Promoting knowledge sharing in the workplace

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ContentslistsavailableatScienceDirect

Chaos, Solitons and Fractals

NonlinearScience, andNonequilibrium andComplexPhenomena journalhomepage:www.elsevier.com/locate/chaos

Frontiers

Promoting knowledge sharing in the workplace: Punishment v. reward

Zaisheng Zhang

^a

, Fang Song

^a^,^∗

, Zongbin Song

^b

aCollege of Management and Economics, Tianjin University, 92, Weijin Road, Nankai District, Tianjin, PR China

bChina Satellite Navigation and Communications Co. Ltd., Shenyang, PR China

a rt i c l e i n f o

Article history:

Received 23 February 2019 Revised 25 September 2019 Accepted 8 November 2019 Available online xxx Keywords:

Knowledge sharing Punishment Reward

Public goods game Simulation

a b s t r a c t

Previousstudieshavenotedthatbothpunishmentandrewardcanimproveknowledgesharingtosome extent;however,whichonebetterpromotesknowledgesharingremainsdebatable.Furthermore,ithas yettobethoroughlyinvestigatedwhetherahigherﬁneorahigherbonusprecipitatesbetterknowledge sharingperformance.Here,weanalyzeknowledgesharingbehaviorbyintroducingfourmodelsofthe publicgoodsgame(PGG)withthefollowingincentivemechanisms:noincentive,areward,apunishment, andamixofrewardandpunishment,todeterminewhichmechanismbestpromotesknowledgesharing intheworkplace.Eachmodelisthenusedtosimultaneouslyconsiderdiﬃcultpressuresandcoworkers’

attitudesinaworkenvironment.AsimulationwasconductedusingtheJavaprogramminglanguage,the resultsofwhichrevealedthefollowing:(1)Bothpunishmentandrewardcanpromoteknowledgesharing behavior,butpunishmentismoreeffectivethanrewardforsustainingknowledgecontribution.Contrary towhatwasexpected,themixedmechanismisnotasefficientaspunishmentorrewardinfacilitating knowledgesharing.(2)Theamountofthefine/bonusisnonlinearlyrelatedtothequalityoftheknowl- edgeshared.Thus, wesuggest thatthe moderate fine/bonusis asatisfactorychoicefor organizations topromoteknowledgesharing.(3)Peerpressure,timepressure,andcoworkers’attitudesallcontribute cruciallytotheequilibriumofthePGG.(4)Itiseasiertoimproveandmaintainknowledgecontribution whenthefacilitatinginfluences,e.g.peerpressure,fromtheworkenvironmentarestrongerthanthein- hibitingones,e.g.timepressure.Ourresearchnotonlypromotesanunderstandingoftheinfluencesof incentivemechanismsandtheeffectsofpressuresandteamatmospheresonknowledgesharing,butalso providespracticalimplicationsfororganizationsandleaders.

1. Introduction

Knowledge sharing refers to theprovision oftaskinformation andknow-howtohelpothersandcollaboratewithotherstosolve problems,developnewideas,orimplementpoliciesorprocedures [1].Knowledgesharinghasreceived considerableattention[2],as it is vital to the development of an organization’s competitive advantage. Additionally, knowledge sharing is integral to knowl- edgemanagement [3].However,sharingpersonalknowledge with coworkersdoesnotcomenaturallytomostindividuals[4];knowl- edgecanbeconsidered asanindividual’sintellectualproperty,an intangible private asset, and power. Accordingly, individuals tend tohoardratherthanshareknowledge,astheknowledgecontribu- tors may fear that diminishing their internal competition makes them expendable, and thus puts their job at risk [5–11]. Schol- arshaveconductedresearchofknowledgesharingintwoprimary ways. The ﬁrst involves identifying important factors that affect

∗ Corresponding author.

E-mail address: [email protected] (F. Song).

knowledgesharingbehavior.Theseinclude(a)thepropertiesofthe environment,includingmacro-levelandmicro-levelenvironmental factors,(b)thepropertiesofmanagement andmanagerialactions, (c)thepropertiesoftheindividuals,and(d)thepropertiesofthe knowledge itself [12]. In real life, decision-making is influenced by externalenvironmental conditionsandan individual’sabilities basedonboundedrationality[13].Therefore,theindividual’swill- ingnesstoshareknowledgeisinevitablyaffectedbytheorganiza- tionalenvironment. Contemporary employeesare facing multiple pressuresfromtheorganizationalenvironment,suchastimepres- sureandpeerpressure;theyarebusierthaneverandrequiremore cooperationthaneverbefore.Somescholarshaveanalyzedthein- fluence of time pressure and peer pressure on knowledge sharing;however,thesehaveallcomprisedempiricalresearch.Thatis, there isno study regardingthose pressures and their relation to knowledgesharinginvolvingthepublicgoodsgame(PGG)method andsimulation. The second approach to investigations of knowl- edgesharinginvolvesprovidingeffectiveincentivesforknowledge sharing.Asmanyresearchershavesuggested,itisdifficulttoform cooperativerelationshipsinthesystemwheneveryonemakesde- https://doi.org/10.1016/j.chaos.2019.109518

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cisionsinpursuitofmaximizing theirown payoffs[14].However, both punishment andreward can improve knowledge sharing to some extent; but which one encourages better knowledge sharing is debatable. Furthermore, a research gap remains regarding whetherahigherfineorahigherbonusleadstobetterknowledge sharingperformance.Here,we analyzeknowledge sharingbehavior by introducing four models of the PGG followed by four incentivemechanisms: noincentive,a reward,a punishment,anda mixedrewardandpunishment.Eachmodelisthenusedtosimul- taneously consider difficultpressures andcoworkers’ attitudes in aworkenvironment.WithJavaprogramminglanguagesimulation, the following issues are investigated: (1) Punishment or reward, which on is better in promoting knowledge sharing? What hap- pens ifwe adopt the mixedincentive mechanism? (2) Does the higherfineorhigherbonusbetterencourageefficiencyinfacilitat- ingknowledgecontribution?(3)Howdotimepressure,peerpressure,andcoworkers’attitudesinfluenceknowledgesharing?

1.1.PGGandknowledgesharing

While previous worksregarding knowledgesharing have con- tributedtoanimprovedunderstandingofknowledgesharing,most havebeenempirical.Thus,thesestudiesinvolveseverallimitations, suchastheuseofvariablesbasedonaquestionnairecompletedby asinglesourceatonetimeperiod[1].Alternatively,somescholars haveinvestigated knowledge sharing from the perspective ofso- cial dilemmas existing in realistic organizations. The frameworks presented in these studies, borrowed from sociological research on cooperation,inform thesocio-psychological processes govern- ing exchangesamong employees.Cabrera & Cabrera suggest that sharedknowledgebecomesapublicgoodfromwhichinterdepen- dentmembersofanorganization canbeneﬁtdirectly,whetheror notthey havecontributed; thismaylead toopportunistic behavior andfree riding [15]. Additionally, personal behaviors are pri- marilymotivated by self-interest, froman economic perspective;

peoplethereforetendtodotheirbesttomaximizeindividualutil- ity[10,11]. Thisimpliesthat knowledgesharing isaphenomenon withthepotential to evoke feelingsofconﬂict ofinterest among theindividuals involved[16,17]. As a resultof this, free riding is oftenthe personal strategy that yields thebest outcome forem- ployees. Accordingly, such free riding resulting from maximizing one’s own utility creates a public goods social dilemma, i.e. situations arise in which individuals’ rational actions performed in anattempttomaximizetheirpersonalbeneﬁtsdamagethecollec- tive[18,19].Evolutionarygametheoryhasbecomeoneofthemost prevalent methods to solve social dilemma situations [20], vari- ousapproachesforpromotingcooperationhavebeendiscussedin- cludingcoevolution[21,22],reputation-based popularity[23],and independentnetworks[24].Meanwhile, PGGalso provides area- sonable explanation for group interactions among multiple players[25].TheknowledgesharingdilemmawiththePGGmodelre- quiresfurther investigation; thus far, this applicationof the PGG model has attracted a reasonable degree of supporting evidence fromotherdisciplineswhichstudyhumansocialbehavior[15]. 1.2.Incentivemechanismsandknowledgesharing

Promotingknowledgesharingisadiﬃculttaskashoardingand guardedly considering knowledge are natural human tendencies [26].Consequently,thewillingnessofanindividualtoshareisone ofthecentralbarrierstoknowledgesharing[27].Researchthrough the lens of providing effective incentives for knowledge sharing hasthusattracted considerableattention. Theirresultsshow that knowledgesharingcannot be forcedormandatedbutcanbe encouraged and facilitated [28,29], as knowledge sharing is most likely to occur when employees perceive that incentives exceed

costs[30].Negativeincentive,orpunishmentisusedtoreducethe free-rider’s payoff, andpositive incentive, or reward, can be uti- lizedtoincreasethecontributor’swelfare[31].Confrontationwith thethreatofpunishmentorthepromiseofrewardcaneffectively induceindividualstocontribute inthePGG,butconsiderationsof whichismoreeffectivehavehistoricallyreturneddifferentresults.

Some researchersbelieve thatpunishment istraditionallyconsid- eredtobemoresuccessfulthanrewardsinceitcan haveastabi- lizingeffectoncooperation[32,33];however,anotherstudyshows thatcostlypunishmentissurprisinglyineffectiveinpromotingco- operation[34].Other scholarssuggest thatrewardis preferredas themaincatalystbehindcollaborativeefforts,arewardhasseveral advantagesoverpunishment[35–37].Furthermore,thereisstill a research gap in this area: does a higher ﬁne or a higher bonus instigate higher knowledge contribution? Inspired by these past worksandcontinuingquestions,wecomparetheknowledgeshar- ingbehaviorbyintroducingfourmodelsofthePGGfollowedbyno incentive,a reward,apunishment,andamixedincentivemechanisms.Then,withaJavaprogramminglanguagesimulation,wein- vestigatetheeffectsofﬁnesandbonusesonknowledgesharingas wellastherelationshipbetweenthefrequencyofpunishmentand knowledgesharing.

1.3. Timepressure,peerpressure,andknowledgesharing

Timepressureoccurswhentheenvironmentcreatesa percep- tion of limited time to complete a task, resulting in feelings of stressandtheneedtocopewiththelimitedtimeconstraint[38]. Today,timeisascarceresourceintheworkplace,andeachactivity requiressomeamountoftime[39].Accordingly,employeesareun- likelytoengageinsharingiftheyarefullyutilizedbytheirregular tasksatwork.Signiﬁcantly,employees’responsestotimepressure reducetheamountoftrustandqualityofcommunicationhadbe- tweeneachother[40,41],whichcanaffectanindividual’sattitude towardknowledge sharing [16,42,43]. Resultingly, thesharing be- haviorbecomesdiscontinued [8,12]. Inaddition totime pressure, peer pressure contributes to the extent to which knowledge is shared.Peerpressurecanbedeﬁnedaspressurefrompeerstodo somethingortokeepfromdoingsomethingelse,nomatterifone personally wantstodo itornot [44]; theexistence ofpeerpres- sureleadsto the beliefthat the peergroup demands conformity toits norms [45]. Thenotion thatpeerpressure canbe an effec- tivemotivatorisnotnew[46].Itplaysacriticalrole inpromoting biologicalcooperationandisofteninvokedtoexplainwhygroup- based incentives are surprisingly successfuldespite the incentive to freeride [47].Furthermore,knowledge sharing occursthrough peerinteraction [48].Employees maychoose toshare knowledge asa waytohelp develop personal relationshipswithpeers orto simplymanage theirimpression onothers[1].Prior researchalso showsthat perceivedcoworkersupporthasastrongpositiverela- tionshipwithknowledgesharing[49].Therefore,peerpressureina publicinstitutionresultsinahigherpropensityofknowledgeshar- ingamongcolleaguesandpeers[50].Thesestudiesinformthere- lationshipsbetweenvarious pressuresandknowledgesharing behavior; however,they are all empirical investigations.As there is currentlynostudyregardingtherelationshipsbetweenworkpres- suresandknowledgesharingthatutilizesthemethodsofthePGG andan ensuing simulation,we aim to providesuch through this work.

Theremainderofthispaperisorganizedasfollows.Thespatial PGGmodels areelaboratedupon inSection 2.The corresponding simulationresultsareprovidedinSection3.Lastly,conclusionsare giveninSection4.

Pleasecitethisarticleas:Z.Zhang,F.SongandZ.Song,Promotingknowledge sharingintheworkplace:Punishmentv.reward,Chaos,

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2. Models

Spatial PGG models are presented to analyze the knowledge sharingbehaviorbyintroducingfourmodelsfollowedbynoincen- tive, areward,apunishment,andamixedincentivemechanisms, respectively. Each modelis then usedto simultaneously consider diﬃcultpressuresandcoworkers’attitudesinaworkenvironment.

Forthesefourmodels, allassumptions andwhole framesarethe same;theonlydifferenceisthepayoff.

AllofthePGGmodelsarerunwithalargenetworksizetoob- tain stableresults; inourmodels, PGGisstagedonnetworksin- cluding 1000 players, wherein each person has a different num- berofneighbors(

κ

^).^That^is,^each^playerparticipatesin

κ

+1PGG groups, where one group is centered on themselvesand other

κ

groupsfocusontheirneighbors.Theper capitanumberofneigh- borsisavn,whichissetasa_vn=36;thelargestnumberofneigh- bors is 100. The neighbors are created randomly, which means some playershavemanyneighborswhileothershavefew.Thisis acceptable as long asa player has one neighbor inthe network, whichisinlinewithreality.

There are threetypesof playerin ourmodels,denoted asCA, CT, andHO: CA isa knowledge contributorwith an altruistic intention, CT is a knowledge contributor, andHO is a player who chooses tohoardknowledge.Fortheconvenienceofpresentation, each typeofplayer, CA,CT,andHO,is settoaccountforadiffer- ent proportionofthe total numberofpeople, represented as

ρ

1,

ρ

2,and

ρ

3,respectively. It isassumed that theCA player always choosesthesharingstrategy,becausepeoplewithaltruisticinten- tions aretypicallyenthusiastictohelpothers.Additionally,theCA player getsalong withothersinpleasant, satisfyingrelationships, inwhichknowledge sharingisdirectlyengaged [51].The original value of

ρ

1 isdeﬁnedas

ρ

1>0,asthisconformsbettertoreality [52].Initially,all theplayersaredistributedrandomlyonthenet- work.ForplayerswhoarenotaCA,theyarerandomlyassignedto be a contributorora free-rider, withtheequal probability.Addi- tionally,

ρ

1+

ρ

2=

ρ

3=50%issetasthestartingvalues,suchthat halfoftheplayerschoosethesharingstrategywhiletheotherhalf choosehoardingintheinitialstate.ThisalsomeansthatCAplay- ersarederived fromCTs,i.e., alloftheCAsare CTs,butnotall of theCTsareCAs.

2.1. Model1:noincentivemechanism

Players choose to shareor to hoard knowledge both simultaneously and independently. Each individual contributes one unit (^C=1) ^to ^the ^public ^pool îf ^the ^player âdopts ^the ^strategy ôf knowledge sharing; conversely,a free-riderindividual contributes nothing,butexploitsfromthepublicpooliftheindividualchooses to hoard. The sumof contributions within a group is multiplied by a synergy factor (r>1), such that the value of r needs to be lessthan thenumberof playersinthegroup to ensurethe exis- tenceofthesocial dilemma[35–53].Next,thetotalcontributions isdistributedamongall groupmembers equally,such thatevery- oneinthegroupcanenjoythepublicgoodsfairly.I.e.,afree-rider canalsobenefitfrompublicgoodswithoutcontribution.Thus,the payoff obtainedbyeachplayercanbecalculatedasfollows:

π

i=

j∈i

r

m∈jCm

k_j+1 −C_i

(1)

InFormula(1),playersarenumberedbyparameteri,where

π

i

representsthepayoff ofplayeri.idenotesthesetofPGGgroups inwhichplayeriparticipates,andgroupjisoneofthesetsofi. k_jdenotesthenumberofneighborstoplayeriingroupj;misone elementofgroupj,correspondingly; Cm indicatesthecontribution ofone player ingroupj; C_iindicates the contributionsofplayer i (C_i=0ifplayeriisafree-rider,C_i=1ifaknowledgecontributor).

Inreallife,playersmakedecisionswithinagivenworkenviron- ment.Accordingly,propensitiesofknowledge sharingare affected bythesituationinanorganization.Inourmodels,parameterE is used to representthe propensity of knowledge sharing for each player,whereinEisrelatedtoseveralworkconditions:timepressure, peer pressure, andcoworkers’ attitudes towards knowledge sharing.Onlyafewpreviousstudieshaveconsideredtheroleofin- dividualpersonalityordispositioninknowledgesharing[51],even thoughit hasbeenconfirmedthat an individual’sdispositionhas a significant impact on work attitudes and behaviors [54,55]. To accountfor individualpersonality anddisposition,inour models, Na isdefinedasthenumberoftheplayerswhoexhibitopenness, agreeableness, and conscientiousness as personality traits. These relatepositivelytohigherworkgroupandindividual attitudesto- wardsknowledge sharing[51,56,57]. N_b isdefinedasthenumber oftheplayerswho havegreater self-interest,whichrelates nega- tivelytotheindividual’sattitudetowardsknowledgesharing[58]. ThepercentageratiosforNaandN_bamongall theplayersare ∅a

and∅b, respectively. Additionally,Pa andP_b denote the inﬂuence coeﬃcientsofN_aandN_b,respectively,whicheitherfacilitateorin- hibitknowledgesharing.Accordingly,thepropensityofknowledge sharingissummedasfollows:

E

(

^t⁺¹

)

⁼^E

(

^t

)

⁺^P^p⁻^P^t⁺^Nâ^Pâ⁻^NbP_b (2) whereP_p andP_t denotepeerpressureandtime pressure,respectively. NaPa and N_bP_b are the positive and negative influences of coworkers’ attitudes towards knowledge sharing, respectively.

Lastly,t represents thetime step. Since theentireevolution pro- cessis a dynamicrepeat-play, E changes with time. In the real- worldsystem,peoplecannot beexpectedtosharetheir ideasand insights simply because itis the right thing to do[59]; e.g., po- tentialknowledgecontributorsmayrefrainfroma knowledgeex- changeiftheyfeeltheycanbetterbenefitbyhoardingratherthan by sharing[26].Therefore, Tr 1 is usedas athreshold, indicating thecriticalvalue at whichtheplayer wouldlike toshare knowledge withothers. When E>Tr, the player makes the decision to shareknowledge, otherwise,theplayer isconsidered tobeprofit- driven.Consequently,the playerpursues themaximizedprofitby imitatinga neighbor.For example,player i chooses toupdate its strategyS_ibylearningthestrategyS_jfromtheneighborj,whois chosenrandomly, witha probabilitygivenby thefollowingFermi rule[60]:

W

S_i←S_j

= 1

1+exp

_π_i₋_π_j

μ

⁽³⁾

where

μ

characterizes the bounded rationality or uncertainty of the player during the course of making the decision.

μ

→0 (

μ

→∞) denotes thecompletely deterministic (random)learning.

Here,

μ

=0.1issetasinRef.[60].Additionally,

π

i−

π

jrepresents the difference of payoffs between player i and player j. Notably, thesetwoplayersacquirepayoffsinthesameway.

2.2.Model2:rewardmechanism

Rewardsmayvaryandcanbeusedatalllevelsofhumanorga- nizationstoenhancecooperation,fromgiftgivingtoteamworkre- warding,andfromcommunitytointernationalorganizations[31]. Accordingly,inModel2,asumofbonusesisofferedtotheplayer

1For each type of the players, the initial values of T rare set as this: for player CA , we assume his propensity E > T r, since he seeks cooperation rather than competition [61] ; for player CT , we let his propensity E = T r, as cooperative behavior always emerges in PGG although defection is an optimal strategy [62] ; and for player HO , we set his propensity E < T r, given free riding is the personal strategy that yields the best outcome for employee [19] .

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whentheplayersharesknowledgewithothersforacertainnum- beroftimes.

δ

1denotesthebonusand

τ

1indicatesthecumulative timesforwhichknowledge sharingoccurred. Thus,thepayoff ob- tainedbyeachplayeriscalculatedasfollows:

π

i=

j∈i

r

m∈jCm

k_j+1 −C_i

+

δ

¹ ⁽⁴⁾

2.3.Model3:punishmentmechanism

InModel3,costisaddedby givingthe playerapenalty when theplayerhoardsknowledgeforacertainnumberoftimes,asthe player mayinstead choose a cooperative strategy to avoidlosing proﬁt.

δ

2 denotesthe ﬁneand

τ

2 indicates the cumulative times forwhich knowledgehoarding occurred. Consequently,thepayoff obtainedbyeachplayerissummedasfollows:

π

i=

j∈i

r

m∈jCm

kj+1 −Ci

−

δ

2 (5)

2.4.Model4:mixedmechanism

In Model 4, both reward and punishment mechanisms are adopted simultaneously by following the same rules of Model 2 andModel 3. Inthis case, the payoff obtained by each player is calculatedasfollows:

π

i=

j∈i

r

m∈jCm

k_j+1 −C_i

+

δ

¹⁻

δ

² ⁽⁶⁾

3. Simulationresultsanddiscussions

Javaprogramminglanguagewasusedtosimulatetheevolution processes of knowledge sharing. All simulations were conducted onanetworkwithN=1000anda_vn=36.Toensurethereliabil- ityoftheevolutionary results,alarge numberofsimulations are conducted.Each datapoint isobtained by averaging20 indepen- dentrunswith10,000timesteps foreach.Arepresentativeindex tocharacterize the knowledge sharingbehavior is thefraction of knowledgecontributors(

θ

^),^definedâs^the^ratioôf^the^knowledge

contributorstothetotalnumberofplayers.Initially,

θ

=0.5.

3.1.Incentivemechanisms

Inthissection,punishment,reward,andmixedincentivemech- anismsare compared to identifywhether reward or punishment better facilitates knowledge sharing. Additionally, simultaneously adoptingrewardandpunishmentmechanisms,inthemixedmech- anism, is considered. The simulation results regarding incentive mechanismsarespeciﬁcallyexhibitedasfollows.

Fig.1aimstocharacterizethedynamicalevolutionaryprocesses ofthefractionofknowledgecontributors(

θ

⁾ ^for^four^types^of^in-

centivemechanisms: no incentive (y1), reward (y2), punishment (y3) andmixedmechanism(y4). Fig.1(a)showstheresultsofy1, y2,y3,andFig.1(b)showstheresultsofy1,y2,y3,y4.InFig.1(a), y2andy3arebothhigherthany1,buttheeffectofy3ismoresig- niﬁcantthanthatofy2.Accordingly,eitherrewardorpunishment canpromoteknowledgesharingbehavior,butknowledgecontribu- tionincreasesmorenoticeablywithpunishmentratherthanwith reward.Meanwhile, in Fig.1(b), thegreen curve (y4) is between theblackcurve (y1)andthered curve(y2).Thus,

θ

^is^hardly^im-

provedinthemixedmechanism.Inotherwords,themixedmech- anismisnotagoodchoicetopromoteknowledgesharing.Imple- mentingone incentivemechanismcan betterpromoteknowledge sharingthanimplementingboth.Furthermore,punishmentismore

effective thanreward in sustainingknowledge sharing. Thisphe- nomenonmaybeexplainedbytheprospecttheory[63],i.e.,losses cause a greater emotional impact on an individual than does an equivalentamountofgain.

Since the punishmentmechanism facilitates better knowledge sharingthandoestherewardmechanism,thepunishmentmecha- nismwasinvestigatedmoredeeply.Regarding theeffectofafine on knowledge sharing, we considered: does a higher fine facilitate a higherknowledge contribution? Additionally,the influence of the frequency of punishment on knowledge sharing was also investigated. During the simulation processes, different punish- mentpatternswereimplementedbyadjustingtwoaspects:chang- ing the amount of fines (

δ

2) and altering the cumulative times (

τ

2) a player chooses the hoarding strategy. This means a player would getthe ﬁne

δ

2 when the player withholdsknowledge for

τ

2 rounds. Fig. 2indicates the differentresults ofthe fractionof knowledgecontributors(

θ

⁾^for^different^ﬁnes⁽^Fig.²^(a))^and^differ-

entcumulativetimes(Fig.2(b)).

Accordingly,severalconclusionsaredrawnfromFig.2:(1)Pun- ishmentcan signiﬁcantlypromoteknowledgesharingbehavior. In Fig.2(a),

θ

împroves^noticeablyâfter^the^fineîs^changed^from⁰^to

10,50,200,and300.(2)Ahigherﬁnedoesnot necessarilyyield a better result. Thatis, theamount ofthe ﬁne is nonlinearlyre- latedtothequalityoftheknowledgeshared.AsFig.2(a)shows,

θ

reachesa maximumvalue when theﬁne is50; then,it doesnot increasefurther butremains roughlyatthesamevalue whenthe ﬁneishigherthan50.Thus,withinacertainrange,

θ

^improves^as

thefineincreases.Itiseasytomakeupfortheplayer’slossbybe- comingafree-riderwhenthefineissmall.Thus,thepayoff-driven playerwouldliketoobtainmorebenefitfromchoosingthehoard- ing strategyeven whendoing sorequirespaying asmallpenalty.

However,thesituationchangesastheﬁnereachesacertainlevel.

When the fine exceeds the benefit from being a free-rider, the player altersthe strategy takento avoid thebig fine,and consequently,theknowledgecontributionimproves.Nevertheless,

θ

^has

amaximumvalue whentheﬁne increases.Thus, amoderateﬁne issuggestedasthesatisfactorychoicetopromoteknowledgeshar- ingwiththepunishmentmechanism. (3)

θ

âttains â^higherêqui-

libriumstatewhenthefrequencyofpenaltyishigher.Fig.2(b)il- lustrates the different results of

θ

^for ^four ^values ^of

τ

2:

τ

2=1, 2, 3, and 5, respectively. The lower value of

τ

2 represents the higherfrequencyofﬁning.Itisshownthat

θ

^achieves^the^highest

equilibriumstatuswhen

τ

2=1(blackcurve).Basedon theabove conclusions, thesatisfactorysolutionto facilitateknowledgeshar- ingwiththepunishmentmechanismistosetahighfrequencyof punishment with a moderate ﬁne. Nonetheless, punishment is a kindofnegativeincentivemechanismthatmaycausedissatisfac- tionamongemployees.Thus,organizationsshouldsetanappropri- ate frequencyof punishment(

τ

2) accordingto their realistic cir- cumstances.

Next,therewardmechanismisconsideredasitignitescoopera- tiveness[64].Particularly, weinvestigatedwhetherabiggerbonus maycontributetoabetterknowledgecontribution.Thesimulation resultsregardingrewardmechanismsareexhibitedasfollows.

Fig.3depictsthedifferentresultsofthefractionofknowledge contributors (

θ

⁾ ^for^different ^bonuses.^Generally, ^the^change ^of

θ

is not particularly signiﬁcant when the bonus is adjusted. How- ever,a moderate bonus can promotecontribution betterthan ei- therahighorlowbonus.Wecomparethevaluesof

θ

^under^three

bonuses(Fig.3(a)and(b)):the bonusequals 10(blackcurve),50 (red curve), and100 (blue curve).Herein,

θ

^reaches ^the ^highest

equilibriumstatewhenthebonus is50.Thelow bonusisnotat- tractiveenoughforafree-ridertotransformintoaknowledgecon- tributor.Understandably, theproﬁt-drivenplayerwouldchooseto hoardknowledgesincethebeneﬁtfrombeingafree-riderishigher thanthesmallreward.Similarly,afree-riderconvertstoaknowl- Pleasecitethisarticleas:Z.Zhang,F.SongandZ.Song,Promotingknowledge sharingintheworkplace:Punishmentv.reward,Chaos,

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Fig. 1. Time evolution of the fraction of knowledge contributors θ for different incentive mechanisms. The y 1, y 2, y 3, y 4 graphs represent Model 1, Model 2, Model 3, and Model 4, respectively. Models 1–4 represent four types of incentive mechanisms, respectively: no incentive, reward, punishment, and mixed mechanism. (a) Shows the results of y 1, y 2, y 3; (b) shows the results of y 1, y 2, y 3, y 4. Other parameter settings are as follows: T r= 25 , r = 1 . 8 , ρ1 = 0 . 1 , ρ2 = 0 . 4 , ρ3= 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a= P b= 0 . 002 , P p= P t = 0 . 5 , δ1= 50 , τ1 = 1 , δ2 = 50 , τ2= 1 .

Fig. 2. Time evolution of the fraction of knowledge contributors θfor different ﬁnes (a) and different cumulative times ( τ2) of a player choosing the hoarding strategy (b) with the punishment mechanism. Other parameter settings for (a) are as follows: T r= 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2= 0 . 4 , ρ3 = 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a= P b= 0 . 002 , P p= P t = 0 . 5 , τ2= 1 , and for (b): T r= 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2= 0 . 4 , ρ3= 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a= P b= 0 . 002 , P p= P t= 0 . 5 , δ2= 50 .

edgecontributorwhenthebonus ishighenough.However,when the bonus exceeds acertain range,the process doesnot work as hypothesized. In Fig. 3(b), the blue curve is lower than the red curve, signifying that a high bonus is lesseffectivein promoting knowledgesharingthanisamoderatebonus.Accordingly,thesat- isfactory solutionto promoteknowledge sharingwiththereward mechanismistosetamoderatebonus.

3.2.Pressuresandcoworkers’attitudes

Inthissection,theimpactsoftimepressure,peerpressure,and coworkers’attitudesontheevolutionofknowledgesharingbehav- iorareconsidered.

Fig.4 explainsthe inﬂuences ofpeerpressure andtime pres- sureonknowledgesharing.Intheabsenceofotherexternalcondi-

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Fig. 3. Time evolution of the fraction of knowledge contributors θfor different bonuses in the reward mechanism. (a) Shows the different results when bonuses equal 10 (black curve) and 50 (red curve). (b) Shows the different results when bonuses equal 50 (red curve) and 100 (blue curve). Other parameter settings include: T r = 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2 = 0 . 4 , ρ3 = 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a = P b= 0 . 002 , P p= P t = 0 . 5 , τ1= 1 . (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

Fig. 4. Time evolution of the fraction of knowledge contributors θ under time pressure ( P t) and peer pressure ( P p). Other parameter settings include: T r = 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2= 0 . 4 , ρ3 = 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a= P b= 0 . 002 .

tions,whenPp(peerpressure)isequaltoP_t(timepressure)(green curve),

θ

îs ^maintained âtâ ^stable ^state ôf âround ^20%. ^This în-

dicates that the effects of Pp and Pt can likely be offset. When P_p exceeds P_t (redcurve),

θ

^reaches^70% ⁱⁿ¹⁰⁰ ^time ^steps;^after

another100time steps,

θ

^achieves^theequilibriumstate of100%.

Thus,Pp hasasigniﬁcanteffecton

θ

^,^as^it ^can^promote^the^rapid

increaseof

θ

^. Conversely, whenP_p islessthan P_t (blue curve),

θ

issustained at about20% formost of the rounds until the time

stepiscloseto10,000.Then,

θ

^drops^sharply^to^0,^signifying^that

Pt hasaninhibitoryimpact on

θ

^;^however,^this^affect^is^not ^very

strong.Overall,knowledgesharingiseasiertopromoteandmain- tainwhenP_pexceedsP_t,thuspartiallyillustratingtheimportance oftheroleofPp.

Then, theeffect ofcoworkers’ attitudeson knowledge sharing behaviorwasinvestigated.Speciﬁcally,therolesofN_a(thenumber ofthe playerswith thepersonality traitsof openness, agreeable- Pleasecitethisarticleas:Z.Zhang,F.SongandZ.Song,Promotingknowledge sharingintheworkplace:Punishmentv.reward,Chaos,

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Fig. 5. (a): Time evolution of the fraction of knowledge contributors θfor P aand P b. N ais the number of the players with personality traits of openness, agreeableness, and conscientiousness; N bis the number of the players who have greater self-interest. ∅ aand ∅ bare the percentage ratios for N aand N bamong all the players, respectively.

Meanwhile, P aand P bare the inﬂuence coeﬃcients of N aand N b, respectively, which either facilitate or inhibit knowledge sharing. Other parameter settings include: T r = 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2 = 0 . 4 , ρ3= 0 . 5 , ∅ a= ∅ b= 0 . 5 , P p= P t= 0 . 5 . (b) Time evolution of the fraction of knowledge contributors θfor varying ∅ a. Other parameter settings include: T r= 25 , r = 1 . 8 , ρ1= 0 . 1 , ρ2= 0 . 4 , ρ3= 0 . 5 , P a= P b= 0 . 002 , P p= P t= 0 . 5 , ∅ a+ ∅ b= 1 .

ness, andconscientiousness),N_b (the numberofthe playerswho havegreaterself-interest),P_a(theinfluencecoefficientofN_a),and P_b(the influencecoefficientofN_b)areconsidered inthePGG. For theconvenienceofexplanation,∅a and∅b aredefinedastheper- centage ratios forN_a and N_b amongall the players, respectively.

Fig.5(a)indicatestheinﬂuences ofPa andP_bonknowledgeshar- ing;theresultshowsthatPa (thepromotioneffect)hasastronger inﬂuenceon

θ

^than^Pb(the inhibitioneffect).Thus,Pacontributes to the quick improvement of

θ

^, ^which ^achieves ^an equilibrium state of100%.Fig.5(b)demonstratesthe impactsof∅aand∅bon knowledgesharing.When∅a=∅b=0.5,

θ

^remains^at^a^stable^sta-

tusofapproximately20%(blackcurve).Forthenextstep,thevalue of∅a isalteredto0,0.1,and0.3respectively(green,red,andblue curves,respectively);contributionsdiegradually,andﬁnally,allthe players turn into free-riders asthe time steps reach 63, 78, and 136, respectively. Alternatively, when ∅a is set to equal 0.55 and 0.6, respectively,theknowledgesharingstrategy isadoptedby all playersafteronly afew rounds,and

θ

^quickly^achieves^the^equi-

librium state of 100%.Therefore, the facilitating effects from the work environmenthaveimportant inﬂuenceson knowledgesharing;theycaninﬂuence

θ

^to^grow^rapidly^and^reach^anequilibrium statusof100%.TheeffectsofPaand∅aon

θ

^are^stronger^than^that

of P_b and ∅b, signifying the relative ease with which knowledge contribution can be improved andmaintained when Pa is bigger thanP_b,orwhen∅^aisbiggerthan∅b.

3.3. Otherparameters

To analyze the models comprehensively, other important pa- rameters,including r(the synergyfactor) and

ρ

1 (the percentage ofCA,knowledgecontributorwithaltruisticintention),needtobe tested.Thesimulationresultsareelaborateduponinthefollowing content.

Fig.6illustratestheeffectsofdifferentvaluesofr(synergyfactor) on knowledge sharing. Four casesare compared here, when ris setto be1.2, 1.8, 3,and5,respectively. As shown,

θ

^reaches

its highestpoint whenr=3(blue curve),signifying that optimal

Fig. 6. Time evolution of the fraction of knowledge contributors θ for different values of r (synergy factor). Other parameter settings include: T r= 25 , ρ1= 0 . 1 , ρ2= 0 . 4 , ρ3 = 0 . 5 , ∅ a = ∅ b= 0 . 5 , P a= P b= 0 . 002 , P p= P t = 0 . 5 .

valueofr(=3)êxists,âllowing ^theêvolution^toâchieveîts^high- point.

Asaminimalnumberofcooperatorsareneededtoelicitcoop- eration[52],adeeper investigationintothe inﬂuenceofCA play- ersonpromoting knowledge sharing isstill needed. As in Fig.7,

θ

^could^be^greatly^increased^as

ρ

1isincreased,suggestingthat

ρ

1

hasasigniﬁcanteffecton

θ

ând^can^promote^the^rapidîncreaseôf

θ

^.

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Fig. 7. Time evolution of the fraction of knowledge contributors θ for different values of ρ1. Other parameter settings include: T r= 25 , r = 1 . 8 , ρ1+ ρ2= 0 . 5 , ρ3= 0 . 5 , ∅ a= ∅ b= 0 . 5 , P a= P b= 0 . 002 , P p= P t= 0 . 5 .

4. Conclusion

Previousstudieshaveelucidatedthatbothpunishmentandre- ward can improve knowledge sharing to some extent; however, whichone better encouragesknowledge sharing hasbeen debatable. Additionally,the ability of either a higher ﬁne or a higher bonusto leadtoa betterknowledge sharingperformance hasre- mainedlargely uninvestigated.Therefore,weanalyzedtheknowl- edge contributionbehavior by introducing four models of a PGG followed by the following incentive mechanisms: no incentive mechanism, areward mechanism, apunishment mechanism, and a mixedincentive mechanism. Each model wasused to simulta- neouslyconsider the effects ofdiﬃcult pressures and coworkers’

attitudesintheworkenvironment.WithaJavasimulation,thefol- lowingconclusionswereascertained:

First, either punishment or reward can promote knowledge sharingbehavior; however,punishment can lead to a much bet- terperformancethan reward.Contrarytowhat wasexpected,the mixedmechanism isnot aseffectiveaseitherpunishmentor reward in facilitating knowledge sharing. Second, the amount of a ﬁneisnonlinearlyrelatedtotheknowledge sharingperformance.

Withinacertainrange,

θ

împrovesâs^the^fineîncreases;^however,

θ

^reachesâ^maximum^value^when^the^fine^reachesâ^certain^level.

Accordingly,amoderateﬁneissuggestedasthemostsatisfactory choicetopromoteknowledgesharingwiththepunishmentmech- anism.Additionally,knowledgesharingcanattainahigherequilib- riumstate when thefrequency ofpenalty is higher.Nonetheless, punishmentis a kind ofnegative incentivemechanism that may causedissatisfactionamongemployees.Thus,organizationsshould setan appropriatefrequencyofpunishmentaccordingtotheir re- alisticcircumstances.Third,thechangeof

θ

îs^notparticularlysig- nificantwhenthebonusamountisadjusted;however,amoderate bonus can promote knowledge contribution better than either a highorlowbonus.Thus,themostsatisfactorysolutiontopromote knowledgesharingwiththerewardmechanismistosetamoder- atebonus. Fourth, theinfluences ofpeerpressure, time pressure, andcoworkers’attitudesonknowledgesharingwere investigated, whereinthey alldemonstratedcrucialrolesinknowledgesharing behavior.Furthermore,itiseasiertoimproveandmaintainknowl-

edgecontributionunderthreeconditions:(1)whenpeerpressure is stronger than time pressure, (2) when the attitude of sharing fromcoworkersisstrongerthanthatofhoarding,and(3)whenthe numberofplayerswhohavepersonalitytraitsofopenness,agreeableness, or conscientiousness is greater than that ofthose with greater self-interest. Lastly, the synergy factor r andthe number ofCAplayersbothhaveimportantinﬂuencesinpromotingknowl- edgesharing.Moreover,thereexistsan optimalvaluer(=3)^that allowstheevolutiontoachieveitshighestpoint.

From the above conclusions, the following management sug- gestions are proposed topromote knowledge sharingin an organization. First, it is necessary to create an open and caring organizational climate, as such an environment is essential to en- couraging knowledge sharing. Organizational climaterefers to an organization’s value system in terms of risk taking, reward systems, andprovidinga warm andsupportive environment [65].A goodclimatecanfacilitateknowledgesharing[66]forseveralrea- sons:(1) Itencourages interactionamong individualsand, consequently, the exchange of learningand knowledge. (2)It helps to reduce the cost ofcommunication betweenemployees whileen- hancing the synergy factor of knowledge sharing. (3) The influ- enceofthegroupnormorsubjectivenorm,suchaspeerpressure, can prompt employees to adopt the strategy of knowledge sharing.Secondly,tomoreeffectivelyovercometheknowledgesharing dilemmainanorganization,punishmentshouldbeadoptedrather thanreward.However,a higherfineorhigherbonusdoesnotin- duce better knowledgesharing. Rather,amoderate fineorbonus is the more satisfactory choice for the organization to promote knowledge sharing.Thirdly,leadersshould paymore attentionto an individual’s personality trait. Different personality traits tend to exhibit different behaviorsand attitudes; namely, whetheran employee has a facilitating orinhibiting attitude towards knowl- edgesharingisrelatedtotheindividual’spersonality.Additionally, different personalitiesare perhaps better suit a differentlevel of pressure. If leaderscould provide the appropriate level andtype of pressure based on an individual’s personality trait, employees maybe better encouraged to shareknowledge and thuscreate a betterlearningenvironment.Lastly,itisbeneficialtohelpemploy- eesdealwithtimepressurewhilereducingthenegativeimpactof timepressure.Thisnotonlypromotesknowledgesharing,butalso ensuresthephysicalandmentalhealthofemployees.Therefore,it is conduciveto theoverall wellbeing of employees,andthus the developmentofthecompetitiveadvantagesofanorganization.Ul- timately,thisworkinformstheuseofincentivemechanismsinthe workplace and seeks a further understanding ofworkplace pres- suresthatimpactknowledgesharing.

DeclarationofCompetingInterest None.

Acknowledgements&funding

ThisworkwasfundedbytheChineseNationalFundingofSocial SciencesunderGrantNo.16BGL138.

WearegratefultoMichaelAllenWatson,andKaladeviSakthivel fortheirsuggestionsandproofreading.

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