Reward systems for intra-organizational knowledge sharing

Transcription

1 European Journal of Operatonal Research 180 (2007) Interfaces wth Other Dscplnes Reward systems for ntra-organzatonal knowledge sharng Dong-Joo Lee a, Jae-Hyeon Ahn b, * a School of Busness Admnstraton, Hansung Unversty, 389 Samseon-dong 3-ga, Seongbuk-gu, Seoul , Republc of Korea b Graduate School of Management, Korea Advanced Insttute of Scence and Technology, , Chongyangr-dong, Dongdaemoon-gu, Seoul , Republc of Korea Receved 25 November 2005; accepted 27 March 2006 Avalable onlne 25 September Abstract Knowledge sharng s one of the most crtcal steps n knowledge management actvtes. To acheve effectve knowledge sharng, t s mportant to encourage workers to share ther knowledge for the best nterests of the frm. However, successfully exertng ths encouragement s very challengng. In ths paper, we develop a formal model and analyze reward systems for ntra-organzatonal knowledge sharng. Specfcally, two common forms of reward systems are consdered; ndvdualbased reward whch s based on the ndvdual contrbuton of valuable knowledge, and group-based reward whch s based on the contrbuton of the whole group through knowledge sharng to the frm performance. Through the analyss, we derve a smple optmal ndvdual-based reward system whch depends on the amount and the productvty of shared knowledge. The system balances the beneft from knowledge sharng of each worker wth the costs related wth t. Next, t s found that group-based reward s not only less effcent than ndvdual-based reward, but t also subject to a potental productvty problem, n whch workers wth more productve knowledge do not partcpate n knowledge sharng. Fnally, t s shown that several organzatonal factors can complement reward systems n ncreasng the performance of KM and can mtgate the productvty problem. Insghts from our analyss could help managers to understand mportant consderatons n rewardng knowledge sharng, and could provde them wth gudes to mplement reward systems. Ó 2006 Elsever B.V. All rghts reserved. Keywords: Economcs; Cost beneft analyss; Intra-organzatonal knowledge sharng; Knowledge management; Reward system desgn 1. Introducton Knowledge sharng s consdered a crtcal step for successful knowledge management (KM). To reman compettve n the marketplace, organzatonal knowledge and expertse must be shared (Gold et al., 2001; Zack, 1999). Therefore, knowledge sharng actvtes are an ndspensable component n KM processes (e.g., Alav and Ledner, 2001; Davenport and Prusak, 1998; Gold et al., 2001; Goodman and Darr, 1998). However, many researchers have argued that knowledge sharng s also a crtcal hurdle for KM (e.g., Hansen, 1999; O Dell and Grayson, 1998; Szulansk, 1996), an ssue that has also been wdely rased by ndustry * Correspondng author. Tel.: ; fax: E-mal addresses: djlee@hansung.ac.kr (D.-J. Lee), jahn@kgsm.kast.ac.kr (J.-H. Ahn) /$ - see front matter Ó 2006 Elsever B.V. All rghts reserved. do: /j.ejor

2 practtoners (Alav and Ledner, 1999; Kng et al., 2002). For example, Kng et al. (2002) report that, from a survey of 2073 KM practtoners and executves, the challenge of how to motvate ndvduals to contrbute ther knowledge to a KM system was cted as one of the top ssues n KM. In fact, there are nherent barrers to knowledge sharng. Under ntensve nternal competton for rewards, status, and promotons n today s organzatons (Menon and Pfeffer, 2003), employees normally regard ther unque knowledge as power to secure ther postons n the organzaton (Ba et al., 2001b; Huber, 1982; Zack, 1999). Ths tendency s ntensfed n the presence of downszng and job nsecurty. In addton, there are nherent costs n sharng knowledge; tme and energy are requred to share knowledge, and these are fnte resources (Davenport and Prusak, 1998; Goodman and Darr, 1998; Szulansk, 1996). To address ths ssue, t has been emphaszed that knowledge sharng should be rewarded through an organzaton s formal ncentve system (Alav and Ledner, 1999; Ba et al., 2001b; Davenport and Prusak, 1998; Gold et al., 2001). There s much emprcal evdence to suggest that organzatonal reward nfluences the behavor and performance of an organzaton s members (e.g., Huber, 1991; Maltz and Kohl, 2000). In fact, many frms reward employees for knowledge sharng. For example, n most management consultng frms, knowledge sharng actvtes are consdered n performance revews and help determne bonuses and promotons. At Ban and Company, a quarter of a partner s annual compensaton s based on how much help he or she has gven other colleagues (Hansen et al., 1999). These practces are also prevalent n other ndustry sectors (Busness Week, 2001). Whle prevous studes have ndcated the mportance of reward n KM, lttle s known about how to desgn a reward system for knowledge sharng. The purpose of ths study s to develop a formal model, and to analyze reward systems for ntra-organzatonal knowledge sharng based on the model. The analyss could help managers to understand mportant consderatons n rewardng knowledge sharng, and could provde them wth gudes to desgn reward systems. The remander of ths paper s organzed as follows: Followng the lterature revew n the subsequent secton, Secton 3 develops the model used n our analyss. In Sectons 4and5, two common reward systems are examned. Secton 6 analyzes the effects of varous factors other than rewards on knowledge sharng. Fnally, Secton 7 concludes wth dscusson and suggestons for future research. 2. Theoretcal background D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) A number of drvers of knowledge sharng have been dentfed. One such drver s organzatonal ctzenshp behavor, whch s defned as ndvdual behavor that s dscretonary, not drectly or explctly recognzed by the formal reward system, and that n the aggregate promotes the effectve functonng of the organzaton (Organ, 1988, p. 4). If the value of organzatonal ctzenshp behavor s shared and renforced throughout the organzaton, knowledge sharng s more lkely to ncrease (Goodman and Darr, 1998). Next, when an organzaton s characterzed by mutual trust and hgh-care relatonshps among workers, ndvduals wll be less lkely to keep knowledge prvate (Hansen, 1999; Nonaka and Takeuch, 1995; O Dell and Grayson, 1998; von Krogh, 1998). Also, strong belefs of organzatonal ownershp norm, whch mples that an organzaton owns the labor of the employees and the resultng outcomes such as deas, nventons, or know-how, can attenuate the ncentve to hoard knowledge (Constant et al., 1994; Jarvenpaa and Staples, 2001). Other organzatonal factors that encourage knowledge sharng nclude procedural justce or farness (Bartol and Srvastava, 2002; Bock et al., 2005), organzaton s commtment to knowledge sharng (Skyrme, 2002), and communcaton clmate such as the extent of horzontal and vertcal nformaton flow, openness, and relablty of nformaton (Malhotra and Majchrzak, 2004; van den Hooff and de Rdder, 2004). Besdes the organzatonal factors, ndvdual motvatonal drvers have been wdely emphaszed (e.g., Alav and Ledner, 1999; Ba et al., 2001b; Davenport and Prusak, 1998; Gold et al., 2001; Goodman and Darr, 1998), whch can be classfed nto ntrnsc motvaton and extrnsc motvaton. Indvduals are ntrnscally motvated when they seek enjoyment, nterest, satsfacton, or self-expresson n the work tself (Amable, 1993). Intrnsc motvaton ncludes self-effcacy and altrusm. For example, by sharng ther knowledge, ndvduals can be satsfed wth the confdence n ther ablty to contrbute to the organzaton or to help others (Constant et al., 1994; Kankanhall et al., 2005). On the other hand, ndvduals are extrnscally motvated when they engage n the work n order to obtan some goal that s apart from the work tself (Amable, 1993,

3 940 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) p. 188). Common extrnsc ncentves nclude monetary rewards, recognton, and promoton. Two basc prerequstes for extrnsc ncentve systems to be effectve are that t should be possble for the organzaton to observe or record the target behavor and to assess ts value (Bartol and Srvastava, 2002). Recently, t has been theorzed that effectve motvatonal nstruments are contngent on KM strategy (Bartol and Srvastava, 2002). Hansen et al. (1999) classfy KM strateges nto one of two categores: the codfcaton strategy, n whch knowledge s codfed and stored n repostores that are easly accessed, or the personalzaton strategy, n whch knowledge s closely ted to ts creator and s shared manly through person-to-person contacts. Bartol and Srvastava (2002) argue that extrnsc ncentves such as monetary reward systems based on ndvdual knowledge sharng behavor are best suted to the codfcaton approach because two basc prerequstes, recordng and measurng the knowledge shared by ndvduals, are met most easly under the approach. On the other hand, they argue that extrnsc ncentves under the personalzaton approach may not be as effectve as under the codfcaton approach: Rewards based on knowledge sharng behavor could play a relatvely lmted role n enablng knowledge sharng n such stuatons as knowledge sharng through formal nteractons (e.g., perodc team or department meetngs) or knowledge sharng through nformal nteractons. Fnally, ntrnsc motvaton s most approprate for nfluencng knowledge sharng wthn communty of practce. Recent emprcal studes (Kankanhall et al., 2005; Ko et al., 2005) show consstent results wth the theoretcal predcton by Bartol and Srvastava (2002). Although extrnsc rewards may sometmes undermne ntrnsc motvaton, extrnsc rewards can also convey a sgnal affrmng competence of the ndvdual that drves ntrnsc motvaton (Bartol and Srvastava, 2002). In addton, ntrnsc motvaton s more dffcult to change, wth more uncertan outcome than relyng on extrnsc motvaton; these nherent shortcomngs often call for extrnsc ncentves (Osterloh and Frey, 2000). Gven the wdely accepted role of extrnsc ncentves, an mportant queston that follows s how to desgn the ncentve system for effectve knowledge sharng, for whch lttle research effort has been made. Ths study deals wth ths queston. Based on the above arguments, formal organzatonal reward systems for knowledge sharng would be most effectve under the codfcaton strategy, whch nvolves explct knowledge contrbuton to repostores. Therefore, the specfc context for ths study s a frm that pursues the codfcaton strategy for KM, and we defne knowledge sharng as the converson of knowledge nto accessble and applcable formats (Grover and Davenport, 2001) n the knowledge management system (KMS). Under the codfcaton strategy, t would be possble for a frm to mplement an organzatonal reward system based on ndvdual knowledge sharng behavor, termed an ndvdual-based reward (IBR) n ths paper. We derved an optmal IBR, whch could provde gudes for frms to desgn reward systems. In some cases, however, t would be costly to reward each knowledge worker on an ndvdual bass by her contrbuton. Then, another type of common ncentve system, group level ncentve system, could be appled. Bartol and Srvastava (2002) suggest that frms can encourage knowledge sharng through ndrect rewards that s, rewards whch depend on factors other than knowledge sharng, but whch are lkely to requre knowledge sharng for successful performance. For example, when outcomes such as performance are rewarded at the group level, an ndvdual who shares knowledge wth others are lkely to thnk that the knowledge she shares wll mprove the performance of others, whch n turn ncreases the reward for her. Therefore, she s lkely to have a hgher motvaton to share knowledge. In ths way, a frm can base the reward on the performance of the whole group (organzaton). Under common group level ncentve system, the total ncentve payment s usually dvded among ndvduals accordng to formulas that do not depend on ndvdual contrbuton (Farrell and Scotchmer, 1988; Mlgrom and Roberts, 1992). 1 Ths type of reward s termed groupbased reward (GBR) n ths study. 2 We fnd that n general, GBR s nferor to IBR n terms of the frm s net payoff from knowledge sharng. Furthermore, we show that workers wth more productve knowledge may not share ther knowledge under a GBR. Through the extenson of the basc model, we fnd that ths potental problem may be mtgated by establshng organzatonal ownershp norm. 1 Examples of reward systems n ths category nclude proft sharng and gan sharng. 2 In addton, GBR could work as a possble reward scheme under the personalzaton approach to KM because t does not requre measurement of ndvdual knowledge contrbuton.

4 In a related study, Sundaresan and Zhang (2004) analyze the mpact of nformaton systems and rewards on knowledge transfer. Payng attenton to the role of IT nvestment n lowerng knowledge transfer costs, they show that an IT nvestment can complement rewards n facltatng knowledge transfer. However, whle they assume that the knowledge needed to complete a task s one dmensonal, we explctly consder an mportant feature of knowledge: complementarty (Ba et al., 2001a). KM nvolves the ntegraton of dfferent bodes of knowledge such as socalzaton and combnaton n knowledge converson modes (Nonaka and Takeuch, 1995). In our model, each worker has a dfferent knd of knowledge, and the complementarty among these knds of knowledge affects the optmal reward system and the workers knowledge sharng behavors. Ryu et al. (2005) dentfy learnng-from-others through knowledge transfer as one of the most mportant leanng processes, and nvestgate patterns of optmal nvestment n learnng processes. In ther model, a worker s wllngness to share her knowledge wth others s exogenously gven, wth no consderaton of the effects of the extrnsc reward. In our model, however, workers decsons on knowledge sharng are endogenzed: Each worker decdes how much knowledge to share, based on the reward system offered by the organzaton. In the followng secton, we develop a model for analyss. 3. Model Consder a frm wth n knowledge workers. Each of them s assumed to be a self-utlty maxmzer as n Ryu et al. (2005). Whle there s a wde range of other motves for human behavor ncludng needs for achevement, responsblty, and recognton (Donaldson, 1990), the smplfed model of ndvdual motvaton to maxmze self-utlty could provde frutful nsghts and does not lmt the possblty of theoretcal ntegraton wth tradtonal management theores (Barney, 1990). The frm s assumed to desre to ncrease the net payoff through KM because organzatonal knowledge ultmately contrbutes to fnancal performance of the frm (Chang and Ahn, 2005; Chen and Edgngton, 2005). Also each knowledge worker s assumed to have unque knowledge, and therefore there s only one possble provder for each knowledge component. Further, a worker may have knowledge possessed by others. However, because common knowledge s not the man target of knowledge sharng, and because the unque and valuable components of ndvduals knowledge stock are the man source of power n an organzaton, we focus on the unque knowledge of each worker The frm s objectve D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) To model ndvdual prvate knowledge, we use the concept of the knowledge unt (Davenport et al., 1996; Zack, 1999), whch s a formally defned, atomc packet of knowledge content that can be labeled, ndexed, stored, retreved, and manpulated (Zack, 1999, p. 48). Let us denote k =(k 1,...,k n ), where k ndcates the unts of unque knowledge that knowledge worker has. For example, n a consultng frm context, each consultant acqures knowledge from the projects that she partcpates n. So, the number of projects the consultant has completed can be a measure of the knowledge unts possessed by that consultant. 3 Then, suppose a stuaton where prvate knowledge s shared and utlzed by other workers. Denote s =(s 1,...,s n ), where s (6k ) represents the unts of knowledge shared out of k by worker. 4 In the followng, k and s are treated as contnuous varables for analytcal smplcty as n Sundaresan and Zhang (2004). Compared wth before knowledge sharng, a frm can generate an addtonal payoff because knowledge that was prevously held prvate can now be utlzed by others. Let F(s;k) denote the addtonal payoff gven s and k. The addtonal payoff from KM can be obtaned by usng the knowledge base to ether ncrease the value or decrease the costs of the frm s products or servces (Chen and Edgngton, 2005; Ofek and Sarvary, 2001). 5 Although there have been some concerns about the dffculty n dentfyng the contrbuton of KM to the frm performance, attempts have been made to measure the value of nvestments n KM (Chang and Ahn, 3 Whle all projects may not be successful, as Teece (1998) argues, knowledge of falures ( ths approach does not work ) s also valuable. 4 At McKnsey and Company, for example, the number of a consultant s publcatons s used as a measure of knowledge sharng and s an mportant factor n determnng promotons (Alav and Ledner, 1999). 5 The ncreased value of products or servces enables the frm to charge hgher prces or to sell more, generatng more revenue.

5 942 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) ; Samaddar and Kadyala, 2006). 6 Addtonally, the dea that KM efforts have measurable outcomes s the underlyng proposton of the stock vew of knowledge (Samaddar and Kadyala, 2006). Furthermore, frms usually measure the performance of ther KM ntatves. For example, Semens estmated that ts KMS, ShareNet, contrbuted a $122 mllon ncrease n sales of ts Informaton and Communcatons Network Group from 1999 to 2000, wth the cost of the program beng $7.8 mllon (Busness Week, 2001). Xerox also estmates that Eureka, ts knowledge sharng system, has saved the corporaton $100 mllon as of 2000 (Brown and Dugud, 2000). 7 Implementng KM s costly for the frm. For example, the frm should mantan KM staff, buld a KMS, and provde rewards. The cost, C f, can be of two types: one s ndependent of the reward system (e.g., costs to mantan KM staff and to buld the knowledge repostory and communcatons networks Ofek and Sarvary, 2001), and the other s reward-specfc. The former can be normalzed to be zero for smplcty, and the frm s net payoff from knowledge sharng (p) s represented by F(s;k) C f (s;k). Then, the frm tres to maxmze the net payoff through KM. The net payoff measures the net fnancal contrbuton of KM to the frm s performance. F s assumed to be ncreasng and concave n s. Ths assumpton has been adopted n the lterature (e.g., Cohen and Levnthal, 1989; Samaddar and Kadyala, 2006) and fts well wth organzatons n whch performance s manly characterzed by ncremental nnovatons rather than by radcal ones. New product development, for example, s one of the most mportant knowledge creatng endeavors (Madhavan and Grover, 1998; Nonaka and Takeuch, 1995), but t s stll domnated by ncremental nnovatons. Accordng to Cooper (2001), only 10% of new products are radcal nnovatons that are new to the world. From the perspectve of performance, Cooper s study shows that products of low nnovaton are as proftable as hghly nnovatve ones. Most knowledge servce frms are also characterzed by ncremental nnovatons. For example, management consultng frms generate busness solutons for ther customers by drawng on ther collectve past and present experences (Ofek and Sarvary, 2001). These frms dentfy, ntegrate, and transfer experence and solutons between clents, so the very nature of most busness solutons suggested by them s ncremental. 8 Although return to knowledge may be characterzed by S-shaped curve n some stuaton, ths possblty s excluded n the analyss because of the analytcal smplcty. Next, we ntroduce two useful concepts n the analyss: Frst, each worker s knowledge s usually dfferent n terms of ts potental contrbuton to the frm performance (Ln et al., 2005). To model ths dfference, the productvty of worker s knowledge s defned as of(s;k)/os, the margnal contrbuton of worker s shared knowledge to the payoff. 9 Ths defnton mples that as the productvty of worker s knowledge ncreases, so does the contrbuton of worker s shared knowledge to the payoff. The defnton also ncorporates the possblty that the productvty of worker s knowledge may depend on other workers knowledge sharng amounts (s j ). Second, KM nvolves the ntegraton of dfferent bodes of knowledge each worker has (Nonaka and Takeuch, 1995). Knowledge components are often nterdependent and complementary wth each other: for example, n a pharmaceutcal company, knowledge of the effects of a certan chemcal substance can be combned wth knowledge of other substances to generate a new drug treatment (Ba et al., 2001a). We capture ths mportant facet of knowledge by the concept of knowledge nterdependence. Postve nterdependence between worker s knowledge and worker j s knowledge ndcates that the productvty of worker s knowledge ncreases n s j. Or, formally, postve knowledge nterdependence mples o 2 F(s;k)/os j os > 0. Under zero nter- 6 Gven s and k, F(s;k) may be stochastc rather than certan due to varous factors such as market competton, and changes n customers needs and the economc envronment. However, the results n ths paper reman the same wth the relaxed assumpton that the frm knows the expected value of the addtonal payoff gven s and k, asnsamaddar and Kadyala (2006). 7 In addton to the measurement of total value contrbuton of KM at the aggregate level, Bartol and Srvastava (2002) argue that t s possble for frms to measure the value of each knowledge contrbuton under the codfcaton approach because knowledge contrbuton s recorded and frms usually have valdaton systems composed of knowledge experts. 8 Ths explans why the consultng ndustry s often blamed for recyclng old advce wthout provdng nnovatve solutons (O Shea and Madagan, 1997). 9 The margnal contrbuton of worker s total prvate knowledge, of/ok, can also be a measure of the productvty of worker s knowledge. However, we do not consder ths alternatve measure because we focus not on the knowledge creaton ssue but on the knowledge sharng ssue gven prvate knowledge.

6 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) dependence, o 2 F (s;k)/os j os = 0. Therefore, hgher knowledge nterdependence mples a hgher level of complementarty or synergy between knowledge components. Although negatve nterdependence may exst n some stuatons, we rule out ths case for smplcty. 10 For expostonal smplcty, the parameter k s omtted whenever possble Knowledge sharng costs ncurred by workers There are nherent barrers to knowledge sharng whch mpose costs on potental knowledge contrbutors. Our model ncludes two mportant types of such costs. Frst, employees normally regard ther unque knowledge as power n the organzaton (Ba et al., 2001b). If other people gan the knowledge, the owners of the knowledge may lose power, whch would threaten ther postons n the organzaton (Ba et al., 2001b; Davenport and Prusak, 1998; Goodman and Darr, 1998; Huber, 1982; Szulansk, 1996). Therefore, workers get utlty by keepng knowledge prvate. P(k ), utlty of power, denotes the utlty n monetary terms worker gets from prvate knowledge amount of k. Then, after sharng s unts of knowledge, worker s utlty of power becomes P(k s ). Thus, P(k ) P(k s ) amounts to costs ncurred by sharng s unts of knowledge. It s reasonably assumed that utlty of power ncreases as the amount of unque knowledge ncreases, that s, P 0 (k ) > 0. We further assume that P 0 (k ) < 0, because a worker wth a lot of unque knowledge would get less ncrease of utlty of power from an addtonal unt of prvate knowledge, compared wth a worker who has only a small amount of knowledge. Ths mples that the more knowledge a worker shares, the more rapdly the utlty s decreased. Another source of dsutlty s the tme and effort to make knowledge explct and to structure t so that t can be dssemnated (Davenport and Prusak, 1998; Goodman and Darr, 1998). Let us denote C(s ) as worker s costs of tme and effort n monetary terms ncurred by sharng s unts of knowledge. Then, C 0 (s ) > 0, that s, the more one shares, the more costs of tme and effort are requred. Snce tme s the frm s resource most lkely to be begrudged to knowledge actvsts (Davenport and Prusak, 1998), workers should contrbute ther knowledge at the cost of ether tme for ther dutes or off hours. Furthermore, under the codfcaton approach, the costs of creatng documents and ndexng them for reuse escalate (Markus, 2001). Based on these arguments and prevous lterature (e.g., Barua et al., 1995; Kandel and Lazear, 1992; Lal and Srnvasan, 1993), C s assumed to be convex n s (C 00 (s ) > 0) and of the same functonal form for all workers. To complete knowledge transfer, knowledge should not only be contrbuted by ts owners but also should be absorbed and appled by the recpents. Markus (2001) dentfes four dstnct types of knowledge reuse stuatons nvolvng dfferent knowledge reusers; shared work producers, shared work practtoners, expertse-seekng novces, and secondary knowledge mners. Among the four stuatons, she argues that applyng knowledge nvolves dffculty only for expertse-seekng novces because of the possble lack of ablty to apply t successfully. Although ths stuaton may be of concern n some cases, we lmt our attenton to the costs from the perspectve of knowledge owners because contrbutng knowledge s the frst step toward leveragng knowledge assets n an organzaton (Kankanhall et al., 2005). Now, suppose the followng stuaton. Frst, the frm announces a reward system on knowledge sharng. Then, each worker decdes to share a certan amount of knowledge, s (>0), or decdes not to partcpate n knowledge sharng. In the latter case, the worker s utlty does not change. Fnally, the frm rewards partcpatng workers based on the reward system. In the followng sectons, we analyzed reward systems based on the model. 4. Analyss of ndvdual-based reward system Under the codfcaton strategy, ndvdual knowledge contrbuton can be easly recorded and measured (Bartol and Srvastava, 2002). In ths secton, we analyze the IBR system, n whch reward for each knowledge worker s determned by her contrbuton to the knowledge repostory. Frst, an ncentve compatble reward system s derved. Then, we nvestgate the effects of knowledge amount and productvty on knowledge sharng. 10 The results n ths paper, however, reman the same under negatve nterdependence.

7 944 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) Incentve compatble reward system Denote R as the reward for worker. It s the worker s problem to decde the optmal level of knowledge sharng to maxmze her total utlty, gven the reward system. After sharng s unts of knowledge, and thereby ncurrng the costs of C(s ), worker has power of P(k s ) and receves reward R (s ). Therefore, worker s problem (P1) and the correspondng frst-order condton (FOC) are as follows: and max s z P1 ¼ Pðk s Þ Cðs ÞþR ð1þ opðk s Þ C 0 ðs Þþ or ¼ 0: os os ð2þ Worker chooses knowledge sharng amount satsfyng Eq. (2). op(k s )/os and C 0 (s ) are margnal loss of power and margnal cost of tme and effort to ncrease the knowledge sharng amount, respectvely. Thus, Eq. (2) mples that n choosng the optmal s, the worker consders the balance between margnal ncrease of costs (loss of power and cost of tme and effort) and margnal ncrease of reward, or (s )/o s, assocated wth knowledge sharng. The frm s problem (P2) s determnng both the optmal level of knowledge sharng and the correspondng reward scheme for each worker, n an effort to maxmze the net payoff, consderng the workers ncentve to maxmze ther own utlty as shown n (2). max s 1 ;...;s n; R 1 ;...;R n X n p P2 ¼ F ðsþ ¼1 R s:t: Pðk s Þ Cðs ÞþR P Pðk Þ; 8; ð4þ opðk s Þ C 0 ðs Þþ or ¼ 0; 8: ð5þ os os The partcpaton constrants n (4) mply that, to encourage the worker to partcpate n knowledge sharng, the frm should provde a reward level whch guarantees that the worker s utlty wll not decrease after sharng knowledge. The ncentve compatblty constrants n (5) are the workers FOC s n (2): they mply that the frm should consder that the workers wll react to the reward system by choosng the knowledge sharng amount whch s optmal for them. To derve an optmal reward system, the followng lemma s used; the proof s shown n Appendx A. Lemma 1. The constrants (4) n (P2) are bndng at the optmum. In other words, Lemma 1 says that at the optmum, the worker s utlty after knowledge sharng wll be the same as the utlty before knowledge sharng. Therefore, after substtutng the equalty partcpaton constrants for R (s )n(3), the frm s FOC s obtaned as follows: of ðsþ þ opðk s Þ C 0 ðs Þ¼0; 8: ð6þ os os Eq. (6) mples that the frm should balance the beneft and costs to the frm of ncreasng knowledge sharng amount. of(s)/os represents the beneft snce t s the margnal ncrease of the payoff. On the other hand, op(k s )/os + C 0 (s ) represents the cost snce t s the sum of margnal loss of power and margnal cost of tme and effort, whch should be compensated to ncrease knowledge sharng amount. Therefore, the optmal s s the amount at whch the margnal beneft of ncreasng knowledge sharng amount s the same as the margnal cost assocated wth t. The second-order condtons are satsfed snce the partal dervatve of the left-hand sde of (6) wth respect to s s negatve. Wth F convex n s, the analyss leads to the same results as long as the correspondng secondorder condton s satsfed, or the convexty of F s moderate. Therefore, our analyss s vald as long as the ð3þ

8 organzaton s not very radcally nnovatve, or knowledge n the organzaton does not generate very sharply ncreasng returns. Denote s ¼ s 1 ;...; s n as the soluton to the frm s FOCs. By comparng (5) and (6), an ncentve compatble reward system can be obtaned as follows, where b s derved usng Lemma 1. Proposton 1. The followng lnear IBR system s ncentve compatble: R ðs Þ¼a s þ b ¼ of ðs Þ os D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) s þ Pðk Þ P k s þ Cs of ðs Þ s ð7þ os Therefore, the smple reward system (7), whch s lnear n knowledge sharng amount of each worker, provdes an ncentve compatble soluton. Note that no restrctons were mposed on the functonal form of R, and R (s ) s used n (7) nstead of R because the above reward system s a functon of s. In the followng, a and b are termed the margnal reward and base reward, respectvely. The reward system n (7) s ndvdualbased because the reward equaton s dfferent for each worker. In addton, the reward system takes nto account both the amount (s ) and the productvty (of(s)/os )of shared knowledge. The margnal reward s the productvty of shared knowledge at the optmum. To understand how changes n the productvty affect the optmal amount of knowledge sharng and reward systems, suppose the productvty of worker s knowledge s ncreased whle that of others reman unchanged under postve knowledge nterdependence. Then, the left-hand sde of Eq. (6) becomes postve at s *, the optmum before the ncrease of the productvty. Therefore, s should be ncreased to satsfy (6). Because ths ncrease of s, n turn, ncreases the left-hand sde of the FOC for j (5)n(6), s j should also be ncreased from s j to satsfy (6). Thus, the ncrease of the productvty of worker s knowledge ncreases the optmal knowledge sharng amount of worker, and ncreases that of other workers under postve nterdependence. In ths case, because op(k s )/os C 0 (s )n(6) decreases n s, of(s)/os at the optmal s should be ncreased. Therefore, the margnal reward for worker (a ) should also be ncreased. Smlarly, the margnal rewards for other workers should also be ncreased. Wth the reward system gven n (7), each worker shares s. Then, the reward for worker and the net payoff of the frm are, respectvely, as follows: R s ¼ Pðk Þ P k s þ Cs ð8þ and p P2 ¼ F ðs Þ Xn Pðk Þ P k s þ Cs : ð9þ ¼1 Eq. (8) shows that under the reward system n (7), the reward receved by the worker exactly equals her loss of utlty of power plus the cost of tme and effort. That s, the worker gets zero surplus f she shares s, and negatve surplus otherwse. Therefore, the frm takes the entre surplus except the costs of knowledge sharng ncurred by each worker, R ðs Þ The effects of knowledge amount and productvty on knowledge sharng Here, we examne the effect of knowledge amount (k ) and the productvty of knowledge on the optmal knowledge sharng s. Lemma 2 summarzes the results; the proof s provded n Appendx A. Lemma 2. The optmal knowledge sharng s s characterzed as follows: Amount of knowledge Interdependence Productvty of knowledge (PK ) PK >PK j PK = PK j PK <PK j k =k j Zero or postve s > s j s ¼ s j s < s j k > k j Zero s > s j s > s j Mostly, s > s j Postve Mostly, s > s j Mostly, s > s j Indetermnate

9 946 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) From the frst row n the above table, when workers are homogeneous n terms of the amount of ther knowledge (k = k j for all 5 j), the optmal knowledge sharng amount s larger for a worker wth more productve knowledge than a worker wth less productve knowledge, regardless of the nterdependence. To nvestgate how a frm should desgn reward systems for workers wth dfferent levels of productvty of knowledge, consder the case n whch worker has more productve knowledge than worker j (PK >PK j ). Then, s > s j. Snce the sgn of the second and the last parentheses n (A.1) n Appendx A s negatve and postve, respectvely, the frst parentheses should be postve to satsfy (A.1). Therefore, a (=of(s * )/os )>a j (=of(s * )/os j ). Next, suppose that b P b j. Then, R (s )=a s + b > R j (s )=a j s + b j for all s. Snce R ðs j Þ¼a s j þ b > R j ðs j Þ¼PðkÞ Pðk s j ÞþC wðs j Þ, worker gets postve net utlty by sharng s j. Ths leads to a contradcton to the result n Secton 3.1 that workers should get zero net utlty. Thus, b < b j. Therefore, other thngs beng equal, a frm should set a hgher margnal reward and a lower base reward for a worker wth more productve knowledge. Next, consder the case where worker has more knowledge than worker j (k > k j ) (the second row n the above table). Then, worker ncurs a lower cost of sharng a gven amount of knowledge than worker j, and therefore a lower margnal cost of sharng. When PK P PK j under zero nterdependence, the frm s beneft from worker s knowledge s equal to or hgher than that from worker j s. Therefore, n ths case, the frm should nduce more knowledge sharng from worker to balance the beneft and cost of knowledge sharng n Eq. (6), that s, s > s j. In the other cases n Lemma 2, however, the relatve amount of the optmal knowledge sharng s not unquely determned although s > s j n most cases. Lemma 2 shows that, n general, a worker wth more amount of knowledge or more productve knowledge should be nduced to share more because a worker wth more knowledge loses less utlty n sharng knowledge and because more productve knowledge contrbutes more to the frm performance. Fg. 1 llustrates optmal knowledge sharng amount under condtons of varyng productvty of knowledge, knowledge amount, and knowledge nterdependence for specfc functonal forms wth n = 3. The functonal forms are gven n Appendx B, and the parameter values are gven n the fgure. Case I s the base case, where all of the three workers have the same amount of knowledge of 10 and the productvty of knowledge s the same for workers 1 and 2. The productvty of worker s knowledge s captured by the parameter a. As the productvty of worker 3 s knowledge (a 3 ) ncreases, so does the worker s optmal knowledge sharng amount (I-2). From the curves I-1 and I-2, the optmal knowledge sharng of worker 3 s lower than that of worker 1 (or worker 2) for a 3 < 0.2(=a 1 = a 2 ), and hgher for a 3 > 0.2. Note that the optmal knowledge sharng of worker 1 also ncreases wth a 3 because of the postve nterdependence (b j = 0.1 for all 5 j). In case II, knowledge nterdependence s stronger (b j = 0.2) than n case I. By comparng I-1 wth II-1 and I-2 wth II-2, respectvely, we can fnd that knowledge sharng ncreases wth the ncrease of knowledge nterdependence. In case III, the amount of worker 3 s knowledge s ncreased compared to case I. Ths ncreases Fg. 1. The effect of the amount and the productvty of knowledge on knowledge sharng.

10 not only the optmal knowledge sharng of worker 1 but also that of the other workers due to the postve nterdependence (compare I-1 wth III-1 and I-2 wth III-2, respectvely). Note, from the curves III-1 and III-2, that whle the optmal knowledge sharng s usually hgher for a worker wth more knowledge (worker 3), a worker wth less knowledge (worker 1 or 2) should share more when the productvty of her knowledge s suffcently hgher. 5. Analyss of group-based reward system In the prevous secton, we derved an optmal IBR, whch could provde desgn prncples for reward systems under the codfcaton strategy. However, t would often be costly to reward each knowledge worker on an ndvdual bass by her contrbuton as n IBR. Then, a frm can base the reward on the performance of the whole group (F) usng a GBR. GBR s usually smpler and less costly to mplement than IBR, because only one reward equaton s needed for all the workers nstead of n reward equatons as n IBR, and because the frm have only to measure F to determne the reward amount nstead of measurng all s for each worker. In addton, GBR can be a practcal means to reward knowledge sharng under the personalzaton strategy because ndvdual contrbuton s nherently unobservable under the strategy. Suppose a GBR system n the smplest form, R (F)=cF(s) +d, n whch each worker receves an equal porton of the total payoff. 11 Then, the worker s problem (P3) s max Z P3 ¼ Pðk s Þ Cðs ÞþcF ðsþþd: ð10þ s The frm s problem (P4) s as follows: max s 1 ;...;s n c;d D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) p P4 ¼ F ðsþ Xn ¼1 ðcf ðsþþdþ ð11þ s:t: Pðk s Þ Cðs ÞþcF ðsþþd P Pðk Þ; 8; ð12þ opðk s Þ C 0 of ðsþ ðs Þþc ¼ 0; 8: ð13þ os os The partcpaton constrants n (12) are equvalent to R ¼ cf ðsþþd ¼ maxfpðk Þ Pðk s ÞþCðs Þg: ð14þ Therefore, when workers are heterogeneous n terms of the productvty of knowledge or the amount of knowledge, some workers usually get postve net utlty from knowledge sharng under the GBR. Although the optmal GBR cannot be derved explctly, t can be shown that the GBR s always nferor to the IBR gven n (7). 12 That s, the frm s net payoff s lower under the GBR than under the IBR. The man reason for ths s that, contrary to the GBR, the IBR can ndvdualze the reward rule based on the productvty and the amount of knowledge contrbuted by each worker. Next, we examne the effects of knowledge amount (k ) and the productvty of knowledge on the optmal knowledge sharng s. Lemma 3 summarzes the results; the proof s shown n Appendx A. Lemma 3. The results n Lemma 2 hold under the GBR system. Lemma 3 shows that the effects of knowledge amount and the productvty of knowledge are unchanged under the GBR. Therefore, n general, a worker wth more amount of knowledge or more productve knowledge s lkely to share more. Under the GBR, a frm may mprove the net payoff by reducng the reward, thereby causng some workers wth bndng partcpaton constrants to not partcpate n knowledge sharng under the reduced reward. 11 Smple lnear reward equatons have been frequently consdered n the compensaton lterature (e.g., Barua et al., 1995; Kandel and Lazear, 1992). 12 However, when all workers are homogeneous n terms of the productvty of knowledge and k = k for all, we can derve an optmal reward system, under whch the amount of knowledge sharng and the frm s net payoff are the same as under the IBR n (7).

11 948 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) Suppose that all workers have the same level of productvty of knowledge, except for worker n, who has a hgher level. If other thngs beng equal, by Lemma 3, s 1 ¼¼s n 1 < s n. Therefore, worker n has a hgher mnmum reward requrement Pðk n Þ P k n s n þ Cs n than the other workers do because she ncurs a greater loss of power and a hgher cost of tme and effort. Snce partcpaton constrants are bndng only for worker n, worker 1 through worker n 1 get postve net utlty from knowledge sharng. If the frm decreases the base reward d, worker n does not partcpate n knowledge sharng snce he gets negatve net utlty gan from sharng. Therefore, F s reduced, whch has a negatve effect on the frm s net payoff. On the other hand, a frm can decrease d as long as the partcpaton constrants are satsfed for worker 1 through worker n 1. Ths change would ncrease the net payoff wthout nfluencng the other n 1 workers optmal choces under s n = 0. Therefore, t s better for a frm to decrease the base reward as long as the gan (reduced reward) from the decrease of the base reward s larger than the loss (reduced payoff). A frm can further ncrease the net payoff by changng both c and d to the optmal level under s n =0. Proposton 2 generalzes the argument. Proposton 2. Under GBR, other thngs beng equal, workers wth more productve knowledge gan less (possbly zero) net utlty from knowledge sharng than workers wth less productve knowledge. In ths case, a frm may reduce the reward to ncrease the net payoff, whch nduces the workers wth more productve knowledge to not share ther knowledge. Fg. 2 shows a numercal example to llustrate Proposton 2 for n = 4. The functonal forms are gven n Appendx B, and the parameter values are gven n the fgure. All the workers have the same amount of knowledge of 10. Whle the productvty of knowledge s the same for workers 1 3, worker 4 has more productve knowledge. The productvty of worker s knowledge s captured by the parameter a. Then, the partcpaton constrants are bndng only for worker 4. The fgure shows the net payoff when the frm nduces all workers to share knowledge (p ** ) and the net payoff when the frm reduces the reward causng worker 4 to not share her knowledge (p 0 ). As the productvty of worker 4 s knowledge (a 4 ) ncreases, p ** decreases because of the ncrease of the reward necessary to make worker 4 share knowledge. Note that the dfference of the mnmum reward requrement between worker 4 and the other workers ncreases wth the dfference of the productvty between them (the dotted lne). In ths case, workers 1 3 get postve net utlty. p ** eventually decreases to a level lower than p 0 (for a 4 > 0.073). Therefore, the frm becomes better off by reducng reward, thereby causng worker 4 to not share. The possbltes for a frm to reduce the reward ncrease as the varaton of mnmum reward requrements across the workers ncreases. In general, the productvty problem s more lkely to occur as the heterogenety of workers n terms of the productvty of knowledge ncreases. The above result represents a paradox n KM. Although frms adopt KM n order to secure valuable knowledge, GBR tend to produce a knowledge base lackng hgh qualty, productve knowledge. Because GBR s awarded wthout consderng the ndvdual Fg. 2. The frm s ncentve to reduce reward.

12 contrbutons of each worker, workers wth productve knowledge may not be compensated suffcently. In ths case, there s an ncentve for the workers to not contrbute ther knowledge to the frm s knowledge base. In the followng model extenson secton, the role of corporate norms regardng knowledge sharng s analyzed as an nstrument to mtgate ths problem. 6. Model extensons In ths secton, the model and the analyses are extended n several ways to nclude other factors that have been emphaszed as drvers of knowledge sharng. The effects of those factors on knowledge sharng and on the frm s net payoff are nvestgated. Addtonally, t s shown that the potental productvty problem under the GBR can be allevated through organzatonal ownershp norm Job securty, trust, care, and organzatonal ctzenshp behavor (OCB) When job securty s low due to frequent layoffs or economc downturns, workers have a strong ncentve to keep ther unque power n the frm (Davenport and Prusak, 1998). Therefore, workers attach more utlty to ther prvate knowledge. Denote k(>0) as a job securty parameter. The effect of job securty can be analyzed by replacng power P by P/k, where hgher k mples hgher job securty. On the other hand, when the level of trust or care between employees, or OCB, s hgh n a frm, workers feel the psychologcal cost of tme and effort needed for sharng less because they are more concerned wth how they can be useful to others and contrbute to solvng organzatonal problems (Constant et al., 1996). To capture the effect of those factors, C s replaced by C/l, where l > 0. A hgher value of l mples a hgher level of trust, care, or OCB. 13 Then, for (P2) under IBR, P and C are replaced by P/k and C/l, respectvely. After substtutng the bndng partcpaton constrants, the frm s FOC becomes of ðsþ þ 1 opðk s Þ 1 os k os l C0 ðs Þ¼0: ð15þ Denote s 1 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) and s 2 as the optmal knowledge sharng under k 1 and k 2 (>k 1 ), respectvely. As k ncreases from k 1. Because each worker should ncrease knowledge sharng to k 2, the left sde of (15) becomes postve under s 1 to satsfy the FOC, os =ok > 0. Smlarly, os =ol > 0. These results show that a hgher level of job securty, trust, care, or OCB leads to ncreased knowledge sharng, whch s consstent wth the prevous lterature (e.g., Hansen, 1999; Jarvenpaa and Staples, 2001; von Krogh, 1998). However, nterestngly, t can be shown that a hgher k or a hgher l does not always ncrease knowledge sharng under GBR. Ths s because an ncrease of k or l, n general, changes the optmal margnal reward c, under whch s does not necessarly ncrease. Therefore, contrary to the common asserton n the prevous lterature, the effect of those factors on knowledge sharng s contngent on the type of reward system used. Next, what s the effect of those factors on the frm s net payoff? It s found that the frm s always better off wth ncreased job securty, trust, care, or OCB (the proof s gven n Appendx A). Fnally, the ncluson of the parameters, k and l, does not affect any of the results n the prevous sectons. Proposton 3 summarzes the results. Proposton 3. Wth a hgher level of job securty, trust, care, or OCB: () The frm s net payoff always ncreases. () Knowledge sharng ncreases under the IBR, but not always under the GBR. () The results n the prevous sectons reman the same Organzatonal ownershp norm (OON) When OON s prevalent, workers feel that knowledge, even f a result of ther hard work, must be used for the beneft of the organzaton as a whole (Jarvenpaa and Staples, 2001). Because the norm works as a 13 Whle OCB refers to observable behavors, trust and care are atttudes dffcult to observe. However, ther effects on the workers utlty are smlar n nature.

13 950 D.-J. Lee, J.-H. Ahn / European Journal of Operatonal Research 180 (2007) gudelne to accepted and expected behavor (Bettenhausen and Murnghan, 1991), employees get more utlty by sharng more knowledge n the presence of strong OON. By contrast, when they share less than others, they get negatve utlty because they fal to conform to the standards of behavor, and therefore they are derogated by others (Menon and Pfeffer, 2003). Therefore, the worker s problem under IBR (P5) can be modeled as follows, where n(>0) denotes the ntensty of OON, and s ¼ð1=nÞ P s j 14 : max s Z P5 ¼ Pðk s Þ Cðs ÞþR þ nðs sþ: ð16þ Then, the frm s problem (P6) becomes max s 1 ;...;s n ; R 1 ;...;R n s:t: X n p P6 ¼ F ðsþ ¼1 R Pðk s Þ Cðs ÞþR þ nðs sþ P Pðk Þ n X j6¼ ð17þ s j ; 8; ð18þ n opðk s Þ C 0 ðs Þþ or þ n n 1 ¼ 0; 8: ð19þ os os n Note from the partcpaton constrant n (18) that the utlty that worker gets when she does not partcpate n knowledge sharng s Pðk Þ n P j6¼ s j=n because of OON. The frm s FOC after substtutng the bndng partcpaton constrants for R n (17) s of ðsþ þ opðk s Þ C 0 ðs Þþn n 1 ¼ 0: os os n ð20þ From (20), t s easy to see that as n ncreases, so does s. Therefore, OON renforces knowledge sharng under the IBR. Addtonally, (20) shows that ths effect s ntensfed as n ncreases. Therefore, as the sze of a frm ncreases, buldng OON can be a more effectve way to nduce knowledge sharng. However, smlar to the effect of k or l, a hgher n does not always ncrease knowledge sharng under GBR. Then, what s the effect of n on the net payoff? It can be shown that a hgher level of OON ncreases the net payoff. The proof s gven n Appendx A. Next, we show that the productvty problem under GBR can be mtgated because a postve n reduces a frm s ncentve to decrease the reward. Other thngs beng equal, the partcpaton constrant for a worker wth the most productve knowledge s bndng whle workers wth less productve knowledge gan postve net utlty (see Proposton 2). 15 By rearrangng the partcpaton constrants, we have the followng nequalty for worker, where the rght-hand sde s the mnmum reward requrement for worker : cf ðsþþd P Pðk Þ Pðk s ÞþCðs Þ n n 1 s : ð21þ n From (21), a postve n has an effect to decrease the mnmum reward requrement through the term, n(n 1)s /n. The effect s larger for workers wth more productve knowledge, who share more. Therefore, as n ncreases, the varaton of the mnmum reward requrement across workers s usually reduced, whch n turn reduces the frm s ncentve to decrease the reward to mprove the net payoff. As a result, there s less possblty for workers wth more productve knowledge to not partcpate n knowledge sharng. Therefore, by establshng a corporate norm that encourages knowledge sharng, a frm adoptng GBR can expect the productvty problem to be allevated. Fnally, the ncluson of n does not affect any of the results n the prevous sectons except Proposton 2. The followng proposton summarzes the results. Proposton 4. Wth a hgher level of OON: () The frm s net payoff always ncreases. () Knowledge sharng ncreases under the IBR, but not always under the GBR, and the effect of OON s ntensfed as n ncreases. ()A 14 The modelng approach s smlar to Kandel and Lazear (1992) and Myazak (1984). 15 Note that Eq. (A.6) n the proof of lemma 3 does not change wth the ncluson of n.