunt 1994; Sheth and Parvatiyar 1995a; Verhoef 003). Increaingly, it i elieved that ucceful and lating relational exchange are thoe in which partner go eyond hort-term tranactional enefit and incorporate ehavioral factor uch a trut and commitment (e.g., Dwyer, Schurr, and Oh 1987; Gundlach, Achrol, and Mentzer 1995; Sirdehmukh, Singh, and Saol 00). Thi elief ha pervaded marketing thought uch that many cholar, epecially in Europe, are calling for a paradigm hift in marketing (e.g., Grönroo 1994; Gummeon 1997). From the eller perpective, the challenge preented y the emerging paradigm of relationhip marketing i to determine a equence of marketing deciion and ehavior capale of etalihing, developing, and maintaining ucceful relationhip with uyer (e.g., Morgan and Hunt 1994). For many cholar, it i no longer poile to focu on marketing mix a the only et of trategic marketing variale (e.g., Grönroo 1994). Given improved technologie, reource, and kill, competitor are increaingly ale to meet the quality of any offer in the market. One of the critical conequence of thi trend ha een an amplified focu on pricing and ale promotion to attract cutomer in the hort term, which, unfortunately, increae cutomer eniility to price and decreae their loyalty to rand. The fundamental idea of relationhip marketing i to go eyond hort-term tranactional marketing action and to uild loyalty to rand and eller. To accomplih thi, The author thank the participant of the INFORMS 003 Marketing Science Conference for the feedack on an earlier draft of the article. The comment provided y Roland Rut a well a two anonymou Journal of Service Reearch reviewer are greatly appreciated. Finally, the econd author thank the School of Buine, Athaaca Univerity for upport of the reearch and Janice Thieen for her ueful comment. Correpondence concerning thi article hould e addreed to Gila E. Fruchter, Graduate School of Buine Adminitration, Bar-Ilan Univerity, Ramat-Gan 5900, Irael; fax: +97 (3) ; fruchtg@mail.iu.ac.il. Journal of Service Reearch, Volume 7, No., Novemer DOI: / Sage Pulication

2 Fruchter, Sigué / RELATIONAL EXCHANGES 143 eller mut deign marketing program uch that loyal and committed cutomer receive more value than diloyal cutomer. There are numerou enefit for eller in puruing uch a paradigm, including increaed acce to market, generating repeat purchae, creating exit arrier, poitive word of mouth, and information haring (ee Anderon 1998; Berry 1995; Dwyer, Schurr, and Oh 1987; Hennig-Thurau, Gwinner, and Gremler 00; Panda 003; Saren and Tzoka 1998). Depite the intene interet in cutomer relationhip management, the growing ody of relationhip marketing and cutomer relationhip management literature till face everal challenge. For example, the critical iue of reource allocation for uilding and maintaining ucceful relational exchange ha not een fully examined. Rather, everal tudie have invetigated the link etween ehavioral antecedent and outcome of relational exchange (e.g., Andalee 1996; Hunt and Morgan 1994; Sirdehmukh, Singh, and Saol 00). On the other hand, reearcher have alo tudied the effectivene of relational marketing effort uch a direct mail, tangile reward, and preferential treatment, a well a cutomer relationhip perception on more operational management contruct, including cutomer retention rate and cutomer hare (e.g., De Wulf, Odekerken-Schröder, and Iacoucci 001; Verhoef 003). Although thee tudie have generated ignificant knowledge on the effectivene of variou relational marketing effort, their methodological approach, generally aed on urvey and aggregated panel data from cutomer, doe not explicitly addre the eller deciion-making proce. Other relevant methodological approache availale in the tranactional marketing literature that can cope with the dyadic or/and dynamic nature of relational exchange have not een extenively ued. For intance, the field of analytic modeling ha een urpriingly timid in addreing relational iue. The firt known exception i the recent ook chapter y Sigué and Elloumi (00). The author of thi chapter ue a ytem of differential equation to decrie how relational commitment are etalihed and maintained. They uild a ridge etween relationhip marketing and a well-known modeling approach ued in applied mathematic to decrie love dynamic etween two individual (e.g., Feichtinger, Jørgenen, and Novak 1999; Rinaldi 1998a, 1998; Rinaldi and Gragnani 1998). The model of love dynamic take three apect of love into account: the forgetting proce, the pleaure of eing loved, and the reaction to the appeal of the partner. Sigué and Elloumi model aume that relational commitment etween two exchange partner are driven y trut, opportunitic ehavior, and the partner appeal. However, the model remain decriptive and doe not indicate how marketing deciion are made in order to etalih and maintain relational exchange. Although a complete marketing program may well include oth tranactional and relational marketing (ee Coviello et al. 00; Hultman and Shaw 003), in thi article, we delierately focu on relational marketing action. We propoe, for the firt time, an analytic model dealing with oth ehavioral conideration etween exchange partner and the determination of relational marketing effort. Our model goe eyond the decriptive dynamic of Sigué and Elloumi and precrie an optimal way of determining relational marketing effort while eller aim at maximizing their dicounted utility. It i our thei that the prolem of etalihing and maintaining long-run relational exchange i an optimal control prolem in which the ultimate goal of the eller i to maximize her intertemporal utility. 1 We conider that the eller relational utility tem from the commitment of the two exchange partner, which are uilt y three main component: (a) the trut/ditrut component, which i the willingne/reluctance of a party to rely on the trutworthine of the other; () the opportunim component, to capture a partner own forgetfulne or failure to rememer previou commitment over time; and (c) the eller relational marketing effort, which can e either an economic reward or other ocial activitie creating ocial and pychological enefit for the uyer. Unlike the ehavioral literature of cutomer relationhip management that ha tudied the effectivene of variou relational marketing intrument, our normative approach aume that the eller i the deciion maker and ha direct control over her relational marketing effort (e.g., De Wulf, Odekerken- Schröder, and Iacoucci 001; Verhoef 003). Our main finding upport the view that the eller relational marketing effort hould increae (decreae) with any increae (decreae) over time of trut etween the two partner, the effectivene of the relational marketing program on the partner commitment, and of the partner contriution to the eller relational enefit. On the other hand, it hould decreae (increae) with any increae (decreae) over time of opportunitic propenitie and ditrut of the two partner. Our model advocate the ue of real-time relational marketing program in the context of relational exchange involving peronal interaction, continuou change in the tructural and contextual relational environment, and a variety of relational marketing intrument, a it i often the cae in the ervice indutry. But it alo applie to conervative partner involved in a tale relationhip in which the parameter affecting the dynamic of their commitment do not change over time, a in the cae of everal reward-aed loyalty program in conumer market. The ret of thi article i organized a follow. Firt, we dicu relational commitment and it driving factor. 1. Hereafter, the eller i a woman and the uyer i a man.

3 144 JOURNAL OF SERVICE RESEARCH / Novemer 004 Second, we preent our model and determine it optimal policy. Third, we conider ome typical ehavioral ituation encountered in relational exchange. In the lat ection, we conclude and dicu our finding. BUILDING A RELATIONAL COMMITMENT One of the mot critical concept of relationhip marketing i relational commitment. Many cholar hare thi view (e.g., Gararino and Johnon 1999; Gundlach, Achrol and Mentzer 1995; Morgan and Hunt 1994). For example, Morgan and Hunt (1994) conidered relational commitment a one of the two key mediating variale of relationhip marketing. Gundlach, Achrol, and Mentzer (1995) viewed commitment a an eential ingredient of ucceful long-term relationhip. With a few empirical exception, the relationhip marketing literature recognize the exitence of poitive relationhip etween commitment among partner and many favorale contruct that create relational value, uch a trut, cooperation, acquiecence, loyalty, functional conflict, communication, and atifaction (De Wulf, Odekerken-Schröder, and Iacoucci 001; Grayon and Amler 1999; Moorman, Zaltman, and Dehpandé 199; Verhoef 003). Relational commitment i generally conidered a a ehavioral outcome of fruitful interaction etween exchange partner (Dwyer, Schurr, and Oh 1987; Geyken, Steenkamp, and Kumar 1999). Following Morgan and Hunt (1994), we aume that relational commitment i an exchange partner elief that an ongoing relationhip with another i ufficiently important a to deerve maximum effort to maintain it. Committed partner are thoe who are ale to make hort-term acrifice to realize long-term enefit. Therefore, the current and future ucce of relational exchange may e evaluated through the partner relational commitment. A a forward-looking concept, commitment implie the preence and conitency over time of oth the attachment and the willingne to maintain a relationhip. Oviouly, the willingne to continue a relationhip tem from the ocial and economic enefit that each partner accumulate from it (Dwyer, Schurr, and Oh 1987; Gaenheimer, Houton, and Davi 1998). Although thi conceptualization eem very comprehenile, it i not clear how partner hould effectively uild and maintain relational commitment among them or what kind of input exchange partner hould ue to reach relational commitment. Drawing on the framework of political economy (ee Gaenheimer, Houton, and Davi 1998; Stern and Reve 1980) and the work of Gundlach, Achrol and Mentzer (1995), we claim that oth economic and ocial driver lead to relational commitment. Succeful long-term relationhip make ue of oth driver. According to Gaenheimer, Houton, and Davi (1998), the economic driver can e explained uing tranactional cot analyi (Williamon 1983). Tranactional cot analyi tree tranactional efficiency and the cot of exiting relationhip. The economic driver of commitment correpond to what Gundlach, Achrol, and Mentzer (1995) called an intrumental view of commitment. In thi cae, commitment i a calculative act in which committed partie want to improve their own economic enefit through reducing tranaction cot and to limit relational opportunim through pecific invetment. Our work orrow from thi view and addree relational invetment and the opportunim of exchange partner. We define relational invetment a marketing effort or invetment undertaken y an exchange partner to create and maintain relational commitment with another partner. The relationhip literature ditinguihe among three level of relationhip marketing activitie, including economic incentive, marketing tactic with ocial attriute, and tructural marketing olution to cutomer prolem (ee Berry 1995). The relationhip marketing theory potulate a poitive relationhip etween relational marketing invetment and commitment. For example, De Wulf, Odekerken-Schröder, and Iacoucci (001) invetigated the impact of perceived relationhip invetment on relationhip quality, including relational commitment, and found a poitive path from the firt to the latter. Note that relational marketing effort are different from traditional or tranactional marketing effort, which can generate ale at a given period ut have very little impact on the level of relational commitment. We define opportunim a an exchange partner propenity to reduce hi or her intantaneou level of commitment at any time, a hi or her previou level of commitment i high. We aume that opportunim i upported y a partner forgetfulne and unwillingne to repect commitment over time, which create inconitency etween previou commitment and the level of commitment at a pecific time. Thi inconitency i mileading for the other exchange partner who i more likely to take previou commitment a a warrant for preent and future commitment. Our conceptualization of opportunim i conitent with the concept of paive opportunim (ee Wathne and Heide 000). Opportunitic partner, purpoely or not, adopt ehavior contrary to the principle of maintaining a long-term relational exchange. Here, we conider that they are characterized y neglectful or elfih failure to rememer their commitment over time. The impact of opportunim on the relational commitment i known to e negative (Gundlach, Achrol, and Mentzer 1995; Rokkan, Heide, and Wathne 003).

4 Fruchter, Sigué / RELATIONAL EXCHANGES 145 The ocial driver of relational commitment come from ocial exchange theory, which argue that partie evaluate relationhip within a ehavioral context (Gaenheimer, Houton, and Davi 1998). In thi cae, commitment i perceived a an attitudinal outcome, which can e decried in term of pychological attachment, identification, and value congruence (Gundlach, Achrol, and Mentzer 1995). Thi attitudinal view of commitment ha een predominant in the marketing literature (e.g., Doney and Cannon 1997; Gararino and Johnon 1999; Sirdehmukh, Singh, and Saol 00). It aociate commitment with prominent ehavioral contruct uch a atifaction and trut. In a recent meta-analyi, Geyken, Steenkamp, and Kumar (1999) found that the poitive relationhip etween trut and commitment i unanimou. Therefore, in a relationhip where there i mutual trut, it i more likely that partner hold higher level of commitment. Converely, mutual ditrut can prevent partie from committing to a relationhip. We aume that trut (ditrut) i a ignificant input to uilding long-term relational commitment. We define trut/ditrut a the willingne/ reluctance of a party to rely on the trutworthine of the other in uilding up it own commitment. Thi definition i conitent with other definition in the literature focuing on cognitive and ehavioral perpective of trut (e.g., Andalee 1996; Anderon and Naru 1990). Finally, we treat economic and ocial driver a additive and eparale force that contriute to relational commitment. Thi conceptualization allow compenation etween the two type of driver. Lack of trut may e alanced y relational marketing invetment and till lead to higher relational commitment. At the ame time, trut may help to overcome ome economic and ocial invetment deficiencie to higher relational commitment. THE MODEL The Dynamic of Commitment We conider a eller who want to uild a long-term relational exchange with a uyer. Let x x (t) and x x (t) e tate variale that, repectively, meaure the level of commitment in the relational exchange of the eller and the uyer at time t. The eller commitment tranlate to the willingne of the eller to tay in the relationhip with the uyer, which, in turn, lead to relational marketing invetment, or the improvement of the relational value offered to the uyer. The uyer commitment lead to loyalty or dicernile repeat purchaing or uying ehavior, facilitate communication, and generate poitive word of mouth (ee Morgan and Hunt 1994; Verhoef 003). There i a reciprocal relational indifference when the value of x and x are zero. Thi will appear when the partner have no interet in taying in a relational exchange. Otherwie, if the two partner are in a relational exchange, their repective commitment i poitive. Thu, we aume x i 0, i {, }. (1) We ue two premie to model relational commitment. One i that the relational commitment etween the eller and the uyer i unalanced. The other i that the eller manage the etalihment of the relational exchange with the uyer. Thee two premie are related and are common in many application of relationhip marketing in conumer market (ee Blatterg and Deighton 1991; De Wulf, Odekerken-Schröder, and Iacoucci 001; Gruen 1995; O Malley and Tynan 000). The firt premie claim that the eller ha more interet in etalihing and maintaining a long-term relational commitment than the uyer. A a conequence, the econd premie give an active role to the eller in the relational exchange, wherea the uyer play a reactive role. Stated differently, the eller i the peron who offer omething of value to the uyer or undertake ome idioyncratic invetment for the relationhip. Thi econd premie i implicit in the growing literature of cutomer relationhip management (ee Berry 1995; Parvatiyar and Sheth 001; Sheth and Parvatiyar 1995a). Let u u(t) e a control variale that repreent the eller relationhip marketing effort at time t. The variale u(t) can e any relationhip marketing activity fitting into Berry (1995) firt two level of relationhip marketing. According to Berry (1995), the firt level relie on economic incentive or offer tangile reward over time to develop and maintain relationhip. The econd level of relationhip marketing focue on ocial apect of a relationhip and offer ocial and pychological enefit to cutomer (ee Panda 003). We aume that whether the eller marketing effort, u(t), create economic value or ocial and pychological enefit for the uyer, it increae the eller own commitment to the relationhip. Thi pecification i conitent with Gundlach, Achrol, and Mentzer (1995) view that commitment poee an input or intrumental component. The eller marketing effort i modeled a an input for uilding up the commitment of the uyer a well a a onding mechanim for the eller herelf. Aume that the level of commitment of the two exchange partner evolve according to the following dynamic:

5 146 JOURNAL OF SERVICE RESEARCH / Novemer 004 x i βixi + θix j + αiu, xi( 0) 0, i j and i, j {, }, where α i α i (t) >0,β i β i (t) >0,θ θ i (td) are timevariant and ounded function in the interval 0 t. The pecification in () aume that the change in partner i level of relational commitment can e conidered a an additive eparale function of three term. The firt term, β i x i, repreent the opportunitic ehavior of partner i, where β i (called the opportunitic propenity coefficient), meaure the honet forgetfulne and neglectful or elfih failure to rememer commitment of partner i over time. The opportunitic propenity coefficient depend on the partner own peronality, value ytem, and care, a well a on the tructural and contextual environment of the exchange. For example, a relational marketing program occurring in a context where oth partie hare trong norm of olidarity i likely to evolve with low opportunitic propenitie from oth ide (Gundlach, Achrol, and Mentzer 1995; Rokkan, Heide, and Wathne 003). Alo, diproportionate tructural invetment etween the two partner can lead to higher opportunitic propenity from the le involved partner (Gundlach, Achrol, and Mentzer 1995). Although uch tructural invetment can alo e conidered a relationhip marketing (Level 3 of relationhip marketing in Berry claification), we conider here that they are exogenou and indirectly affect the commitment of the partner through their opportunitic propenity. The econd term, θ i x j, i a reaction function of partner i to partner j commitment. Parameter θ i capture partner i level of trut/ditrut over time. A poitive θ i mean that partner i trut partner j and relie on partner j trutworthine. A negative θ i indicate that partner i ditrut partner j and doe not rely on partner j trutworthine. Finally, partner i i trut-indifferent to partner j when θ i 0. Our pecification aume that exogenou factor to the model influence the level of trut/ditrut etween the two exchange partner. The literature identifie everal antecedent of trut, including relationhip termination cot, hared value, communication, and opportunitic ehavior that can influence the trut/ditrut etween the two partner (e.g., Geyken, Steenkamp, and Kumar 1999; Morgan and Hunt 1994). According to our model pecification, a truting partner will increae hi or her intantaneou level of commitment a the commitment of hi or her partner increae. Thi tem from the application of the principle of reciprocity that foter poitive relational exchange (Bagozzi 1995; De Wulf, Odekerken-Schröder, and Iacoucci 001). Converely, a ditruting partner will decreae hi or her intantaneou level of commitment a the commitment of hi or her partner increae. For the () firt cae, the partner commitment i deired; for the latter, it i not welcomed. In the latter cae, many reearcher have recognized the exitence of cenario in which the eller wihe for a long-term relationhip, wherea the uyer doe not (ee Barne 1994; Berry 1995; Sheth and Parvatiyar 1995). The third term, α i u, repreent the impact of the eller relational marketing effort on her own and the uyer level of commitment at time t. The parameter α i repreent the effectivene of the eller relational marketing effort on partner i commitment. In a imilar pecification, Sigué and Elloumi (00) called the third term the intrinic exchange enefit and conidered it a a ujective concept capturing the appeal of partner i to partner j. In addition, they aumed time-invariant parameter and did not treat the appeal a an outcome of purpoeful marketing deciion. In our pecification, α could e conidered a the effectivene of the eller marketing effort in uilding and maintaining the uyer commitment or the level of interet of the uyer to the eller relational marketing effort over time. There i empirical evidence that α change with the nature of the eller relationhip marketing activitie and the uyer characteritic (ee De Wulf, Odekerken-Schröder, and Iacoucci 001; Verhoef 003). On the other ide, α indicate the effectivene of the relational marketing effort on the eller own commitment over time. Several factor may influence thi effectivene, including the value of the uyer and the cot of deigning and implementing the program. Therefore, we potulate that a relational marketing program that ha a high value for the eller and meet the interet of the uyer will generate higher level of commitment from oth ide. We aume in () that, at the tarting point, the two relational partner level of commitment are zero. Thi aumption allow u to determine what level of marketing effort i needed to tart a relational exchange. Note that our aumption of time-variale parameter in () mean that, at any time of the relationhip, every exchange partner actively creen availale data to determine the current value of opportunitic propenity, trut/ ditrut, and the effectivene of the eller relational marketing effort in uilding relational commitment. Thi pecification include, of coure, the particular cae of time-invariant parameter in () that may occur if the exchange partner do not change their opportunitic propenity, trut/ditrut, and interet for the eller relationhip marketing program. We refer to thee type of relational partner a conervative partner. Conervative partner favor relational taility and are more likely to remain committed a long a the initial condition that led to their original commitment do not change. Prior to their commitment, they have hearay evidence on their partner trutworthine, opportunitic propenity, and repone to

6 Fruchter, Sigué / RELATIONAL EXCHANGES 147 relational invetment on which they rely during the time their relational exchange lat (ee Palmer 000). Thi i particularly true ecaue trut aout a partner may e uilt through market intelligence, a it i often the cae for onetime tranaction uch a uying a houe (Parvatiyar and Sheth 001). The Seller Prolem Our goal in thi tudy i to invetigate how a eller can manage (etalih and maintain) a long-lating relationhip with the uyer. Specifically, auming the impact of relational marketing effort, u, depend on her economic and pychological effort, our ojective i to determine how the eller hould chooe u in order to maximize her utility from the relational commitment over time. We have two aumption here. Firt, we uppoe that relational enefit may go eyond ale and profit and incorporate everal other dimenion for the eller. A a matter of fact, thi i conitent with the view of Parvatiyar and Sheth (001) that, although the overall purpoe of a relational marketing program i to increae marketing productivity and enhance mutual value for the partner, the eller can pecify her relational enefit (ojective) in term of financial goal, marketing goal, trategic goal, operational goal, and organizational goal. We pecify the eller relational enefit a a function of oth relational commitment, ƒ(x, x ). Note ƒ(x, x ) i a function that tranform the two partner commitment into relational enefit for the eller. Second, a mentioned, the eller upport cot for undertaking relational marketing effort with a uyer that, according to Hiard et al. (001), encompa economic, pychological, and opportunity cot involved from forgone alternative. We aume thee cot can e tranlated to a ingle unit (e.g., monetary term) and repreented a follow: C C(u). Conidering the aove aumption, and the dynamic of oth partner relational commitment, the generic prolem of how the eller can etalih and maintain a long-lating relationhip with the uyer over a planning period can e tated formally y the following optimal control prolem: rt Max e f x x C u dt u ( (, ) ( )) 0 t.. x βx + θx + α u, x ( 0) 0. x βx + θx + αu, x( 0) 0 x 0 and x 0 (3) In prolem (3), r denote the eller contant and poitive dicount rate, which can alo e conidered a the eller rate of time preference for future utility. Higher value of r mean that the eller i hortighted and dicount heavily future relational utility, which may e the attainment of any comination of financial goal, marketing goal, trategic goal, operational goal, and organizational goal through a relational exchange with a uyer. For implicity we aume that the relationhip enefit function ƒ i a linear comination of oth relational commitment, that i, ƒ(x, x ) c x + c x, (4) where c c (t) and c c (t) are nonnegative time-variant parameter denoting, repectively, the contriution of each partner commitment into the eller relational enefit. Note that the linear eparale function pecification in (4) doe not account for ituation where the joint effect of the two partner commitment increae or decreae the eller relational enefit. Although uch a general pecification i poile y adding a third multiplicative term involving the two commitment into the right-hand ide of (4), it add nontrivial mathematical intricacie to the prolem. The utility function in (4) can e ued, for example, in finding an optimal relational marketing policy that maximize the profit earned from a cutomer over the entire period of a relational exchange. Thi i imilar to maximizing the lifetime value of the cutomer, which can e defined a the profit generated from an individual cutomer over time (ee Berger, Weinerg, and Hanna 003; Gupta and Lehmann 003; Jain and Singh 00). In thi context, the parameter c and c of the eller relational enefit in (4) could repectively e conidered a the converion rate of the uyer commitment to gro margin and the efficiency gain (e.g., tranaction cot reduction) generated due to the eller own commitment. A i common in the marketing literature, the impact of marketing effort ha the property of decreaing return. The tudy of Hiard et al. (001) alo upport thi property in the context of relational marketing activitie. With thi in mind, again for implicity, we conider the following pecification for eller relational marketing effort cot: 1 C C() u u. (5) The cot function C(u) doe not take into account other marketing cot (advertiing, for example) that the eller will upport in the aence of a relational marketing program. For implicity, we aume thee cot are zero if they do not change when the eller introduce her relational marketing program. Otherwie, in the cae where

7 148 JOURNAL OF SERVICE RESEARCH / Novemer 004 the relational marketing program help reduce the other marketing cot, a ha een claimed in the literature, we conider that it generate a gain of efficiency, which i taken into account in (4) through the poitive contriution of the eller commitment into the eller relational enefit (ee Kalwani and Narayanda 1995). OPTIMAL POLICY To olve prolem (3) y conidering (4) and (5), we ue dynamic optimization technique (e.g., Kamien and Schwartz 1991). We conclude with the following reult. Theorem 1 (optimal policy): Conider the relational enefit optimization prolem (3)-(5). Then, the optimal relational marketing effort (pending) to etalih and maintain a relational commitment etween the eller and the uyer i time-variant and nonzero if and only if the eller and uyer commitment are poitive (nonzero). In cae of poitive commitment, the magnitude of thi relational marketing effort depend nonlinearly on everal factor, including the contriution of each partner commitment into the eller relational enefit, the opportunitic propenity and the trut/ditrut coefficient of the two partner, the eller preference for future utility, and the repone of each partner to the relational marketing effort or invetment. Formally, it ha the following tructure: * 1 * C () t ( u ()) t (6) α()[ t c()( t r+ β()) t + θ () t c() t ] 1 + α( t)[ c( t)( r+ β( t)) + θ( t) c( t)]. ( β ( t) + r)( β ( t) + r) θ ( t) θ ( t) 0 t. Proof: See appendix. The optimal deciion rule in (6) i very appealing and require that the eller hould make real-time relational marketing deciion aed on the current value of the model parameter. Practically, thi mean that, at any time t, the eller hould ae the tate of the relationhip etween herelf and the uyer and adjut her relational marketing effort in view of that aement. The optimal deciion rule in (6) reveal that the eller invetment in relationhip marketing at any time t hould e high if the two exchange partner mutually maintain high level of trut and value thi type of invetment in uilding and maintaining their commitment. In addition, the eller hould allocate heavy reource to uilding and maintaining relational commitment if he i farighted and receive igger contriution to her relational enefit from the uyer and her own commitment. A expected, in a context characterized y high opportunitic propenitie or ditrut either from the eller herelf or from the uyer, the eller hould allocate minor reource to relational marketing effort. The pecial form of the optimal control rule (6) lead to the following important reult. Theorem : Conider the relational enefit optimization prolem (3)-(5). Then the optimal relational marketing effort (pending) that etalihe and maintain relational commitment etween the eller and the uyer i contant over time if and only if the opportunitic propenitie, the trut/ditrut coefficient of the two partner, the repone of each partner to the relational marketing effort, and the contriution of each partner commitment into the eller relational enefit, are all time-invariant. Proof: See appendix. A tated earlier, the cae of time-invariant parameter decried in Theorem i more likely to occur when the tructural and contextual environment of the relationhip remain unchanged and the two exchange partner are conervative. In uch a context, etalihing and maintaining a relational commitment with the uyer require the ame level of marketing effort for the eller at any time. Several loyalty program in conumer market that, according to ome cholar, create commitment to incentive (marketing effort) rather than commitment to the eller fall into thi category (e.g., Barne 1994). Note that utituting (6) into () lead to a nonhomogeneou ytem of differential equation with time-variant coefficient that can e olved analytically to otain the optimal commitment trajectorie, x (t) and x (t) (ee Boyce and Diprima 1986, p. 387). Conidering the optimal policy (6), we otain the following reult. Propoition 1: The eller relational marketing effort increae (decreae) with an increae (decreae) over time of trut etween the two partner, the effectivene of the relational marketing program on the partner commitment, and the partner contriution to the eller relational enefit. On the other hand, it decreae (increae) with an increae (decreae) over time of opportunitic propenitie of the two partner. Proof: See appendix.

8 Fruchter, Sigué / RELATIONAL EXCHANGES 149 Although we have treated trut/ditrut, opportunity propenity, the effectivene of the eller relational marketing, and the relational enefit contriution a exogenou factor to our model, Propoition 1 reveal that in cae they change over time, the eller relational marketing effort will necearily change to reflect the current ituation. To improve the eller relational enefit over time, other action different from relational marketing effort tudied in our model hould e planned to increae trut, the effectivene of the eller relational marketing effort, and the relational enefit contriution of the two exchange partner, a well a to decreae opportunitic propenitie and ditrut over time. TYPICAL BEHAVIORAL SITUATIONS We can get etter inight into the optimal policy y examining pecial cae that reflect typical ehavioral ituation encountered in the marketing literature. Trut/Ditrut Effect We firt focu on the effect of the two partner trut/ ditrut on their relational commitment. For thi purpoe, let u examine ome hypothetical cae y auming that oth partner experience equal opportunitic propenitie, value identically the eller marketing effort in uilding their commitment, and that their contriution to the eller relational enefit are the ame over time. In other word, we have the following relationhip etween the parameter of our model: β () t β () t (opportunitic propenity coefficient) (7) α () t α () t (effectivene of marketing effort). c ( t) c ( t) (commitment contriution coefficient) Keeping all other parameter ymmetric a in (7), we want to analyze three trut cenario: mutual trut over time (θ (t)θ (t) > 0), trut-ditrut over time (Sign [θ θ ] 1), when the eller i the truting partner, wherea the uyer i the ditruting partner, thu θ (t) < 0 and θ (t) > 0 and finally aymmetric-trut over time (with the eller holding a higher level of trut, θ (t) > θ (t) > 0). Conidering Theorem 1, we have the following reult for thee cenario. Propoition (trut effect): Aume (7). Then over time: a. The level of commitment of oth the uyer and eller in a mutual trut cenario are equal.. The eller marketing effort in a trut-ditrut cenario i lower than the marketing effort for mutual trut. In the long run (teady tate): c. The level of commitment of a trut-ditrut cenario are lower than the level of commitment of a mutual trut cenario. d. In a trut-ditrut cenario, the level of commitment of the eller i higher than that of the uyer. e. If the eller trut the uyer more, then the level of commitment of the eller i higher than that of the uyer. Proof: See appendix. Propoition highlight everal important effect of trut on the level of commitment and on the eller marketing effort. In item (a), mutual and ymmetric truting partner holding poitive expectation of their partner commitment develop equal level of commitment over time. In the longer term, however, the level of commitment of mutually ymmetric truting partner prevail over thoe of trutditruting partner (item c). Thi reult can e explained y the fact that the eller in a mutually ymmetric truting cenario invet more in relational marketing than in the oppoite ituation (item ). From item (), it can alo e aid that the lack of reciprocity etween the two exchange partner prevent the eller from allocating heavy reource to relational marketing program (Bagozzi 1995). From item (d) and (e), whether with a trut-ditrut cenario or a mutual aymmetric trut cenario, the more truting party, here the eller, maintain a higher level of commitment than the le truting, the uyer. Opportunim Effect Now let u focu on the opportunitic propenity of the partner. To thi end, we aume that oth partner experience the ame level of trut, value identically the eller marketing effort in uilding their commitment, and that the two partner contriution to the eller relational enefit are the ame. In other word, we have the following relationhip etween the model parameter: θ () t θ ()( t trut / ditrut coefficient) (8) α () t α () t (effectivene of marketing effort). c () t c () t (commitment contriution coefficient) We analyze a cenario when the uyer (eller) i more opportunitic than the eller (uyer), that i, β (t) >β (t) (β (t) >β (t)). Conidering (8) and again Theorem 1, we have the following reult. Propoition 3 (opportunitic ehavior effect): Aume (8). Then in the long run (teady tate), if the uyer i more (le) opportunitic than the eller, then the level of commitment of the uyer i lower (higher) than that of the eller.

9 150 JOURNAL OF SERVICE RESEARCH / Novemer 004 Proof: See appendix. The effect of opportunitic ehavior on the level of commitment of the two partner are traightforward. The partner with the higher opportunitic propenity commit le than the other. Thi reult i conitent with the relationhip marketing literature, which conider opportunitic ehavior a a detrimental factor for commitment. CONCLUSION AND DISCUSSION Thi reearch tudied how a eller can manage an optimal intertemporal marketing program that maintain long-term relational commitment with a uyer and maximize utility. Our main meage i that the prolem of etalihing and maintaining relational exchange can e tudied uing the methodology of optimal control. Thi approach i poile in thoe application of relationhip marketing in conumer market in which the eller deign a marketing program to gain the commitment of the uyer. It may alo e poile in the ervice indutry and ome uine-to-uine exchange where the eller undertake invetment for the relationhip and the uyer doe not. Contriution Building on a well-known modeling approach ued in applied mathematic for love dynamic and on the ehavioral marketing literature, we developed an analytic model of two-partner relational commitment. We potulated that the ucce of relational exchange could e meaured through the partner commitment, which are the ource of relational enefit. Our model pecification aume that the partner relational commitment are driven y the trut/ditrut component, the opportunim component, and the eller relational marketing effort. In thi context, we wih to how how the eller hould determine her optimal marketing effort to uild and maintain fruitful relational commitment with a uyer. Thi reearch extend the emerging paradigm of relationhip marketing and cutomer relationhip management, which ha focued on relational ehavior and the tudy of the effectivene of relational marketing intrument with little attention to deciion making or ha indirectly addreed deciionmaking iue without the formal approach of optimal control (e.g., Berry 1995; De Wulf, Odekerken-Schröder, and Iacoucci 001; Dwyer, Schurr, and Oh 1987; Hiard et al. 001; Morgan and Hunt 1994; Sigué and Elloumi 00; Verhoef 003). Our main finding upport the view that an optimal control rule for uilding and maintaining long-term relational commitment that maximize the eller dicounted utility conit of a time-variant relational marketing program. At any time, the eller relational marketing effort depend nonlinearly on the current value of everal parameter, including the contriution of each partner commitment to the eller relational enefit, the opportunitic propenity and trut/ditrut coefficient of the two partner, the eller preference for future utility, and the effectivene of the eller relational marketing effort in uilding her own and the uyer commitment. In particular, the eller relational marketing effort increae (decreae) with an increae (decreae) over time of the trut etween the two partner, the effectivene of the relational marketing program on the partner commitment, and the partner contriution to the eller relational enefit. On the other hand, it decreae (increae) with an increae (decreae) over time of opportunitic propenitie and ditrut of the two partner. We elieve that thi type of real-time relational marketing program applie to relational exchange involving more peronal interaction, continuou change in the tructural and contextual relational environment, and a variety of relational marketing intrument, a in the context of the ervice indutry. Thee require that the eller contantly liten and crutinize the requirement and ehavior of cutomer and adjut her relational marketing activitie a a reult. Our finding alo apply to what we have called conervative partner or partner involved in a tale relationhip where the parameter affecting the dynamic of their commitment do not change over time. It i our elief that thi i the cae in everal reward-aed loyalty program in conumer market in which the main driver of a conumer commitment i the reward itelf (Barne 1994). On the other hand, the eller relational marketing i tandard for many conumer and doe not need a continuou adjutment to the ituation of a particular conumer (De Wulf, Odekerken-Schröder, and Iacoucci 001). Since the work y Moorman, Zaltman, and Dehpandé (199), followed y the replication of Grayon and Amler (1999), the effectivene of long-term relationhip marketing over time ha een quetioned. Recently, Hiard et al. (001) concluded that although relational commitment and other component of relationhip marketing continue to have a poitive effect on the performance of exchange partner, thi poitive effect diminihe over time. Hiard and colleague (001) then uggeted that manager hould recognize that there i a downide to uing relational marketing trategy and conequently, identify the true cot of the input neceary for maintaining ucceful and mutually eneficial relational exchange. Our generic model upport thi view and demontrate that the determination of an optimal relational marketing program over time hould e aed on a continuou cotenefit analyi. In addition, it hould alo integrate rele-

10 Fruchter, Sigué / RELATIONAL EXCHANGES 151 vant evaluation over time of the partner opportunim, trut/ditrut, and repone to the marketing effort that have een proved to e critical in the relationhip marketing literature (e.g., Dwyer, Schurr, and Oh 1987; Gundlach, Achrol, and Mentzer 1995; Morgan and Hunt 1994). A a matter of fact, our analyi of typical ehavioral ituation in Propoition and 3 upport the relationhip marketing theory that trut and opportunitic ehavior are repectively eneficial and detrimental oth for the eller relational marketing effort and the two partner relational commitment. Lat, our model offer a general framework for undertanding and managing relational exchange. For example, an increae of relational commitment over time may not e ueful for the eller if, at the ame time, either her own commitment contriution or the contriution of the uyer commitment to her relational enefit decreae ignificantly over time. According to Kalwani and Narayanda (1995), thi i more likely to occur if, in the longer term, the uyer ecome more enile to the economic value of the eller offer and trive to hare equitaly relational enefit or erving the uyer ecome very cotly for the eller. On the other hand, heavy invetment in relationhip marketing effort may e uele if they provide no ignificant value to the uyer to jutify hi commitment or, at the ame time, occur in the context of opportunitic ehavior and ditrut, epecially from the uyer. A a conequence, our finding upport that the eller hould continuouly ae the effectivene of her relationhip marketing program. A recent tudie have hown, not all relational marketing intrument are effective in uilding relational commitment with all conumer (De Wulf, Odekerken-Schröder, and Iacoucci 001; Verhoef 003). The ue of ineffective intrument hould not lead to the quetioning of the theory of relationhip marketing. Alo, even with effective intrument that fit into the firt two level of relationhip marketing according to Berry (1995) claification, we elieve that the eller may need additional action either to reduce opportunitic ehavior or to increae/decreae trut/ditrut. Therefore, aeing the effectivene of relational marketing effort on the uyer commitment hould alo pay attention to the tructural and contextual environment of the relationhip. The importance of the tructural and contextual environment of relationhip i well recognized in the literature. For example, a tudy y Wathne, Biong, and Heide (001) downplay the role of interperonal relationhip econd level of relationhip marketing in Berry (1995) claification in the context of uine-touine ervice, and how that witching arrier and traditional marketing variale (price and product readth) play a ignificant role in the uyer choice of a upplier. The author then conclude that a cutomer role a friend may aume le importance in the preence of explicit competitive offer (Wathne, Biong, and Heide 001, p. 6). The ame thing can eaily e aid for relational marketing program aed on ome economic reward. Limitation and Future Reearch We delierately made our theoretical approach imple in order to allow for analytic inight. Some of our aumption can e relaxed. Firt, we have aumed a linear additive eparale function for the eller relational enefit. Thi aumption allow a degenerate feedack olution, which doe not depend on the relational commitment. Although more advanced pecification of the eller relational enefit function hould e conidered for future extenion, in many cae, however, their tractaility might e a cumerome tak. Second, our current model aume an unalanced relationhip etween the two exchange partner wherein the eller i the only party inveting in the relational exchange. We acknowledge that thi unalance could e either in the uyer favor when a product i eing old (e.g., Kalwani and Naraynada 1995) or in the eller favor when a ervice i eing old (e.g., Kumar 1999). Alo, in many uine-to-uine cae thi aumption doe not hold. Both the eller and the uyer often invet in the relational exchange to enhance their mutual commitment. Third, our model doe not take competition into account. In the real world, competitor often duplicate relational marketing program to reduce their competitive power. Relational marketing program uch a recommended here could then e ineffective in the face of o-called me-too relational marketing program. Third, even uing our approach, it eem worthwhile to attempt to modify the commitment dynamic to generate more complex relational marketing program. The author are actively working in thi direction. APPENDIX Proof of Theorem 1 Conider the optimal control prolem (3) with the aumption in (1). The current-value Hamiltonian i given y H(x, x, u, λ, λ ) ƒ(x, x ) C(u) + λ ( βx + θ x + α u) + λ ( β x + θ x + α u) + µ x + µ x, where λ and λ are the adjoint variale or, in our context, the net enefit (or damage) of increaing the level of relational commitment of the uyer to the eller and of the eller to the uyer, re- (continued)

11 15 JOURNAL OF SERVICE RESEARCH / Novemer 004 APPENDIX (continued) pectively, y one additional unit. µ and µ are adjoint variale aociated with the contraint on x and x, taking the value, λ c()( t r + β()) t + θ () t c() t () t. ( β ( t) + tr)( β ( t) +r) +θ ( t) θ ( t) (A8) 0x () t 0, i {, }. 0x () t > 0 i µ i i The neceary optimality condition i given y H C( u) + λα + λα 0; The adjoint equation are the following: H λ rλ rλ f β λ θ λ µ x + x H λ rλ rλ f θ λ β λ µ x + and the oundary condition are lim λ e t rt x (A1) (A) (A3) rt 0 and lim λ e 0. (A4) t Conidering (5) and (A1), the optimal marketing effort atifie u λ α + λ α. (A5) The relation in (A5) mean that the optimal marketing effort to etalih and maintain mutual commitment etween the two partner i a linear comination of the net enefit (damage) of increaing y one unit the level of commitment of the eller and of the uyer, and the reactivene of oth partner to the eller marketing effort. If x >0andx > 0, then utituting (4) into (A)-(A4) lead to rt λ ( r + β ) λ θ λ c, lim λ e 0 (A6) t rt λ θ λ + ( r + β ) λ c, lim λ e 0. (A7) t The pecial oundary condition in (A6) and (A7) and the aumption that the coefficient are all ounded function in 0 t, we conclude with the olution and λ c()( t r + β()) t + θ() t c() t () t ( β ( t) + r)( β ( t) + r) +θ ( t) θ ( t) (A8a) Sutituting (A8a-A8) into (A5) lead to (6). If x x 0, then from () we otain u 0. On the other hand, if u 0, the ytem () ecome a homogeneou ytem of differential equation with contant coefficient. Thu, if the initial olution i zero, o are the olution, that i, x 0 and x 0. Proof of Theorem Thi follow directly from the nature of the formula in (6). If, and only if, all the time-variant function that compoe the formula (6) will ecome time-invariant, then u will ecome timeinvariant. Proof of Propoition 1 The propoition follow y taking the derivative of u with the repective variale: c( β + r) + cθ / α, ( β + r)( β + r) θθ c ( β + r) + cθ / α ( β + r)( β + r) θ θ [ α( β + r) + α θ][ c( β + r) + cθ ] / β, [( β + r)( β + r) θθ ] [ α ( β + r) + αθ ][ c( β + r) + cθ] / β [( β + r)( β + r) θ θ ] [ α ( β + r) + αθ ][ c( β + r) + cθ ] / θ, [( β + r)( β + r) θθ ] [ α( β + r) + α θ][ c( β + r) + cθ] / θ [( β + r)( β + r) θ θ ] α( β + r) + α β / c, ( β + r)( β + r) θθ α ( β + r) + αθ / c. ( β + r)( β + r) θ θ Proof of Propoition (a) Thi follow directly from the ymmetry of the aumption, the equation in () and the reult in (6). () Thi follow y utituting the condition (1) and () into (6) and comparing the reult. (c) In the long run, it i eay to ee that (continued)