An Intelligent Agent Negotiation Strategy in the Electronic Marketplace Environment

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1 An Inellgen Agen Negoon regy n he Elecronc Mreplce Envronmen Mlm Lou, Ionn Rouss, Lmbros Pechlvnos 3 Technologcl Educonl Insue of Wesern Mcedon, Deprmen of Busness Admnsron, Kol, Kozn 5, GREECE e-ml: lou@elecom.nu.gr Nonl Techncl Unversy of Ahens, 9 Heroon Polyechneou r., 5 773, Ahens, GREECE e-ml: nnro@elecom.nu.gr 3 Ahens Unversy of Economcs nd Busness, 76 Psson r., 4 34, Ahens, GREECE e-ml: lpech@ueb.gr Absrc: E-commerce wll srongly penere he mre f coupled wh ppropre echnologes nd mechnsms. Moble gens my enhnce he nellgence nd mprove he effcency of sysems n he e-mreplce. We propose dynmc mullerl negoon model nd consruc n effcen negoon sregy bsed on rnng mechnsm h does no requre complced ronle on behlf of he buyer gens. Ths sregy cn be used o exend he funconly of uonomous nellgen gens, so h hey qucly rech o n greemen mng o mxmse her owner s uly. The frmewor proposed consders boh conrc nd decson ssues, s bsed on rel mre condons, nd hs been emprclly evlued. Moreover, s shown h n lner frmewor le he one we employ more elbore rnng mechnsms do no necessrly mprove effcency. Keywords: Inellgen Agens, Negoon Proocol & Model, regy, Rnng Mechnsm. INTRODUCTION The ongong lberlson nd deregulon of he elecommuncon mre wll nroduce new cors (Zudweg e l., 999). In prncple, he mn role of ll plyers n such compeve envronmen wll be o consnly monor he user demnd, nd n response o cree, promoe nd provde he desred servces nd servce feures. The followng re some ey fcors for success. Frs, he effcency wh whch servces wll be developed. econd,

2 he quly level, n relon wh he correspondng cos, of new servces. Thrd, he effcency wh whch he servces wll be opered (conrolled, mnned, dmnsered, ec.). The chllenges oulned bove hve brough o he foreground severl new mporn reserch res. ome of hem re he defnon of new busness models, he elboron on e- busness conceps (Ghosh, 998; Feld nd Wdner, ), he specfcon of servce rchecures (As) & servce creon envronmens (CEs) (Tg, 996) nd he exploon of dvnced sofwre echnologes, (e.g., dsrbued objec compung nd nellgen moble gens (Glho, 998)). The m of hs pper s, n ccordnce wh effcen servce operon objecves, o propose enhncemens o he sophscon of he negoon funconly h cn be offered by e-commerce sysems n open compeve communcons envronmens. Ths sudy s bsed upon he noon of nercng nellgen gens whch prcpe n rdng cves on behlf of her owners, whle exhbng properes such s uonomy, recvon, nd pro-cvon, n order o cheve prculr objecves nd ccomplsh her gols. Moble nellgen gens cn c s medors n fve of he sx e-commerce phses (He e l., 3): need denfcon, produc broerng, buyer colon formon, merchn broerng nd negoon. Afer user s need hs been denfed (need denfcon), he gen cng on behlf of he user s nvolved n deermnng wh produc o buy o ssfy he specfc need (produc broerng) nd fndng n ppropre merchn o purchse he good from (merchn broerng), eher lone or formng group wh oher smlr buyers (buyer colon formon), hus explong poenl economes of scle. The nex sep s o negoe he erms nd condons (e.g., delvery me, gf servces, wrrny, quly of servce, performnce) under whch he desred produc wll be delvered (negoon phse). However, s ofen he cse h he mos ppropre merchn s denfed fer he gen hs negoed wh ll cndde merchns (Lou e l., ). Negoon my be defned s he process by whch jon decson s mde by wo or more pres. The pres frs verblse conrdcory demnds nd hen move owrds greemen by process of concesson or serch for new lernves (Pru, 98). In humn negoons, he pres brgn o deermne he prce or oher rnscon erms. In uomed negoons, sofwre gens engge n brodly smlr processes. In more del, he gens prepre bds for nd evlue offers on behlf of he pres hey represen mng o obn he mxmum benef for her owners, followng specfc negoon sreges. Auomed negoon s very brod nd encompssng feld. For hs reson, s mporn o undersnd he dmensons nd rnge of opons h re vlble. When Correspondng Auhor: Asssn Professor Mlm D. Lou

3 buldng uonomous gens cpble of sophsced nd flexble negoon, hree brod res need o be consdered (Frn e l., 998): () wh negoon proocol nd model wll be doped, () wh re he ssues over whch negoon wll e plce, nd () wh negoon sreges wll he gens employ. The negoon proocol defnes he rules of encouner beween he gens (Rosenschen nd Zlon, 994). Then, dependng on he gols se for he gens nd he negoon proocol, he negoon sreges re deermned (Rouss nd Lou, 3). Gven he wde vrey of possbles, here s no unverslly bes pproch or echnque for uomed negoons (Jennngs e l., ), rher proocols, models nd sreges need o be se ccordng o he prevlng suon. Ths pper concenres predomnnly on he frs ssue, proposng negoon proocol o be employed n n uomc mul-lerl mul-ssue negoon model nd on he hrd pon provdng n effcen negoon sregy for he elecronc Busness-o-Consumer (BC) mreplce. In hs frmewor, he roles of he negoon gens my be clssfed no wo mn cegores h, n prncple, re n conflc. Thus, he negong gens my be dvded no wo subses: { Agens} { elleragens} { BuyerAgens} =. The Buyer Agens (BAs) nd he eller Agens (As) re consdered o be self-neresed, mng o mxmse her owners prof. The purpose of hs pper s wofold. Frs, o explo mul-round negoon mechnsm, whch demonsres nheren compuonl nd communcon dvnges over sngle sep mechnsms n such complex frmewors (Conzer nd ndholm, 3). In essence, he gens hold prve nformon, whch my be reveled ncremenlly, only on n s-needed bss. Ths s ofen he cse when he dsclosure of nformon s no ccepble, possble, or desred by he pres nvolved n he rnscon (e.g., he Buyer s no wllng o revel he mxmum prce o py for specfc servce o eller n fer of frs-degree prce dscrmnon wh he eller (unfrly) cpurng he whole surplus n he mre). The negoon envronmen consdered covers mul-ssue conrcs nd mul-pry suons, whle beng hghly dynmc one, n he sense h s vrbles, rbues nd objecves my chnge over me. econd, o provde n effcen negoon sregy, for he cse where he negoors fce src dedlnes, whch s n mos cses prve nformon (Vuln, 999), nd sss gens o rech o ssfcory greemen whn he specfed me-lms. The res of he pper s srucured s follows. In econ, he negoon proocol nd model doped re presened. A smple conrc rnng mechnsm s employed nsed of he usul lernng sequenl offers pern, whle he concep of decson ssues s hp:// 3

4 nroduced. econ 3 presens he desgned negoon sregy, whch demonsres exceponl effcency n cses where he Buyer s no ble o provde ll hs/her requremens n compleely qunfed wy, whle beng cpble of selecng he conrc h bes ssfes hs/her needs. In econ 4, se of resuls demonsrng he effcency of he proposed frmewor s provded, whle comprson wh oher frmewors s gven. Fnlly, n econ 5, conclusons re drwn nd drecons for fuure plns re presened.. NEGOTIATION PROTOCOL & MODEL In order o cree successful negoon frmewor, he desgn of n ppropre proocol h wll govern he nercons beween he negoon prcpns s necessry. Dependng on he specfc negoon problem h needs o be solved, proocol s he se of rules h correspondngly consrn he proposls h he negoon pres re ble o me. In hs secon, fer brefly revewng exsng negoon proocols, we dscuss on proocol bsed on rnng mechnsm on he Buyer s sde, whch s doped n he conex of hs sudy. ubsequenly, n effcen dynmc negoon model s presened, bsed on he mulssue vlue scorng sysem nroduced by Rff (Rff, 98), n he conex of blerl negoons. Our m s o exend hs frmewor no mul-pry, mul-ssue, dynmc model. Bsed on he desgned negoon proocol, he proposed model s exploed by he eller o cree subsequen conrcs, nd by he Buyer o evlue he conrcs offered. In subsecon., n overvew of he reled reserch wor s provded, whle n subsecon. he desgned negoon proocol nd model re presened.. Reled wor Mechnsm desgn nvolves he desgn of proocols for governng mul-gen nercons, such h hese proocols hve cern desrble properes (Rosenschen nd Zlon, 994; ndholm, 999): compuonl effcency, communcon effcency, ndvdul ronly, dsrbuon of compuon, mxmzon of socl welfre. I s dffcul o desgn negoon proocol h clerly demonsres ll he qules foremenoned. Neverheless, hese properes cn be used s reference pon of wh n del proocol should offer o he negoon pres. In (Jennngs e l., ) generc frmewor for uomed negoon s presened. The smples proocol, whch mnmses he complexy of he ronle behnd he decson models of he gens, specfes h he gens cn only ccep or rejec ohers proposls. Neverheless, n complex cses where mulple ssues re consdered, hs convenon my led o very me-consumng nd neffcen process, snce he gens hve no mens o verfy why he specfc proposl s unccepble, or owrds whch drecon of he negoon spce hey should move. Hence, he proposer s essenlly offerng conrcs on 4

5 he bss of hs belefs s o wh he oher pry prefers. In order o mprove on he effcency of he negoon process, he respondng gen should be ble o rnsm o he offer generng pry some feedbc on he proposl receves. One possble form hs feedbc my e s crque, whch s ls of commens on elemens of he proposl he gen les or dsles. A specfc crque my sugges consrns on prculr negoon ssues (e.g., I m wllng o py for he specfc servce requesed up o P mx ), or my ndce he specfc ssues of he proposl h re volng he pry s consrns consung hus he offer unccepble (e.g., he quly of he servce s fne, bu he prce s oo hgh). The feedbc sen by he recpen of proposl o he offer generng pry my e he form of couner proposl. I s n lernve proposl more fvorble o s sender, genered n response o n offer, hus ncresng he probbly of n greemen. Couner proposls my chnge prs of he proposl (.e., he vlue of some of he ssues under negoon), or exend he nl proposl (.e., nroduce new ssues o be consdered). Couner proposls dffer from crques n he sense h he feedbc he proposer receves s less explc. The nl proposer hs o consder he couner proposl nd nfer he oher pry s preferences/consrns from he wy s re-composed. However, he couner proposls scheme ofen enbles he nl proposer o denfy he conrc spce of he couner pry. The foremenoned proocol ypes my be exended n order for he pres o be ble o jusfy o her opponen prculr poson hey hve employed n he conex of negoon (e.g., he delvery de of prculr cr could no be erler s he cr eller s ou of soc), or even ry o persude hem o chnge her negoon ude (e.g., he cr eller provdes rdo CD gf n order o me hs/her offer more rcve or o convnce he Buyer h specfc feure of he cr provded s more mporn hn he one whch currenly consues he offer unccepble for he Buyer). Thus, he bly o provde some form of ddonl nformon (jusfcon for negoon ude, rgumens for specfc poson, ec) my led o he esblshmen of greemens n more me-effcen mnner. There s wde rnge of rgumen ypes he negong pres my dop (Krlns nd Abelson, 97; Krous e l., 998). Common cegores nclude: hres (flure o ccep hs proposl would resul o negve consequences), rewrds (f you ccep he proposl you wll receve posve pyoff), nd ppels (hs opon should be preferred over he lernve one for some reson). In generl, he role of he rgumenon bsed negoon s eher o modfy he recpen s ccepble conrc regon or s evluon funcon. Concernng he negoon models, exensve reserch hs been performed n he economcs (mnly n gme heory) nd n he rfcl nellgence (AI) felds. Consderng non-cooperve gme heory, mul-ssue negoons re no rcble, s relevn problems 5

6 re mnly ddressed by her decomposon no ssue-by-ssue negoons (Rff, 98; Bc nd Rff, 996; Fershmn, ; Rubnsen, 985; Pons nd ovcs, 998; Busch nd Horsmnn, ; Chen, ; In nd errno, 4). The relevn negoon procedures cn be sepre, smulneous or sequenl (Inders, ; Gerdng e l., ). In he conex of cooperve gme heory (Hesnen e l., ; Hesnen, 999; Kl, 977; Pons nd Wson, 997; Myerson, 98; Ehmo e l., ; Peers, 986; Rh, ), reserchers hve ld focus on he desgn of mehods h led o Preo-opml soluons by ssumng h gens coopere nd cn solve mul-crer-decson-mng problems. everl AI reserch groups hve suded mul-ssue negoons crred ou by uonomous gens (Frn e l., 998; Krus nd Lehmnn, 995; Fm e l., ; Fm e l., 4; Luo e l., 3; L nd Tesuro, 3; yr, 989; yr, 99). Usully hey m desgnng uomed mul-ssue negoon models nd rcble negoon sreges, whle hey ofen ulse heursc or lernng mehods n hs respec. In nushell, hree mn reserch drecons cn be dsngushed n economcs nd AI domns h del wh mul-ssue negoons: ssue-by-ssue negoons, cooperve mul-ssue negoon, nd mul-ssue negoon bsed on heurscs. One of he mos well-nown pproches deque for mul-ssue negoons ws proposed by Rff (Rff, 98). In hs negoon frmewor, wn-wn suons cn be cheved, s one pry s gn ncrese does no necessrly led o ncreses on noher pry s losses. Addonlly, Rff hs ddressed vrous specs of mul-ssue negoons such s: uly funcons, negoon gends, rdeoffs, sregc msrepresenons, ec. However, hs been rgued n he lerure (e.g., (Frn e l., 998)) h Rff s frmewor s bsed on severl mplc ssumpons h, even hough hey my led o good opmson resuls, hey re nppropre for he needs of he e-mreplce. uch ssues re he followng: () prvcy of nformon for he negoors s no suppored, () he uly funcon models mus be dsclosed, () he vlue regons for he conrc ssues for boh pres mus be denfed n dvnce, (v) he only prmeers h deermne he uly of he conrcs for he negoors re he vlues of he ssues under negoon.. The proposed negoon proocol & model In reled reserch lerure, he nercons mong he pres follow mosly he rules of n lernng sequenl proocol n whch he gens e urns o me offers nd couner offers (Rubnsen, 98). Ths model however necesses n dvnced resonng componen on behlf of he BA s well s he A. In hs sudy, we nlly cle smpler cse where BA does no gve couner offer (whch nvolves ncorporng o he model ll BA s rde-offs beween he vrous rbues) o he A bu nsed rns he A s offers. Ths rnng s hen provded o he A, n order o sequenlly genere hopefully beer 6

7 proposl (move o dfferen regon of he conrc spce) nd fnd muully ccepble conrc. Ths process connues unl muully ccepble conrc s reched. Ths s more effcen n cses where he BA s no ble o exrc ll user requremens nd preferences n compleely qunfed wy, whle beng cpble of selecng, clssfyng or rng he conrc(s) proposed. Essenlly, he rnng of he proposls s form of crque, whou however provdng oher nformon bou prs of he conrcs offered. In hs sense, he rnng concep, even hough requrng lmed resources on behlf of he BA, my led o n exensve negoon phse s no oher explc nformon bou specfc preferences or consrns wll be provded o he A. The rnng concep doped n hs pper s borrowed from Conjon Anlyss (Crne, 99), que populr mreng ool for denfyng nd mreng new produc feures, relevng he consumer of specfyng hese feures explcly. The proocol doped n he conex of hs sudy cn be descrbed s follows. Once he gens hve deermned he se of ssues over whch hey wll negoe, he negoon process consss of n lerne successon of conrc proposls on behlf of he A nd subsequen rnng of hem by he BA ccordng o s preferences nd curren condons. Thus, ech round, he A sends o he BA N conrcs (.e., N pces conssng on n - ples of vlues of he n conrc ssues), whch re subsequenly evlued by he BA nd rn vecor s reurned o he A. Ths process connues unl conrc proposed by he A s cceped by he BA or one of he gens ermnes he negoon (e.g., f he me dedlne s reched whou n greemen beng n plce). Even hough negoon cn be ned by As or BAs, only he As propose concree conrcs, s here s no couner offer generon mechnsm for he BAs. In hs pper, we consder he cse where he negoon process s ned by he BA who sends o he A n nl Reques for Proposl (RFP) specfyng he ypes nd nure of he conrc ssues nd he vlues of ll non negoble prmeers. The mn ssue s ssumed o be he prce of he good/servce under negoon, whle vrous oher ssues my be consdered s well. Concernng he negoon model, he Mul Arbue Uly Theory (MAUT) hs been consdered (Keeney nd Rff, 993), whch hs evolved o one of he mos mporn opcs n mulple crer decson mng (Prdlos e l., 995; Fguer e l., 5; Brugh, 4) nd hs mny pplcons n complex rel world problems. MAUT ms o represen nd model he decson mer s preferences hrough uly funcon u(g) ggregng ll he evluon rbues, where g s he vecor of he evluon rbues g, g, g n. When he decson problem s deermnsc, he problem of choosng he bes lernve s reduced o he problem of ssgnng vlue funcon V(g, g, g n ) over he evluon crer. The opml lernve s hen he one h hs he lrges vlue s deermned by he vlue funcon. Consderng se of muully ndependen evluon rbues, he vlue for he se 7

8 cn be found by summng he vlue of ech evluon rbue (lner ddve model), whch s perhps he smples pproch o vlue modellng. For mny suons lner vlue model s deque. In ohers s ofen good frs pproxmon o furher refne or use for sensvy nlyss. However, for some suons, mulplcve vlue funcon or Cobb- Dougls funcon my be more ppropre. In (Krp, 3) he ddve uly funcon s exended n order o cover mulple smulneous vlues for n rbue under negoon. The proposed dynmc negoon model s bsed on he mul-ssue vlue scorng sysem nroduced by Rff (Rff, 98) nd used o buld model for blerl negoons bou se of qunve vrbles. As lredy menoned, n Rff s pproch, he only prmeers h deermne he uly of he conrcs for he negoors re he vlues of he ssues under negoon. Neverheless, here re usully severl ssues, h even hough her vlues re no under negoon nd hey re no ncluded n he conrc prmeers, hey ffec he evluon of he vlues of he conrc ssues. Whou beng exhusve, such ssues my conss of: he number of compeor compnes, he number of subsue or complemenry producs/servces, he quny of produc n soc, he number of curren poenl buyers, he repuon/relbly of ech eller/buyer, he me unl he negoon dedlne expres, he resources vlbly nd resrcons, ec. We wll refer o hese ssues s decson ssues (DIs). The vlues of he DIs my chnge overme, dependng on he e- mreplce condons nd on he eller s nd Buyer s se. The DIs do no only ffec he evluon of he conrcs, bu hey lso hve n mpc on he generon of subsequen offers. A hs pon should be noed h DIs vlues do no necessrly depend on he cons of he negong pry hey ffec, whle hey my ffec one or boh negoors. The vlues of he DIs should hve srong nd drec nfluence on he behvour of he negong gens, whch should be ble o evlue he uly of he conrcs under he curren crcumsnces n he e-mreplce nd c ccordngly. From he bove nlyss, s cler h opml soluons cnno be found n he e- commerce domns, s compuonl nd communcon resources usully mpose non-zero negoon duron, nd me-vryng ssues my chnge he negoon condons for boh pres. Thus, we propose dynmc model for gen negoon h cn be exploed by sreges n order o consruc conrcs ccepble o he opponen pres bu whch, neverheless, mxmse he gen s own uly funcon. The gens h represen ellers wll be denoed by {,,... } represen poenl Buyers wll be denoed by B = { B, B,... } = nd he ones h. For presenon smplcy resons, we wll n he followng nlyss confne our descrpon o he relevn blerl negoon problem. However, our proposed frmewor my redly be exended o mul pry suons consderng N x M ndependen negoon hreds, under he ssumpon h 8

9 here re no furher sregc nercons beween he Buyers or he ellers. In essence, hs mens h neher he eller, nor he Buyer chnge her sreges n he conex of negoon, ng no ccoun possble nermede oucomes from he res of he negoon conexs whch hey my be nvolved. The DIs vlues, however, my be ffeced by he dynmclly chngng e-mre plce condons. For exmple, n ncresed number of negong Buyers (poenl cusomers) for he sme produc my resul o hgh prced eller s offer, or on he oher hnd, ssumng ncresed eller compeon, he ellers could lm her mrgnl prof n order o succeed n esblshng n greemen wh he Buyer, ec. Our nlyss drws hevly from Rouss nd Lou (3). Le ( B) represen he negong gens of he wo pres nd ( {,..., n} ) he ssues under negoon,.e., he ssues, he vlues of whch re ncluded n he proposed conrcs. The number of hese ssues n rel world negoons s lwys fne. Le c [ m, M ] be vlue for he conrc ssue ccepble by gen. I should be menoned here h we only consder ssues he vlues of whch le whn delmed rnge defned by ech conrc proposng gen. Le C = { c,..., c } n denoe conrc, or n oher words selecon of vlues for ll he conrc ssues, h s vlue n he mul-dmensonl spce defned by he n ssues vlue rnges. For he vlues of he DIs we wll use he followng noon: d, j j =,..., m. We my now nroduce he uly funcon of he proposed frmewor s follows. Le [ m, M ] [,] U : denoe he uly h gen ssgns o vlue of conrc ssue n he rnge of s ccepble vlues. Le w be he mpornce of ssue for gen. Moreover U c ) s ssumed o be connuous nd monoonc. The weghs w re deermned bsed ( on he preferences, prores nd objecves of he pry represened by gen. Th s, n cse he negoor vlues more conrc ssue hn conrc ssue j, hen should snd h: n = w w > wj. We ssume he weghs of ll gens re normlsed o dd up o,.e., =. Usng he bove noon, he gen s uly funcon for conrc n = = { c cn} cn be defned s follows: U ( C ) = w U ( c d j ) C,..., j =,...,m, s he vlue of decson ssue d he me j, when conrc =,, where d =, C s proposed. In he conex of hs sudy, he Buyer s/eller s uly funcon for conrc consders lner ddve model ncorporng he ules of ech conrc ssue h s nvolved n he j 9

10 negoon. In essence, we ssume h he vrous ssues re subsues, e.g. prce nd quly. Lnery cn lso be resul of ssumng rs neurl gens. (Keeney nd Rff, 993). However, should be noed h he uly funcon of ech ndvdul conrc ssue my be of ny connuous nd monoonc funconl form, eher concve or convex, (e.g., lner, polynoml, exponenl, mulplcve, qus-lner, ec) of he conrc ssue vlue nd he decson ssue vlue he me he conrc s proposed, whou ffecng he bsc des of our proposed negoon model nd sreges. In order for he uly funcon of ny conrc ssue for ny negoor o le whn he rnge [,], he vlue of ssue mus le whn he rnge of s ccepble vlues. To ensure hs, we nroduce he noon of vlue consrns, h s expressed s follows: m c M. In cse he vlue consrns hold for ll conrc ssues, he uly funcon cn be used o mesure he ssfcon of negoor s fr s he proposed conrc s concerned. Neverheless, ofen, he vlue consrns re no me for some conrc ssues, hus consung he conrc compleely unccepble, regrdless of he uly level. In hs cse, here s no much vlue n usng he bove specfed uly funcon o mesure he ssfcon degree of hs negoor, s he conrc s compleely unccepble. In h sense, gens exhb lexcogrphc preferences. Thus, we my nroduce vlue consrn vldy vecor: [ VCV ] VCV =,,..., n =, where VCV {,}, dependng on wheher he vlue consrn for negong pry s me for conrc ssue (.e., VCV = ) or no (.e., VCV = ). In order o refer o he cse where he mere presence or bsence of prculr feure s requred by negoor, we could dd boolen consrns o our model. However, s hey cn be reduced o vlue consrns, hey wll no be furher nlysed. In prncple, As nd BAs presen conflcng neress n he vlues of he conrc ssues. Thus, he uly funcons mus verfy h gven eller gen nd Buyer gen B B negong he vlue for conrc ssue, hen: [ ( U ) c ] [ ( U ) c ] <,.e., under he sme condons, n cse hgher vlues of conrc ssue resul n hgher (lower) uly for he A he sme me hey resul n lower (hgher) uly for he BA. Neverheless, mus be menoned h here re cses where he As nd BAs my hve muul neres for he vlue of conrc ssue (Rff, 98). As lredy menoned, he BA rns he conrcs proposed by he A. For he smples rnng funcon, he rns h my be ssgned o ny conrc proposed re boolen vrbles,.e., one nsnce of he se { ccep, rejec}. In more sophsced pproch, he c represens he vlue of he conrc ssue for he conrc.

11 rns le whn rnge [ m r, M r ], where ny conrc red wh less hn M s no r ccepble by he BA, whle, when conrc s red wh M, hen he proposed by he A r conrc s cceped by he BA. The second formulon of he rnng funcon rnge (whch s doped n hs verson of he sudy) s more flexble hn he smple { ccep, rejec} rng sysem, s hghly conrbues o reducng he duron of he negoon procedure. In order o sgnl he cse where les one vlue consrn s no me for he BA for cern conrc, we nroduce noher prmeer clled conrc vlue consrns vldy h wll be denoed by CVCV = VCV n = CVCV for conrc C nd s gven by he followng equon:. Bsed on he prevous nlyss, n cse ll vlue consrns re me for conrc C, snds h CVCV =. On he oher hnd, n cse les one vlue consrn s no vld for conrc defnely rejeced. C, snds h CVCV =, nd hen he prculr conrc s In order o nroduce he me prmeer n our negoon model, we represen by { C C } P,..., = he vecor of he N conrcs proposed by he eller gen o he N Buyer gen B me, by C { c,..., c } n = he vecor of he n conrc ssues vlues proposed by o B me for he -conrc of hs proposl ( =,..., N ), nd by ( =,..., n ) he vlue for ssue proposed by o B me for he -conrc of hs proposl. Le now R { r,..., r } = be he vecor of rnng vlues h B ssgns me o N c he prevous conrcs proposl mde by, nd r ( =,..., N ) be he rn h B ssgns me o he -conrc of hs proposl. The rnge of vlues ccepble o gen { B} for ssue wll be represened s he nervl [ M ], m,. A conrc pcge proposl s cceped by B when les one conrc s red wh M r, whle he negoon ermnes eher n cse he gen(s) dedlne s reched or n cse boolen vrble expressng he wsh of he gens o qu he negoon s se o rue. The wsh of o qu (connue) he negoon me wll be expressed by Q = ( Q = ), whle he wsh of B o qu (connue) he negoon me wll be expressed by Q = ( Q = ). If n greemen s fnlly reched we cll he negoon successful, B B whle n cse one of he negong pres qus (.e., s dedlne expred) s clled unsuccessful. In ny oher cse, we sy h he negoon hred s cve. In he nlyss bove, we hve ddressed he cse of qunve conrc ssues. The proposed model cn esly be exended for qulve conrc ssues. Herefer, n exmple

12 of such n exenson s provded. Le { x } c be vlue se for he qulve conrc ssue c x ccepble by gen, where c cn be n neger, rel number, srng, boolen, ec. Ech gen hs uly funcon U :{ c x } [,], whch provdes he uly h gen ssgns o vlue of conrc ssue n he rnge of s ccepble vlue se. Noce h he gen s uly funcon for conrc C { c,..., c } before,.e. U ( C ) = w U ( c ) n = = cn be expressed by he sme equon s. n In (Rouss e l., 4) he proposed model ws ppled o smple es cse nvolvng wo pres nd wo conrc ssues, v whch we llusred he fc h he uly of dfferen conrcs nd he resulng conrc preference herrchy for he wo negoors, my hghly depend no only on he vlues of he conrc ssues, bu lso on he vlues of he decson ssues h re no under negoon, whle her vlues do no depend les drecly on he cons of he wo pres. The sme concluson s reched for mullerl negoon suons, bsed on some more complced es cses (Rouss nd Lou, 3). 3. THE PROPOED NEGOTIATION TRATEGY Herefer, our focus s ld on he ronle of he A, snce s doped sregy wll defne he oucome of he negoon, whle rher smplfed ssumpons regrdng BA s logc re subsequenly mde. We consder h negoon s successful, f muully ccepble conrc s reched whn resonble me. nce n exhusve exploron of he possble conrc spce my form compuonlly nensve s for he A, should be ble o nfer he ccepble conrc spce for he BA unl predefned dedlne. To be more specfc, As herefer wll be provded wh mechnsm enblng hem o fnd good (ner opml) soluons n resonble me, by mens of compuonlly effcen lgorhms. The res of hs secon s srucured s follows. In subsecon 3. he negoon problem s formlly descrbed nd n subsecon 3. he focl ssumpons, on whch he negoon sregy s bul, re provded. In subsecon 3.3 he rnng mechnsm of he Buyer s presened, whle n subsecon 3.4 he conrc generon mechnsm of he eller s horoughly descrbed. 3. Negoon Problem Descrpon The objecve of our problem s o fnd conrc C = c, c,..., c } h fnl { fnl fnl nfnl mxmses he A s overll uly funcon U C ),.e., he A s ssfcon semmng ( fnl from he proposed conrc. The consrns of our problem re he followng. Frs, ech conrc ssue ( =,..., n ) should le whn he ccepble vlue rnges for boh he BA nd he A,.e., no vlue consrn volon should exs for boh pres. econd, he

13 consrn regrdng he BA s (A s) uly reservon vlue should be preserved. Therefore, he ol BA s (A s) uly for proposed conrc should no le below predefned vlue B U mn Acc ( U mn Acc ) represenng he mnmum ssfcon h my be experenced by he BA (A) n order for n greemen o be reched. Thus, he condons B B U C ) U mn nd ( fnl U ( C fnl ) U mn Acc should hold. Fnlly, he consrn regrdng he A s dedlne should be preserved. Therefore, n greemen wh he BA my be reched only f Acc l T, where T denoes he A s dedlne nd l he me of negoon round l durng whch conrc s proposed. C fnl Thus, bsed on he seleced proocol nd he proposed model, desgnng negoon sregy cn be reduced o decson problem h cn formlly be sed s follows: Gven: () wo negong pres: n A h my provde specfc good (.e., servce or produc) nd BA h s neresed n hs good s cquson, () n conrc ssues (ndex: =,..., n ) defned by he negoors nd he ccepble for he A rnges [ M ] m, whn whch her vlues mus le, () m decson ssues nd her curren vlues d j, j =,..., m, (v) dedlne T up o whch he A mus hve compleed he negoon wh he BA, (v) he vecor { } l l P = C,..., C l of he N conrcs { } l l C c,..., c l N proposed by he A o he BA durng he prevous round l, (v) he vecor { } l l R r,..., r l l = of he rnng vlues r ( N = ( =,..., N ) n =,..., N ) h he BA ssgns o he prevously mde by he A conrc proposl he negoon round l, nd B (v) he vlue consrn vldy vecor { VCV } B of he conrcs proposed, VCV = ( =,..., n ) for les one l + fnd he vecor { } l +,..., l+ P = C C l + of he N conrcs { } l +,..., l+ C = c c N ( =,..., N ) h should be proposed by he A o he BA n he nex round l +, n order o evenully rech o n ccepble (ner opml) greemen beween he wo pres, whle he A ms o mxmse s ndvdul uly of he greed conrc under he A s consrns,.e., = { } = VCV VCV ( =,..., n ), ( l + U C ) U mn nd l T, nd subjec o he exsen resource nd compuonl lmons. Acc n 3

14 In generl, here my be sgnfcn moun of compuons ssoced wh he opml soluon of he negoon problem presened bove. Exhusve serch (.e., lgorhms scnnng he enre conrc spce) should be conduced only n cse he soluon spce s no prohbvely lrge. The cos of he respecve soluons s evlued nd fnlly, he bes soluon s mnned. The complexy of he negoon problem s ncresed wh regrds o he number of he conrc ssues nvolved nd he rnge of her ccepble vlues. In hs respec, he desgn of compuonlly effcen lgorhms (e.g., smuled nnelng (Ars nd Kors, 989), bu serch, genec or greedy lgorhms, hybrd or heursc echnques, ec. (Ppdmrou nd eglz, 98)) h my provde good (ner-opml) soluons n resonble me s requred. Thus, he A should be cpble of selecng dsnc conrc pons from he ccepble conrc spce n order o rech o n greemen wh he BA whn he predefned me lms. 3. Generl Negoon regy Elemens on he eller de The proposed negoon sregy s desgned bsed on he followng focl ssumpons. Frs, he A nd he BA wll rech o n greemen, only f conrc s found, where he conrc ssues vlues le whn he ccepble rnges of boh negong pres, whle her ndvdul ules re bove mnmum ccepble hreshold. econd, s ssumed h he vlues of ll decson ssues re nvrble nd equl o { } d d = for he mxmum possble duron T of he negoon procedure beween he A nd he specfc BA, where s he non me of he specfc negoon hred. Thrd, he compuonl nd communcon cpbles of he wo negong gens, s well s her locons n he communcon newor, re ssumed o led o n lmos consn duron of ech negoon round. Thus, s ssumed h quny l+ l s consn l nd h he A s wre of s vlue. Thus, he mxmum number of rounds whn whch he A s uhorsed o complee he negoon wh he BA s: Τ L = INT l + l. As lredy presened n he negoon proocol nlyss, we consder he cse where he negoon process s ned by he BA who sends o he A n RFP specfyng he ypes of he conrc ssues nd he vlues of ll non negoble prmeers. Alernvely, he RFP my comprse complee specfcon of he servce requesed (.e., vlues ssgned for n conrc ssues). A could explo hs ddonl nformon by deployng lernng from experence echnques n order o nfer he bounds of he muully non volng conrc spce (conrc nersecon regon) n qucer mnner. Ths lerne pproch s consdered o be sndlone ssue, whch hs been ddressed n (Lou e l., 5). Bsed on hs RFP, he A proposes n nl conrc { },..., c c j C = n o he BA =, seng 4

15 [ ( ) ] U C, d ll conrc ssues he vlues h mxmse he A s uly (.e., f > hen he A ses [ ( )], whle n cse U C, d < c = M The uly of he nl conrc, mx c c, hen he A ses, c = m ). U C, d = U, s C for he A wll be denoed by: ( ), U s he mxmum uly h cn be cheved for he A, gven he vlues of he decson ssues { } d d = j me =. mx The generl de of he proposed pproches s h ll conrcs l C ( =,..., n ) of negoon round l re genered by he sme source conrc h wll be herefer denoed s l C. All conrcs of he sme round re genered so h hey presen equl ules for he A, gven he vlues of he decson ssues U l ( C d ) U ( C, d ) l =,, ' {,..., n }, ' d he begnnng of he negoon,.e.,, l =,..., L. If n greemen s no reched unl round l, hen he nex round l, he A wll me compromse (concesson), l l reducng s uly by cern quny ( ) ( ) l,, = U C d U C d Θ. Ths quny Θ l cn be me dependen, cn be resource dependen (Frn e l., 998), dependng on he curren vlues of he decson ssues followng Boulwre (Rff, 98), Conceder (Pru, 98) or Lner scheme, my be bsed on mve behvour of he A (Axelrod, 984; Axelrod, 997), dependng on he uly compromse of he BA, ec. As only he resuls nd no he formulon of he desgned negoon sregy depend on he exc vlue of Θ l, whou loss of generly, we my ssume h l Θ s consn,.e., l = Θ Θ, l l =,..., L. However, hs ssumpon my be drwn nd he prmeer Θ cn be deermned by he A ng no ccoun he specfc consrns nd condons of he e- mre h nfluence s decson ssues vlues n ech negoon round. Ths ssue wll be consdered n fuure verson of hs sudy. Herefer, ccordng o he prevous nlyss, we, L hve he followng: U ( C, d ) = U nd U ( C d ) U mx equons we my defne quny Θ s follows:, =. Usng hese wo, U mx U Θ = L mn Acc mn Acc. Ths mens h ech negoon round, ll conrcs proposed by he A wll presen A uly reduced by U, mx U L mn Acc, wh regrds o he conrcs of he prevous negoon round. 5

16 As lredy menoned, conrc U C, d = U s he C for whch snds ( ), source conrc of he frs complee negoon round ( l = ),.e., C = C. The core concep of he proposed A s sregy s o propose N conrcs ech negoon round l, whch yeld he sme uly concesson o Θ wh respec o he source conrc uly of he conrcs proposed s equl o ( l l ) ( ) l l U ( C d ) = U ( C, d ) =,..., n,, L followng: U ( C, d ) = U nd U ( C d ) U mx U C mx l C. Thus, he, d = U C, d Θ, whle. Accordng o he prevous nlyss, we hve he, =. I s noed h n cse n mn Acc greemen beween BA nd A s fesble (h s here exs les one conrc C for l U C l B l B whch snds: ( ) nd ( ) U mn Acc U C U mn Acc ), our pproch wll succeed n rechng whn he negoon hred upon n greemen due o he ssumpon h s s dedlne pproches, he eller concedes up o s reservon vlue U mn. As lredy descrbed n subsecon., he A provdes he BA wh conrc proposl { } l l P C,..., Cn l l vecor R { r,..., r } = ech negoon round l. The BA n reurn, sends o he A he rnng l = for he respecve conrc pcge proposl, long wh he vlue n B, consrn vldy vecor { } l B, VCV VCV l B, round, where VCV l {,} =, =,..., n, for les one conrc of he, dependng on wheher he vlue consrn of he BA s me for conrc ssue (.e., B, l B, VCV = ) or no (.e., VCV l = ) for hs conrc. 3.3 The Rnng Mechnsm of he Buyer The sregy proposed n hs pper consders he cse where he BA reurns o he A n denfcon sgn of he bes conrc comprsed n he conrc pcge proposl { } l C C l = n he conex of ech negoon round l. In essence, he BA n such P l,..., N cse my only denfy he conrc h beer ssfes hs/her needs, requremens nd consrns nd no provde specfc rn s mesure of hs/her ssfcon semmng from he proposed conrcs. Therefore, he BA s ronle my be que smple, bu he A s s s sll que dffcul due o he lmed nformon provded. The bes conrc Acc C ech negoon round l s denfed by rn sgnl BC (.e., { } l l l R,..., BC,..., l wheres n cse conrc l l = ), C s cceped o form he fnl greemen beween he negong pres he specfc rn provded he respecve conrc poson of he rnng vecor l R s se equl o (.e., { } l l l R,...,,..., l = ). A hs pon should be noed h N N n cse ll conrcs proposed presen vlue consrn volon (.e., f for l c, =,..., n, 6

17 =,..., N, snds h B, l l VCV = ), he rns comprsed n he rnng vecor R reurned o he A re se equl o (.e., r l =, =,..., N ). 3.4 The Conrc Generon Mechnsm of he eller The bss for he proposed negoon sregy for he eller s horoughly descrbed n subsecon 3.. As lredy menoned, conrc U C, d = U C for whch snds ( ), s he source conrc of he frs complee negoon round ( l = ),.e. C = C. Wh respec o hs nl conrc C wo dsnc cses my be denfed. Frs, no vlue consrn volon exss nd he conrc C s rned by he BA wh rn sgnl BC (.e., r = BC ). econd, vlue consrn volon occurs, n whch cse r =, nd he B, BA provdes lso s vlue consrn vldy vecor VCV. In cse he nl conrc C presens vlue consrn volon, he A, s frs sep, res o cqure conrc h respecs BA s vlue consrns. We wll refer o hs sep s negoon phse I, durng whch unl non vlue consrn volng conrc l C s cqured (hus, mx l r ), ech negoon round l > only one new conrc s genered on he bss of he conrc C l l proposed negoon round l (whch n essence forms he source conrc C,.e., C l = l C ), reducng A s uly by quny Θ. In he conex of negoon phse I, new conrc s genered bsed on he conrc l C proposed negoon round l, whch n prncple hs ll conrc ssues vlues equl o he ones of conrc C l, excep from he vlue(s) c l of conrc ssue(s), for B, whch consrn volon hs occurred, ( VCV l = ). For exmple, n cse conrc ssue of conrc C l voles he vlue consrns, he new conrc proposl would be l l l l l { c c, c', c c } l =. The vlue(s) of conrc ssue(s), ' l C ( ) ( ),...,,..., + n c, re l seleced so h he uly of conrc C for he A s equl o: U ( ) l l, (, ) C d U C d Θ =. In order o rech o non volng conrc whn resonble number of negoon rounds, s ssumed h he concesson quny Θ s shred eqully mongs he conrc ssues whose vlue s no ccepble o he BA. The exc vlues of conrc ssues re deermned n ccordnce wh he followng: l c ' : U l ( c d ) U ( c', d )= n l B, Θ, VCV l = w. 7

18 Ths process connues unl non vlue consrn volng conrc l C s cqured (.e., r l ), whle hs pon he A s sregy s modfed n order o cqure muully ccepble conrc whn resonble me. pecfclly, hs conrc becomes he source conrc for he nex negoon round, durng whch he A provdes he BA wh conrc pcge proposl comprsng N = n conrcs. The negoon round upon whch he frs negoon phse ends (hence, he sregy of he eller s modfed) wll be herefer denoed s nr fs. I s noed h n ny negoon round l > nrfs, due o he specfc pproch doped (.e., sequenl uly concesson by quny Θ ), no conrc proposed my presen ny vlue consrn volon. Movng now o negoon phse II, concernng he generon process of he source conrc l C of negoon round l > nrfs, he curren verson of hs sudy consders he smples possble ssumpon, h s he bes conrc proposed o he BA he negoon l round l, s deermned by he rnng vecor R reurned o he A, forms he source conrc for negoon round l. Alernvely, for he specfcon of he source conrc C l, he A could employ exploron echnques. To hs end, severl pproches could be found n he lerure, e.g., he Bolzmnn exploron sregy (Kelblng e l., 996; Kpens nd Kudeno, ). Up o hs pon, we hve no ye presened he wy he N = n conrcs of ny negoon round l l > re genered by he round s source conrc C. As frs sep, nrfs he conrc generon mechnsm my consder he rellocon of he uly concesson of ech round o ech one of he conrc ssues consdered n he negoon process. As second sep, we modfed he conrc generon mechnsm bsed on he de h n ny C he A ech negoon round l + my n prncple concede mosly wh respec o l + he conrc ssue whch hve been on he prevous negoon round l preferred by he BA, whle hrough he modfcon of one ddonl conrc ssue up o cern moun he A nfers he drecon owrds whch should move n order o rech o n greemen wh he BA. Consderng he frs negoon round l of negoon phse II (.e., l nr + ), he = fs A proposes n conrcs, whch wll n prncple hve ll conrc ssues vlues equl o he ones of he source conrc l l l l l { c c, c, c c } l C,..., ( ) ( + ),..., conrc l C, excep from he vlue n c of conrc ssue l =,.e., l =. The vlue c s seleced so h he uly of l l l C for he A s equl o: U ( C d ) U ( C, d ) Θ, =. ubsequenly, he A explores wh s he mpc of he vlue concesson of ech one of he conrc ssues. The A 8

19 my observe h for he bes conrc C ndced by he BA, he sme A uly l reducon Θ due o djusmens on he vlue c of conrc ssue l =, s vlued hgher by he BA. On he oher hnd, n cse ny conrc C s no ndced s he bes conrc l on negoon round l (where ll eller uly reducon Θ s due o djusmens on he vlue c of conrc ssue = ), hs ndces h conrc ssue = s no very mporn for he BA. Thus, n he conex of he nex negoon round, he A explos he bes conrc, s ndced by he BA n he for he nex round. Thus, n cse hs conrc s l R vecor, whch forms he source conrc l C (.e., l l C = C + ), does worh for he A o propose durng he nex negoon round l + conrc pcge proposl, whose mn chrcersc s h hgh percenge of he ol eller uly reducon Θ s due o djusmens on he vlue l c = c l of conrc ssue =. + We herefer nroduce wh respec o ech conrc ssue vrble clled uly concesson degree, denoed s ucd (), represenng he percenge of he ol eller uly reducon Θ due o he djusmen of he conrc ssue vlue. I holds ucd () [,]. The n conrcs consung he conrc pcge proposl consdered n negoon round l + my be genered s follows. The frs conrc s creed by modfyng only he vlue c of conrc ssue, whose djusmen on he prevous negoon round l ws l + preferred by he BA. Thus, he eller s uly reducon Θ s nroduced only by djusng + c n he source conrc. The vlue c l my be clculed by mens of he followng l + + equon c l l l+ : U ( c, d ) U ( c, d )= Θ ucd( ), where ucd ( ) =. The res w n conrcs re genered by modfyng ech conrc he vlue c l of one more ssue j ( j ) n he source conrc, up o cern degree ucd ( j), whle he uly concesson degree ucd () of he conrc ssue s properly djused, so h ucd ( j) + ucd( ) =. Ths wy, he mpc of he combned eller s uly reducon wh respec o boh modfed conrc ssues s explored. The conrcs whch re specfed n ccordnce wh hs concep + wll be herefer clled exploron conrcs. The vlues c l + nd c l of conrc ssues nd h w = j, j respecvely my be cqured by he foremenoned equon. I snds + l l [ U ( c, d ) U ( c, d )] = Θ, whch ndces h he eller s uly of he n conrcs of negoon round l + s less hn he eller s uly of he negoon s jj + j 9

20 round l by he quny Θ, whch s fully conssen wh he presened pproch. For he generon of he n exploron conrcs, ucd () s se equl o.7, whle ucd ( j) equls.3, s s esmed h 3% s deque for exploron purposes. Alernvely, more grdul modfcon of he uly concesson degrees could be consdered, whch s effecve n cse he frs prl dervves of he Buyer s uly funcons re no seeply lered by he chnges nroduced by he eller o he vlues of he respecve conrc ssues (.e., U ( C ) c B s que smll). In such cse, he eller es no ccoun he oucome of negoon round l, n conjuncon o he resuls obned on negoon round l so s o deermne he conrcs C + for he negoon round l +. In cse he BA rns hgher he nroducon of he modfcon of conrc ssue j wh respec o he vlue djusmen of conrc ssue, s nex sep, he respecve uly concesson degrees ucd ( j) nd ucd () re modfed so h he relve preference of he BA for conrc ssue j s nroduced n he generon process of he nex negoon round l +. pecfclly, consderng he nex negoon round conrc generon, he uly concesson degree of conrc ssue j s ncresed, whle he uly concesson degree of conrc ssue s decresed s we consder h he A should concede mosly wh respec o conrc ssue j. Thus, ucd ( j) s se equl o.7, whle he res.3 poron of he uly concesson quny Θ s ech conrc ssgned o ech one of he conrc ssues m n mnner smlr o he exploron polcy nroduced bove. + Accordng o he proposed pproch, n cse he resulng vlue c l of conrc ssue n conrc C l+ ends up o le ousde he ccepble rnge of he A, hen f c l < m (or c l > M ), he vlue seleced s c l = m (or c l = M ), whle he remnng uly s eqully dsrbued mong he res of he conrc ssues h hve no ye reched her lm vlues. In order o me he proposed conrc generon mechnsm more comprehensve o he reder, n Tble we presen he logc underlyng by mens of smple exmple, consderng he cse of hree conrc ssues. In hs ble, he conrc generon process s suded n he conex of negoon phse II (h s non vlue consrn volng conrc C l (.e., r l ) hs been cqured durng negoon phse I). Consderng he frs negoon round l of negoon phse II (.e., l nr + ), he A proposes n = 3 conrcs, whch = fs wll n prncple hve ll conrc ssues vlues equl o he ones of he source conrc C l l l l = ( c, c, c3 ), excep from he vlue of one conrc ssue ( ech conrc), so h ech

21 me he eller my explore wh s he mpc of he vlue concesson of ech one of he l l l conrc ssues. As llusred n Tble, he Buyer ndces c, c', c ) s bes conrc ( 3 (h mens h he Buyer vlues more he uly concesson of he second conrc ssue), whch forms he source conrc of he l + negoon round. Therefer, he eller proposes gn n = 3 conrcs. The frs one consders he modfcon of only he second conrc ssue ( ucd ( ) = ), whose modfcon hs been preferred by he Buyer durng he prevous negoon round. The oher wo conrcs consder he modfcon of he second conrc ssue (where ucd ( ) =. 7 ) nd one ddonl conrc ssue ( ucd ( ) =. 3 or ucd ( 3) =.3), so s o explore he mpc of he combned eller s uly reducon. As my be seen he bes conrc ndced by he Buyer he l + negoon round s ( 3 l+ l+ l+ c, c', c' ), ucd ( ) =. 7, ucd ( 3) =. 3. Thus, he Buyer prefers he uly concesson of he hrd conrc ssue wh respec o he uly concesson of he second conrc ssue. To hs respec, he conrc generon mechnsm n he l + negoon round fvors he uly concesson of he hrd conrc ssue, whle for exploron purposes, wo of he hree conrcs consder combned uly modfcon, s ndced n Tble. 4. REULT The resuls of hs secon m o evlue he proposed negoon model nd sregy (ncludng boh A s conrc generon mechnsm nd he BA s rnng scheme) h could be doped n he overll e-mreplce frmewor for rechng n greemen n he conex of specfc servce reques. As frs sep, he negoon model nd sregy wll be ppled o n llusrve es cse n order o become comprehensve o he reder. As nex sep, he proposed sregy wll be compred o wo lerne negoon sreges desgned n he conex of (Rouss nd Lou, 3). Concernng he mplemenon ssues of our expermens, he whole negoon sesson hs been mplemened n Jv (Goslng, 996). The OrbxWeb CORBA compln plform 3 ws used for he ner-componen communcon. Moreover, he BA nd he A hve been mplemened s nellgen, moble gens bsed on he use of he Voyger plform 4. The frmewor of he seleced es cse s brefly descrbed subsequenly. We consder eller gen nd Buyer gen B h negoe over he purchse of specfc produc (e.g., cern quny of boles of fresh juce). Two negoon ssues exs for he wo 3 hp:// 4 hp://

22 negoors: prce nd delvery de,.e., he prce per em requred by he eller o provde he boles requesed nd he me requred from he momen when n greemen s reched unl he boles of juce re delvered o he Buyer. Accordng o he negoon model proposed, we my use he followng noon: c = prce _ vlue nd c = delvery _ de _ vlue, where =, n =. As decson ssue we consder he me unl he expron de of he juce o be purchsed ( d ) whch hs n mpc on he uly funcon of he Buyer s well s of he eller. The ccepble vlue rnges for he wo conrc ssues for he wo negong pres re: [ m, M ] = [,], [ ] B, M B = [ 8,8] [ m, M ] = [,] nd [ m ] B, M B = [, ] ssue s: [ ] [,4] d, M = d m,, whle he possble vlue rnge for he decson m (.e., he me from he producon de unl he expron de of he produc s equl o M d = 4 dys). The weghs for he conrc ssues uly { B} funcons U {,, } n he overll uly funcon B B [ w, w, w ] [.8,.6,.,.4], = { B} U, for he wo negong pres re: w, where he weghs re normlsed,.e., = w = = w B =. The eller nd he Buyer wll rech o n greemen, only f conrc s found, where he conrc ssues vlues le whn he ccepble rnges of boh negong pres, whle her ndvdul ules re bove mnmum ccepble hreshold. For he presened es cse we consder he followng vlues for he mnmum ccepble uly B vlues for he eller nd he Buyer, respecvely: U mn =. 38 nd U mn =. 4 (.e., for he fnl greemen conrc C { c,..., c } U ( C ). 38 nd B ( C ). 4 fnl fnl U ). fnl f Acc fn Acc =, he followng mus hold: I s resonble o ssume h he eller would vlue more purchse of relvely old produc hn he one of freshly produced boled juce. Th s becuse he produc vlue declnes s he expron de (ED) pproches nd he eller sees o reduce he produc quny n soc, n fer of beng forced o sell very low prces or even no sellng ll. I s lso ssumed h he ED of he boled juce o be purchsed lso ffec he uly for poenl Buyers, s hey mgh no be ble o use/resell hem shorly. Thus, f d s low (.e., he ED of he produc pproches) he vlue of he quny purchsed s low for he Buyer nd hgh for he eller, whle he eller would more pprece n erly delvery de. Tng he bove nlyss no consderon, we my model he uly of conrc s follows: C for he ssue

23 () U () U B M d d c m =.8+., c [ ] M M m, d M m B d M c =.8+., c [ ] B B M B M B m, d M m () U (v) U B c m =, c [ ] M m, M m B d M c =.6+.4, c [ ] B B M B M B m, d M m Followng he negoon sregy proposed, we ssume h = he vlue of he decson ssue s: d 3 (.e., here re 3 dys unl he expron de of he produc). = Thus, he ules of he conrc ssues for he wo negoors cn be expressed s follows: () =.85 c. 85 U, [ ] U, [,] () =. c. c,, () U B c c, (v) U B. c =, c [ ] 8,8 =, c [ ], From he equons bove we my compue he mxmum possble ules for he wo, B,, B, negoors: U. 85, U. 95, U, U. 9. Thus, we hve: mx = mx = mx = mx =, B, U.88 & U. 93, whle U =.68 c +. c. 7 mx = mx = & U B =.57 c.4 c In Fgure, he ules of he wo negoors re depced wh regrds o he vlues of he wo conrc ssues. The mnmum ccepble uly level hs been hghlghed n boh dgrms. Noce h n cse he vlue of les one conrc ssue does no le whn he nersecon of he ccepble vlue rnges of he eller nd he Buyer (.e., when c [,8] nd/or c [,] wo negoors s negve. ), he uly of les one of he Bsed on our negoon model nd sregy, consderng he cse foremenoned, f c < nd/or f c <, he eller does no propose he conrc genered, bu sees o propose noher conrc whn hs/her ccepble conrc domn. On he oher hnd, f negve uly conrc s proposed by he eller (h s f c > 8 nd/or f c > ) hen he Buyer ssgns zero rn o he specfc conrc, whle seng o zero he respecve elemen of he vlue consrn vldy vecor of he source conrc of he round o be provded o he eller. 3

24 The negoon process s ned by he Buyer who sends o he eller n nl RFP specfyng he ypes of he conrc ssues (prce nd delvery de). Bsed on hs RFP, he eller proposes n nl conrc = [,] C o he Buyer =, seng ll conrc ssues he vlues h mxmse he eller s uly (.e., mxmum prce nd les delvery, U C, d =.88 = U. For he Negoon regy presened n hs mx de). Obvously, ( ) verson of he sudy, he nl conrc C s rned wh r =, s boh conrc ssues vlues do no le whn he Buyer s ccepble rnge ( c = [ 5,5] nd = [, ] c ). Thus, he vlue consrn vldy vecor of he Buyer provded o he eller s now: [,] B, VCV =. Conrc round ( = l ),.e., = C [,] = C wll be he source conrc of he frs complee negoon C. The mxmum possble duron of negoon hred s equl o T = sec, where T s n upper me bound defned by he eller. The compuonl nd communcon cpbles of he wo negong gens, s well s her locons n he communcon newor, re ssumed o led o n lmos consn duron of ech negoon round, h s l sec l. Thus, he mxmum number of rounds whn whch he eller s + l uhorsed o complee he negoon wh he Buyer s: L = INT l+ Τ sec = INT L =. Ths vlue ndces h he mxmum l sec ccepble by he eller number of rounds s equl o L = l. For ech negoon, l l l round l he eller s uly reducon ( = U ( C, d ) U ( C, d ) Θ ) wll be consdered o be consn. Thus, he followng snds:,, l U mx U mn Acc Θ = Θ = =. 5 U L ( ) ( ) l l C, d = U C, d. 5 = ( C, d ). 5 l = U, l =,...,. Tble provdes he oucome of he pplcon of he proposed Negoon regy. nce he nl conrc does no belong o he BA s ccepble regon, he A s conrc generon mechnsm follows he proposed pproch for he negoon phse I, unl non volng conrc s reched. As depced n Tble, negoon phse II srs round l = 5, snce he end of round l = 4, he [7.79, 9.5] conrc hs been proposed, whch belongs o he A s nd BA s conrc nersecon regon. In ccordnce wh he proposed pproch for negoon phse II, he conrc generon mechnsm doped by he A ech negoon round l > 5 explos he resuls of he prevous negoon round l. Th s, ssumng h he conrc ssue ws preferred by he BA on negoon round l, he A 4