Overcoming the Fixed-Pie Bias in Multi-Issue Negotiation

Transcription

1 Overcoming the Fixed-Pie Bis in Multi-Issue Negotition Rymund Lin Institute of Informtion Mngement Ntionl Tiwn University Tipei, Tiwn Seng-Cho T. Chou Institute of Informtion Mngement Ntionl Tiwn University Tipei, Tiwn Abstrct Multi-issue negotition my produce mutul beneficil results to both negotitors while single-issue negotition cn not. However, there re difficulties in utomting multi-issue negotition, since the serch spce grows drmticlly s the number of issues increses. Although mny concession strtegy lerning mechnisms hve been proposed to del with the problem, recent reserch uncovered tht the fixed strtegy of concession nd the fixed-pie bis re the two mjor interferences in the utomtion of multi-issue negotition. It is suggested tht the lck of communiction between gents my hve impeded informtion shring nd joint-problem solving possibilities. In this pper, we show tht the fixed-pie bis cn interfere with the negotition outcome if there re non-conflicting issues. We propose new negotition model nd n innovtive lgorithm tht not only llows informtion to be shred in controlled wy, but lso llows the informtion shred to be effectively used for conducting systemtic serch over the negotition problem spce. The combined mechnism is cpble of using strtegies lerned from counter-offers nd is immune to the fixed-strtegy limittion nd the fixed-pie bis. It contributes to the utomtion of multi-issue negotition in the context of open nd dynmic environments. 1. Introduction Negotition is humn behvior existed since there is trde. People exchnge products in order to give out wht they hve for wht they need. In the ge of electronic commerce, negotition hs been utomted by softwre gents or supported by negotition support systems (NSS). Reserch [10] [16] [11] [5] indicted tht these utomtion mechnisms were ble to reduce significntly the negotition time nd llevite the negtive effects of humn cognitive bis nd limittion. The evolution went from single-issue negotition to multi-issue negotition. In single-issue negotition, the term negotited is limited to price. Although this kind of negotition works for some cses such s uction houses, most compnies on the Internet re generlly ginst it since it brings out price wrs tht not only cuses chos in mrkets but lso ignores the importnce of other issues such s wrrnty period nd delivery time. Multi-issue negotition becomes n importnt reserch re in the e-commerce domin, since it is more beneficil compring to single-issue negotition [14]. However, there re difficulties in utomting multi-issue negotition. Tke bilterl multi-issue negotition, where there is buyer nd seller performing one-to-one negotition, for exmple. Issues cn be negotited sequentilly or simultneously. The issue-by-issue pproch suffers the drwbck of being unble (or costly) to go bck to lredy negotited issues. Hence it is inpproprite for solving problems with inter-dependent issues. In the simultneous pproch, on the other hnd, negotitors get lost esily in the complex decision tree of concessions, nd the serch spce grows drmticlly s the number of issues increses. Since we ssume self-interested gents, n gent will not disclose his utility function, being frid of the fct tht the opponent will tke dvntge of it to squeeze surplus out of him. Given the sitution, the only informtion disclosed re the offers proposed nd the informtion of cceptnce or rejection on the proposed offers. An lgorithm is required to serch the negotition problem spce for mutul beneficil greements bse on the limited informtion. Adopting the simultneous pproch, there re three types of lgorithms: 1. Brute force: suppose tht buyer is bidding for goods from seller. He then queries the seller for cceptnce of ech offer in mind, from the one with highest utility to the one with lowest. The seller my ccept it or reject it. This process continues until the buyer hs run out of lterntives. To speed up the process, the seller cn counter-offer using the sme method s the buyer. Once n offer is ccepted by one of two plyers, the negotition ends. This pproch is similr to the continuous double uction used in Ksbh [2], nd my work fine in the single-issue negotition without time constrints (i.e. dedline, brgining cost, etc.). However, it is hrdly pplicble to the multi-issue negotition since there re generlly too mny lterntives generted by combining options of ll the issues. Simply generting nd sorting them will require lot of memory spce, not to mention querying them one by one, which cn be very time-consuming. 2. Use concession strtegy lerned from pst negotitions: this pproch works gret if the mrket is sttic, which mens tht the generl utility function of buyers/sellers does not chnge rdiclly over time. Although we do not know exctly the utility function of the opponent, we lern from pst negotitions to get the best concession strtegy tht cn both speed up the negotition nd get better outcomes. However, if the

2 mrket is dynmic, this fixed strtegy my not chieve mutully beneficil outcomes ech time, since different opponents my hve quite different utility functions over the vrious issues. Reserch [13] [12] [17] belongs to this type. 3. Use concession strtegy lerned from counter offers: lthough rrely seen in the reserch, it is possible to lern concession strtegy from counter offers within negotition session. The rtionle behind it is to find out which terms re importnt (weighted more in the utility) to the opponent, but less importnt to us. Conceding on these issues increses the possibility of being ccepted by the opponent, while preserving our interests. Reserch [4] uses similrity criteri to mke issue trde-offs; it is believed tht by mking n offer similr to the one by the opponent cn pproximte the preference structure of the opponent. In n open nd dynmic environment, such s the Internet, the third type lgorithm becomes importnt. Goh et l. [6] conducted n experimentl study on computer-supported brgining in the context of electronic commerce, nd uncovered tht the fixed strtegy of concession nd the fixed pie bis re the two mjor interferences in the utomtion of negotition. It is suggested tht the lck of communiction between gents my hve impeded informtion shring nd joint-problem solving possibilities. The problem of fixed strtegy hs been ddressed lter in [4] (though the existence of too mny ssumptions hs cused their reserch to be less pplicble to rel cses). However, the joint-problem solving possibilities re still constrined by the fixed-pie bis nd the informtion shred. In this pper, we propose new negotition model nd n innovtive lgorithm tht not only llows informtion to be shred in controlled wy, but lso llows the informtion shred to be effectively used for conducting systemtic serch over the negotition problem spce. The combined mechnism is cpble of using strtegies lerned from counter-offers nd is immune to the fixed-strtegy limittion nd fixed-pie bis. It contributes to the utomtion of multi-issue negotition in the context of open nd dynmic environments. The sections re orgnized s follows: section 2 firstly explins the rtionle for informtion shring. Section 3 describes the negotition model used, nd section 4 gives detils of the serching lgorithm. Section 5 contins experimentl nlysis nd finlly the conclusion nd future work is presented in section The Rtionle for Informtion Shring In the context of Gme Theory, the two-plyer brgining gme is defined s non-coopertive gme where two plyers ttempt to divide good, sy pie, between them. However, the pie-dividing concept my introduce the fixed-pie bis, which is tendency for negotitors to ssume tht their own interests directly conflict with those of the other prty [1] [18]. The problem cused by this bis seldom occurs in brgining since most of them re deling with conflicting issues. Let us consider more generl two-plyer multi-issue negotition problem, where the plyers not only negotite for the price, but lso dte for delivering the product. The utility gined from settling for different dte is illustrted in Figure 1. At the beginning, their preferences seemed to be conflicting; nevertheless, they mnged to meet t dy 7, which is the best solution for both of them. The f curve occurs when plyer wishes to get the product immeditely or on lter dte if he cn not get it immeditely. This exmple illustrtes tht sometimes the pie-dividing concept my be misguiding, cusing both negotitors to neglect mutully beneficil solution if they do not communicte. Sme problems cn occur when deling with qulittive issues such s the choice of colors, since the utility gined by ech color my not lwys be conflicting with the opponent s preference. Figure 1. Non-conflicting utility cse Reserch [4] ws bsed on the pie-dividing concept; however, they llow different levels of importnce to be ttched to vrious negotition decision vribles. This mkes the negotition non-zero-sum gme, where plyers cn find mutully beneficil greements by mking trde-offs over issues insted of conceding t the utility. Tht is to sy, by incresing some decision vribles in vlue nd decresing some others my crete n offer tht will benefit one or both of the plyers simultneously. However, considering the bove delivery time cse, we find tht mutully beneficil offer cn be found by simply incresing the utility of one of the decision vribles without decresing ny other (insted of conceding, one cn rise the utility of the new offer). In other words, better solutions cn be found if we void the fixed-pie bis. Nevertheless, by voiding the fixed-pie bis, we re gin lost in the enormous possible pths of solution serching. It is our belief tht, by disclosing little more informtion, the plyer with less privcy concerns cn improve the negotition outcome, nd therefore benefits himself. And it is lso common tht, in the rel life sitution, plyer with less privcy concerns will simply relese trde-off informtion, such s you cn deliver the product to me immeditely or week lter.

3 One my rgue tht, in the bove delivery dte cse, the opponent will propose the offer of dy 7 eventully if you did not propose it, yet in the multi-issue cse, there cn be lot of lterntives tht it is too hrd to enumerte them ll. Therefore how the informtion cn be shred in systemtic wy such tht the opponent cn use it to improve the solution serching process is the mjor concern here. Besides, the informtion should be disclosed in controlled wy so tht it not only mtches our privcy preference but lso complies with our negotition strtegy. To tckle this problem, we propose new negotition model nd n innovtive solution to the serching problem in the following sections. 3. Tgged Multi-offer Negotition Model In this section we first provide n overview of our negotition model. Then we discuss the issues of time constrints nd informtion sttes. 3.1 The Negotition Model The settings of our negotition model re bsed on non-coopertive, multi-stge, incomplete-informtion, nd two-plyer brgining gme. Since this is non-coopertive gme, ech plyer does his best to mximize his own interest nd will not shre informtion more with the other thn necessry. We ssume ech plyer knows neither the other s preferences on issues, nor the utility function; therefore it is gme with incomplete informtion. Given such sitution, in order to rech n greement tht is beneficil to both plyers, the negotition will continue for more thn one stge. Rubinstein proposed multi-stge brgining gme [15], in which ech plyer of the gme proposes n offer in turn nd the other my ccept or reject it. The gme will continue until n offer is ccepted. Our model differs from [15] in tht: Firstly, we llow multiple offers to be proposed t one time. For exmple, seller cn propose two offers t one time, sying you cn buy product A t price B with delivery time C or buy product A t price D with delivery time E. The buyer my counter propose with syings like I cn only buy product A t price F with delivery time G or buy product A t price H with delivery time K. This relxtion of multiple lternting offers enbles plyer to disclose possible trde-off informtion over which the opponent cn consider. It cn speed up the serching process nd void flling into locl optim in the solution lndscpe too erly. Besides the relxtion of multiple lternting offers, we llow plyers to tg informtion of their preferences over proposed offers. For exmple, vector <<A, 3>, <B, 2>, <C, 1>> indictes tht offer A is the most preferred, offer B is the second most preferred, while offer C is the lest preferred. We llow the multiple lternting offers nd the tgging of preference informtion becuse we believe the informtion my be necessry for both plyers to rech n greement tht is beneficil to both of them. However, how much informtion will be shred is decision mde by the plyers. An elegnt controlling mechnism is embedded in our serching lgorithm (detiled in the next section), nd it cn be tuned ccording to the privcy preference of the plyer. Finlly, the negotition gme will end in known period of time, no mtter whether n greement hs been reched. If n greement hs been reched before the dedline, the plyers will continue to improve it until the dedline. If no greement hs been reched before the dedline, the negotition fils. If more thn one greement hs been reched, the ltest one is chosen. This design permits better solutions to be found fter the first greement hs been reched. We nme this negotition model TAMON (TAgged Multi-Offer Negotition) model. 3.2 Time Constrints Rubinstein s model hs bsic ssumption tht time is vluble during the negotition, nd the fixed brgining cost or fixed discounting fctor my ffect the strtegy used in the brgining. If ech plyer hs complete informtion bout the preferences of the other, weker plyer (i.e. the one with higher fixed brgining cost) will lwys lose. However, ssuming ech plyer does not know the preference structure of the other (incomplete informtion), the weker plyer my try to chet the other plyer by mking the other plyer believe tht he is ctully stronger. To simplify the TAMON model (voiding the considertion of time-relted strtegies), we ssume the cost of time is negligible during TAMON gme. In other words, by choosing resonble period of time to ply the negotition gme, it is possible for both plyers to gree tht there cn be no time constrints during the period of negotition. By this simplifiction we mke TAMON micro negotition gme. It does not men tht there re no time constrints ny more, but tht the time constrints re omitted during the TAMON gme. The time constrints still exist between the current TAMON gme nd the next TAMON gme. Tht is to sy, to chieve n greement, both plyers cn ply series of TAMON gme tht is time constrined. This simplifiction hs two benefits: 1. The environment is stble during TAMON gme; therefore plyers cn focus on the serching nd improving of solutions without the need to del with chnging environmentl prmeters. 2. Existed time-dependent bidding strtegies such s NDF [3] cn be pplied directly to series of TAMON gme without conflicting with micro level strtegies used in the TAMON gme. This ssumption lso indictes tht the gol of micro level strtegies will be to find solution given the constrints from mcro level strtegies. And mcro level strtegies re pplied on series of TAMON gme.

4 3.3 The Informtion Stte Ech plyer (let b denotes buyer nd s denotes seller) in TAMON gme is modeled s 5-tuple I with utility function U, utility, degree U of informtion shring D, micro level strtegy S nd mutully greed period of time T to ply the gme: { } I = U, U, D, S, T, where b, s. (1) We define the utility function to be sum of weighted contributions of N issues: N i* i, i [ 0,1] i 1. (2) U = w u where u = nd w = i= 1 i= 1 N The utility contributed by ech issue, however, is not necessrily depending only on the vlue of this specific issue, but lso on the vlues of K other issues in the offer. The occurnces of this interdependency will mke it inpproprite to be negotited in n issue-by-issue wy. The micro level strtegy S is defined by the lgorithm nd the lgorithm prmeters used for generting nd ccepting offers (detiled in section 5). In this pper, we will ssume there is only one choice of lgorithm, the BGA (discussed in the next sub-section), nd D does not chnge during the series of TAMON gme. Therefore the mcro level strtegies contin only functions determining the vlue ofu. The serch spce bounded by U in TAMON gme is illustrted in Figure 2. Figure 2. The Serch Spce in TAMON Gme 4. The Bilterl Genetic Algorithm To serch in the spce of TAMON gme, we need heuristic method tht is computtionlly trctble; since the overll serch spce is too lrge tht n exhustive fshion of serch is not possible. Considering single-issue negotition for delivery time in Figure 3, if both negotitors re using the sme liner time-dependent mcro level function for decresing the U, their greement cn be found t the intersection of utility x. In this cse, the offer generting process would be too simple tht the micro level TAMON gme cn be set to propose only one offer in turn nd be plyed for only two turns (in the first turn, the buyer proposes nd the seller ccepts or rejects, in the second turn the seller proposes nd the buyer ccepts or rejects). However, in multi-issue serch spce, it is lmost impossible to generte ll the offers with utility x (while there re only two offers of utility x evluted using f or g in Figure 3, there cn be huge number of offers of utility x in multi-issue serch spce, especilly when given nonliner utility functions). Therefore, the serching lgorithm cn only propose some of them, nd there is gret chnce tht the serch lgorithm will miss the right one. Suppose tht solution is guessed out t utility x ' of time y '' lter, nd then mechnism will be required to bck-serch for the rel optiml solution of utility x. The Bilterl Genetic Algorithm (BGA) is proposed to del with this problem.

5 Figure 3. The Mtching Point 4.1 Overview of BGA BGA is n lgorithm for serching solutions to the TAMON problem. We pply the concepts of genetic lgorithm (GA [8]) to the domin of offers. Tht is, we use joint utility to express the fitness of n offer, nd use n evolutionry pproch to find out the best offer if possible. A very simple design of such n ide is to encode n offer into single chromosome nd let the fitness of it be the product (product is used insted of sum for firness) of two utility vlues from the buyer nd the seller. For exmple, let chromosome {100, 5, 2, 3} (for redbility, we use n-ry gene encoding) represents n offer with price of 100, quntity of 5 units, delivery time of 2 dys nd wrrnty period of 3 yers. If the joint utility of this chromosome is high, the number of this individul will grow exponentilly in the popultion, s stted in GA. And the popultion will eventully converge to the nswers we wnt. However, since the gents re self-interested in our scenrio, ech gent does not shre informtion of his utility with the other. Lcking the utility function from the other gent, n gent will not be ble to determine the joint utility of chromosome. Hence, both the buyer gent nd the seller gent re not ble to perform the selection using genetic opertors on the popultion of offers. To overcome this problem, we propose n innovtive lgorithm BGA, which divides the popultion for evolution into buyer side popultion nd seller side popultion, nd uses two specil genetic opertors, B-selection nd B-recombintion, to hndle the selection nd recombintion process in the presence of incomplete fitness function. Both gents must perform the genetic B-selection process nd B-recombintion process seprtely. The B-selected popultion will be proposed to the other plyer while the received popultion will be used to B-recombine with our B-selected popultion, s illustrted in Figure 4. The B-selection hs tunble smpling rte, which cn select offers for proposing ccording to the D prmeter. We will discuss the detils of ech opertion in the following sub-sections, nd then explin why it works. Before we discuss the genetic opertors used in BGA, we firstly define the prmeters used in BGA: Popultion Size: Z popultion. Crossover Rte: R = [ 0,1 ]. Muttion Rte: M = [ 0,1 ]. Chromosomes: Ci, where i nd 1 i Z popultion. b, s. Agin: { } Figure 4. The BGA Evolution Process

6 4.2 B-selection, B-recombintion nd B-muttion The selection process of GA will produce new popultion with the distribution of chromosomes being propotionl to the fitness of ech chromosome from the old one. The one with higher fitness gets higher probbility to be selected in the resulted popultion. B-selection does little more: it will propose the popultion of chromosomes to the other gent, nd the size of it will be ffected by the degree of informtion shring (prmeter D ). The ctul size of popultion proposed is: Zoffers = Zpopultion D. (3) During the gent communictions, duplicted offers cn be represented using vector formt <Offer, Number>. The B-selected popultion then becomes offers proposed to the other plyer in tgged multi-offer formt. The higher vlue in D, the richer informtion in the proposed offers. If Z equls to 1, it becomes norml offers lternting offer protocol tht proposes only one offer turn. The B-recombintion opertor differs from the GA recombintion in tht it recombines chromosomes from the different-side B-selected popultions. In other words, one of the prent chromosomes comes from the buyer-side B-selected popultion while the other from the seller-side B-selected popultion. Since the popultion B-selected by the other gent might hve different size from ours, both the received popultion nd our B-selected popultion re rescled to hlf of our popultion size before they cn be put together into joined popultion of size Z (see popultion Figure 5). The joined popultion is then redy for B-recombintion. It should be noted tht, ech gent might hve joined popultion of different size, since their Z vlues might be different. popultion Figure 6. Performing B-recombintion B-recombintion of two chromosomes produces chromosomes tht represent offers pplying different concession strtegies. For exmple, recombining buyer proposl {100, 4, 2, 4} with seller proposl {120, 3, 2, 2} my produce proposl {100, 3, 2, 2} denoting tht the seller concedes t the price of vlue 100, nd proposl {120, 4, 2, 4} denoting tht the seller concedes t quntity, delivery time nd wrrnty period. Ech gent performs B-recombintion t his own memory spce; therefore the crossover rtes cn be different t the two sides. After the B-muttion process, the newly generted popultion then replces the old one (noted tht the first genertion is rndomly generted). The B-muttion is similr to the GA muttion process except tht it is performed seprtely t both sides. We use uniform crossover in B-recombintion, lthough it is considered to be mximlly disruptive when the episttic interctions re the nerest neighbors [9]. We believe it is required in our scenrio, becuse it helps the B-recombintion generte more possibilities of concessions ssuming tht the two negotiting gents my hve different informtion spces. For exmple, if the buyer cn propose only one chromosome {A, B, C}, nd the seller cn propose only one chromosome {D, E, F}, uniform crossover mkes it possible to generte chromosome with {A, E, C} while one-point crossover cnnot. In the finl lgorithm, the B-selection is ctully processed twice (Figure 7) by n gent in turn; one for proposing offers, nd one for generting hlf of popultion for next join. We need to seprte these two popultions since the proposed one is bounded by the utility while the reserved one for next join is not. The detil of the lgorithm is not explined in this pper. For interested reders, plese check the web site: Figure 5. The Joined Popultion

7 Figure 7. The BGA lgorithm 4.3 Preliminry Agreements At the beginning of BGA process, ll chromosomes (i.e. offers) with utility higher thn or equl to U re ssigned fitness vlue F = 0.99* U. The coefficient 0.99 is designed to mke the fitness vlue little smller thn the U. Once preliminry greement ( proposed offer tht is ccepted) is reched, the ssocited chromosome will be given fitness equls to its rel utility, which is higher thn F. The number of this chromosome will then strt to increse becuse of its high utility (further explined in the next sub-section). The discovery of preliminry greement lso cuses the vlue of U to climb up to the utility equling to the one of the preliminry greement. This climbing behvior ensures tht the newly proposed offers will hve higher utility thn preliminry greements. It is the bck-serching mechnism mentioned in the first prgrph of this section. In the view of mcro level strtegies, the vlue of U often goes down (decresing) nd does not go up, only when some preliminry greement hs been reched, it then mkes sense to revert the U to the new high utility reched. This ction is nmed utility reverting. 4.4 Implicit Prllelism in BGA The min ide of BGA is to utilize the implicit prllelism of GA to explore ll possible concession strtegies nd ccumulte useful building blocks [7] t one time. Implicit prllelism, nmed by Hollnd [8], is property tht: Even though ech genertion we perform computtion proportionl to the size of the popultion, we get useful processing of something like n 3 schemt in prllel with no specil bookkeeping or memory other thn the popultion itself In BGA, only preliminry greements contin useful building blocks tht need to be ccumulted in the lter serch. Tht is why we restore fitness of chromosomes to their ctul utility vlue fter they re found to be preliminry greements (before tht, ll fitness vlues re lower thn U ). By B-recombining chromosomes from two popultions of different sides, chromosomes representing vrious offer-improving possibilities re generted. The offer-improving behvior is little bit like the similrity pproximtion in [4], since B-recombintion try to generte n offer by recombining chromosomes from the two different popultions nd the resulted chromosomes will be similr to their prents. In fct, the BGA lgorithm does better job then [4] for locting offers similr to the opponent s. Becuse reserch [4] try to find similr offers by decresing the utility distnce, which is impossible if certin kinds of informtion bout the opponent s utility function is unvillbe. Their simultions work simply becuse there re too mny ssumptions (liner, conflicting, sme vlue rnge nd equl discrimintion power over the reservtion vlues) being plced on the opponent s utility function in their reserch. It mkes the ssumption of incomplete informtion quite wek.

8 B-recombintion does not hve fixed-pie bis, since it does not ssume utility conceding is necessry when trying to generte n lterntive. In fct, the BGA never decrese the utility of new offers, nd try to increse the utility whenever possible. Once n offer cceptble to both sides is found, the utility is incresed, nd the useful genetic informtion in the offer will then be ccumulted in n evolutionry wy. To conclude, BGA cn del with the serching problem of TAMON gme in computtionlly trctble wy, nd no specific ssumptions re plced upon the utility function of the opponent. 5. Experimentl Anlysis A negotition cse with mixed (including liner nd nonliner) utility function is prepred to test the cpbility of BGA. The utility functions for 5 issues in buying cr re listed in Tble 1 (for simplicity, some of the functions re not showed in detil; mechnisms used to ensure the rnge of ech utility vlue re omitted; for interested reders, complete source codes cn be found t Two exceptions re dded to override the defult utility functions. They provide extr interdependency mong these issues, nd re the episttic interctions s explined in [9]. Tble 1. Utility functions Buyer Seller Price (200 - ( (v*v)/200 )) (v-20)/300 /200 Time Cos( (2*Pi* (v mod 7))/7 ) Sin( (2*Pi* (v mod 30))/30 ) Type {0.1, 0.2, 0.9, 0.5, v/4 0.1} Color {0.3, 0.4, 0.2, 0.7, {0.5, 0.5, 1, 0.5, 0.5} 0.9} Option (10-v)/10 v/10 Exceptions If (Type = 1) nd (Color = 2) then both issues get n utility vlue of 0.9. If (Time = 77) nd (Type = 1) then both issues get n utility vlue of 1. Eighteen combintions of prmeters (Tble 2) re used to run the simultions. They re designed to nswer the following questions: 1. Should I be the first mover? (should I propose offers firstly?) 2. How do I propose? (how much informtion cn be disclosed?) 3. How do I response? (how much informtion should be fed bck to the opponent regrding his proposing?) In question 2, the degree of informtion shring determines the smpling rte for proposing offers in mind, nd in question 3, the feedbck rte of preliminry greements determines how much informtion regrding one s evlution on the opponent s offers will be fed bck to him. Tble 2. Experiment prmeters Q Prmeter Nme Prmeters 1 First Mover seller first buyer first 2 Degree of Informtion Shring (DoIS for short) 1 (ll) Feedbck of Preliminry Agreements (FoPA) (ll) As expected, the first mover hs disdvntge in the TAMON gme. The explntion is intuitive: since the first mover shres informtion firstly, the opponent is then ble to increse his utility firstly when preliminry greements re found in the first turn. Reders cn compre Figure 8 nd Figure 9 to find out the difference (noted tht the X-xis in them represents the product of DoIS nd FoPA, nd Y-xis the utility). Figure 8. Buyer utility Figure 9. Seller Utility Judging from the results showed in the following Figure 10 (FoPA = 1) nd Figure 11 (DoIS = 1), we cn conclude tht the effects of informtion shring hve higher impct on the negotition results then feedbcks. The reson lies t tht the number of preliminry greements is smll compring to the proposed offers. Since both negotitors tend to decrese the utility slowly in the progress of negotition, the number of preliminry greements cn not be very lrge. We lso found tht the degree of informtion shring need

9 not to be very high for stisfctory negotition results to be gined. Figure 10. Effects of informtion shring Figure 12. BGA simultions The results in Tble 3 show tht BGA performs better when informtion is shred vi the TAMON protocol. In the lst cse, where the degree of informtion shring equls to , only one offer ws proposed in turn (sme s trditionl negotition model), nd the rtio of verge negotition results drops drmticlly. However, it is lso found tht by extending the TAMON gme period, the results cn be improved (see Figure 13, X-xis represents the degree of informtion shring, nd Y-xis the resulting utility product). Figure 11. Effects of feedbck In Figure 12 (X-xis represents the buyer utility nd Y-xis the seller utility, ssuming FoPA = 1), the BGA simultion results re compred to GA simultions with sme crossover rte (0.7) nd muttion rte (0.02). Both popultion sizes re set to 400. In GA simultions, however, the lgorithm hs complete informtion of both negotitors utility functions, nd the product of buyer utility nd seller utility is used s the fitness vlue genertions were run for the GA simultions while period of 10 seconds ws used in ech micro level TAMON gme simultion. We ssume sme brgining power in the BGA simultions, therefore the utility decreses t sme speed (0.1 per micro level gme) for both negotitors. Both GA nd BGA simultions were run 30 times to get the verge negotition results in Tble 3. The best result found by the brute force lgorithm (testing ll combintions) is lso mrked on Figure 12. Tble 3. Simultion results Buyer Utility * Rtio Seller Utility (Avg) Best GA BGA BGA BGA Figure 13. Effects of negotition period 6. Conclusion nd Future Work We proposed the TAMON negotition model nd the BGA lgorithm in this pper. The TAMON model defines micro two-plyer negotition gme without time constrints, nd llows more informtion to be exchnged in the negotition gme. The exclusion of time constrints is importnt for simplifying TAMON gme, since most serch lgorithms re not of rel-time, nd the serch spce tends to be sttic during the serching. It lso permits more complex serch process to be conducted in TAMON gme, with constrint tht the process should be terminted fter period of time. By llowing more informtion to be disclosed in tgged multi-offer formt, the TAMON model incorportes the informtion shring behvior into the negotition model. We cn sy tht the TAMON model provides dimension for joint problem solving possibilities, yet it is still in the context of non-coopertive gme.

10 The BGA proposed in this pper utilizes the implicit prllelism of GA to serch the solutions in TAMON gme. The elegnce of the BGA is tht it perfectly fits in the TAMON gme since the popultion to be proposed is meningfully trnsformed into the tgged multi-offer formt, nd with the degree of informtion shring being tken into considertion. The lgorithm is immune to the fixed-strtegy limittion nd the fixed-pie bis, nd it is computtionlly trctble. It should be noted tht it is not required tht both plyers use the sme lgorithm in the negotition. However, since the BGA cn explore multiple strtegies simultneously, we re investigting tht given the limittion of computtionl trctbility, whether the BGA-like lgorithm will be the only rtionl choice in TAMON gme. We re developing theory to mesure the informtion disclosed in the tgged multi-offer protocol nd to determine the precise effects cused by the informtion shring in multi-issue negotition. A theory for guiding the choosing of BGA prmeters, including the popultion size, the crossover rte nd the muttion rte will lso be ddressed in the future work. References [1] Bzermn, M.H. nd Crroll, J.S. Negotitor cognition, Reserch in Orgniztionl Behvior (9), B.M. Stw nd L.L. Cummings (eds.), Greenwich, CT: JAI Press, [2] Chvez, A. nd Mes, P. Ksbh: An gent mrketplce for buying nd selling goods, 1st Intl Conf on Prcticl Appli. of Intelligent Agents Technology, [3] Frtin, P., Sierr, C. nd Jennings, N.R. Negotition decision functions for utonomous gents, Interntionl Journl of Robotics nd Autonomous Systems, 1998, (24:3-4), [4] Frtin, P., Sierr, C. nd Jennings, N.R. Using similrity criteri to mke trde-offs in utomted negotitions, Artificil Intelligence nd Int. Journl of Autonomous Agents nd Multi-Agent Systems, (to pper, downlodble t f) [5] Foroughi, A. Minimizing negotition process losses with computerized negotition support systems, The Journl of Applied Business Reserch, 1998, (14:4), [6] Goh, K.Y., Teo, H.H., Wu, H. nd Wei, K.K. Computer-supported negotitions: n experimentl study of brgining in electronic commerce, in Proceedings of the 21st Annul Interntionl Conference on Informtion Systems, Brisbne, Austrli, 2000, [7] Goldberg, D.E. Genetic lgorithms in serch, optimiztion, nd mchine lerning, Addison-Wesley, [8] Hollnd, J.H. Adpttion in nturl nd rtificil systems, The MIT Press, [9] Hordijk, W. nd Mnderick, B. The usefulness of recombintion, In F. Morn, A. Moreno, J.J. Merelo, nd P. Chcon (eds.), Advnces in Artificl Life: Proceedings of the Third Europen Conference on Artificil Life, Springer-Verlg, 1995, [10] Lomuscio, M.W. nd Jennings, N.R. A clssifiction scheme for negotition in electronic commerce. In F. Dignum nd C. Sierr, editors, Agent-Medited Electronic Commerce: A Europen Agentlink Perspective, Springer-Verlg, [11] Mes, R.P. nd Mouks, A.G. Agents tht buy nd sell, Communictions of the ACM, 1999, (42:3), [12] Mtwin, S., Szpiro, T., nd High, K. Genetic lgorithms pproch to negotition support system, IEEE Trnsctions on Systems, Mn, nd Cybernetics, 1991, (21:1), [13] Oliver, J.R. A mchine lerning pproch to utomted negotition nd prospects for electronic commerce, Journl of Mngement Informtion Systems, 1997, (13:3), [14] Riff, H. The Art nd Science of Negotition, Hrvrd University Press, Cmbridge, USA, [15] Rubinstein, A. Perfect equilibrium in brgining model, Econometric, 1982, (50:1), [16] Sndholm, T. Agents in electronic commerce: component technologies for utomted negotition nd colition formtion, Autonomous Agents nd Multi-Agent Systems, 2000, (3:1), [17] Sycr, K.P. Negotition plnning: n AI pproch, Europen Journl of Opertionl Reserch, 1990, (46), [18] Thompson, L.L. nd Hstie, R. Socil perception in negotition, Orgniztionl Behvior nd Humn Decision Processes, 1990, (47),