Non-symmetric matching information for negotiation support in electronic markets BARTEL VAN DE WALLE
VEERLE VAN DER SLUYS
New Jersey Institute of Technology IS Department Newark NJ 07102, USA
[email protected]
Actonomy NV 105 Lock Street Newark NJ 07103, USA
[email protected]
Abstract Electronic markets are virtual meeting places where buyers and sellers meet and interact to trade products or services. In this paper, we consider an agent-based information system to support the ongoing negotiations among the traders in such a market. The information system's agents are active within certain market categories of which they carry a multi-criteria description. This enables the specification of a Request for Quotes (RFQ)/Request for Proposals (RFP) protocol through which the negotiations are conducted. We illustrate this approach for the specific case of an electronic market for diamonds, and we motivate the importance of providing relevant matching information to the market participants. We explore a nonsymmetric matching technique based on the composition of fuzzy relations first proposed by Bandler and Kohout. We show how these compositions allow us to express various significant matching relations among the market participants and the market products. We argue that this information is crucial to improve the effectiveness of market negotiations. Keywords: electronic marketplace; multicriteria decision making; negotiation support; fuzzy relations; matching. 1. INTRODUCTION Electronic commerce, or ecommerce, covers the processes of buying, selling, or exchanging products, services, or information over computer networks,
including the Internet (Turban et al. 1999). Electronic marketplaces, or emarkets, are ecommerce sites on the Internet that allow large communities of buyers and suppliers to meet and trade with each other. They present ideal structures for commercial exchange, with the potential of achieving new levels of market efficiency by tightening and automating the relationships between buyer and supplier. Emarkets usually are either horizontal or vertical marketplaces. Horizontal emarkets are emarkets that integrate across industries, providing generic products and functional services like office supplies, maintenance, and surplus asset liquidations. While eprocurement received the most hype in the media and stock markets, the benefits of ecommerce and emarkets extend beyond the purchasing departments of organizations into several other functional areas, which include the sales and marketing, inventory management, human resources and IT management (Legg Mason 2000). Other markets focus on the whole value chain of a single industry. As they integrate over the entirety or parts of the chain from raw materials to the finished product, they are called vertical markets. In the following section, we describe a diamond trading emarket and outline how this particular emarket operates on a RFQ/RFP mechanism through which buyers and sellers specify their offers or counteroffers in terms of multiple criteria. Based on these specifications, it is indicated how well the various trading parties match. Upon viewing this information, either party may decide to initiate a negotiation with the other party and invite a counteroffer. In Section 3 we touch upon a key issue in any marketplace: the appropriate matching of buyers and sellers. We motivate why the matching process
deserves our attention, and we propose a new matching method that is non-symmetric in nature: the matching value of a seller to a buyer is not necessarily identical to the matching value of that buyer to that seller. Section 4 illustrates the new approach through the construction of specific matching relations. We conclude in Section 5 by summarizing our results. 2. MULTI-CRITERIA NEGOTIATION SUPPORT IN A DIAMOND EMARKET Intellitrade is an agent-based information system to support multi-criteria decision making and negotiation in electronic marketplaces, developed by Actonomy NV, a software company headquartered in Belgium with R&D offices in New Jersey (USA). Using Intellitrade, buyers and sellers can create software agents to engage in and support their buying and selling transactions on the emarket (see Maes et al. 1999 for a discussion on the use of software agents in ecommerce). The diamond emarket is described by different catalogs of particular types of diamonds, for example round or pear-shaped diamonds. Every catalog is characterized by a set of specific criteria, such as the carat or cut of a diamond. The size of a diamond is expressed in carat weight, while the cut of a diamond represents its roundness, depth and width and the uniformity of the facets. When a buyer or seller logs on to the market, they create a software agent in a specific catalog to announce their offer (for a seller) or prepare their request (for a buyer). The agents are created by indicating which of the catalog’s criteria are relevant (for instance, in addition to cut or carat, the price or delivery time) and what values the participant is offering or looking for (for instance a carat of 1000, and a cut of 4 (the ideal cut), a price of 100,000 dollar and a delivery time of two days. The participant also indicates the relative importance of every criterion, and whether the values selected are negotiable or not (see Figure 1). Once the agent’s specifications are completed, it automatically scans the catalog in which it resides to identify how well its specification matches with the other agents that are active in the catalog.
Figure 1. A software agent is initiated in a diamond catalog These matching values are shown to the participants, upon which a negotiation with a party that is indicated as a good match can be started. When the other party responds, both parties can then monitor their ongoing negotiation through their respective agents’ negotiation history displays as shown in Figure 2, until the negotiation ends – hopefully leading to the execution of a transaction.
Figure 2. Monitoring the exchange of offers and counter-offers 3. THE ROLE AND IMPORTANCE OF MATCHING In general, the business interactions between two parties, such as buyers and sellers, can be classified in four general phases (Strobel 2000):
• • • •
A knowledge or intelligence phase: to collect information on the parties and the products that are offered; An intention phase in which supply and demand are expressed by both parties; An agreement phase during which the terms and conditions of the transaction are specified; And a settlement phase, where the agreed-upon contract is executed.
Within the agreement phase, matching usually is the first process: suitable offers are identified, for instance through a constraint-based search mechanism. Once these offers are found, they can be evaluated by means of a scoring mechanism, for instance by using a multi-criteria decision technique. Based upon the scores, the offers can then be rankordered. Consequently, both parties either reach a final agreement or engage in a process of further negotiation when agreement is not yet within reach. This negotiation process usually implies that one or both parties modify their offer to better accommodate the counter-party (Van de Walle et al. 2001, 2002; Faratin 2001). Clearly, the process of matching two parties is a key process in preparing for successful negotiations. The better the two parties’ offers match, the more likely it is that agreement can be reached, and negotiations may even be avoided completely. Though many examples of matching functions in the literature can be found, most have one property in common: they represent a symmetric function. The symmetry of these matching functions is a rather severe restriction, as we may be interested in the containment of features that are not symmetric, for, if A contains a set of features F of B, B may not always contain all the features of A, as described by F. This indicates that the commonly used symmetric matching functions are rather special relations, which restricts the ‘matching’ in a rather undesirable fashion (Bandler et al. 1984). For this reason, we introduce in the following section Bandler and Kohout's non-symmetric relational compositions. 4. NON-SYMMETRIC MATCHING BASED ON THE COMPOSITION OF RELATIONS 4.1 The composition of crisp relations
Assume for instance that we are dealing with two different relations: the relation R being a relation
from a set X to another set Y, and the relation S a relation from the set Y to a third set Z. This composition of R and S, denoted as R○S, is defined as: R○S = { (x,z) | there exists an element y in Y such that xRy and yRz}. Recall that the R-afterset of an element x of X, denoted xR, consists of all elements of Y that are Rrelated to x , and the R-foreset of an element y of Y, denoted Ry, consists of all elements of X that are Rrelated to y. We can then easily rewrite the composition condition in terms of fore- and aftersets as R○S = { (x,z) | xR ∩ Sz ≠∅}, or, in words, the intersection of the R-afterset of x and the S-foreset of z is not empty. The nonemptyness of the intersection of xR and Sz obviously is not a very strong condition. This makes it on the one hand easy to satisfy, but on the other hand it is not very informative since we don't know how many elements belong to the intersection or how "strong" the composition really is. Bandler and Kohout have introduced other types of compositions which each impose stronger conditions on the intersecting set xR ∩ Sz, and hence are more difficult to satisfy, but in doing so, are much more informative (Bandler and Kohout 1980). The first such composition is the socalled triangular sub-composition of R and S, denoted as R S, and defined as: R S = { (x,z) | xR ∩ Sz ≠∅ and xR is a subset of Sz}. In addition to the non-emptyness condition of the circular composition, the triangular sub-composition (or shortly sub-composition hereafter) requires that the R-afterset of x is a subset of the S-foreset of z. In the same spirit, the (triangular) super-composition of R and S, denoted as R S, is defined as: R S = { (x,z) | xR ∩ Sz ≠∅ and Sz is a subset of xR}. The super-composition switches the roles of xR and Sz, now requiring that the S-foreset of z is a subset of the R-afterset of x. Finally, the square composition of R and S, denoted as R □ S, is defined as:
R □ S = { (x,z) | xR ∩ Sz ≠∅ and xR = Sz}. Clearly, the square composition is the intersection of the super-composition and the sub-composition, i.e., R □ S = (R S) ∩ (R S), meaning that the square composition is the most restrictive type of composition. 4.2. The composition of fuzzy relations Let R be a fuzzy relation from X to Y, i.e., a mapping from X × Y into [0,1]. For every ordered pair (x,y) ∈ X × Y the quantity R(x,y), taking values in [0,1], is to be interpreted as the strength of the existing (fuzzy) R-relation between x and y. As such, the Rafterset of x associates to every y∈Y the degree in which x is R-related to y; while the R-foreset of y associates to every x∈X the degree in which x is Rrelated to y; Technically speaking, there are different ways to define the composition of two fuzzy relations. The most popular extension of the classical circular composition to the fuzzy case is the so-called maxmin composition defined as follows. Let X, Y and Z be ordinary non-empty and finite sets, R a fuzzy relation from X to Y and S a fuzzy relation from Y to Z. The max-min composition of R and S is the fuzzy relation R○S from X to Z defined by x(R○S)z = max y∈Y min (R(x,y), S(y,z)), for all (x,z) ∈ X × Z. This means that the strength of the relation between x and z is defined as the strongest of all possible "connections" between x and z, where the strength of a connection is equal to the strength of its weakest connecting part. The extension of the sub-, super- and square composition to the fuzzy case requires the introduction of additional mathematical operators. Assume the relations R and S are fuzzy relations. Then the R-afterset of x, xR, and the S-foreset of z, Sz, obviously are fuzzy sets in Y. The common definition of inclusion of the fuzzy set xR in Y in the fuzzy set Sz in Y is given by xR ⊆ Sz ⇔ (∀ y ∈ Y)( xR(y) ≤ Sz(y)).
However, this definition represents an unconscious step backward to the realm of dichotomy as Bandler and Kohout already noted. Far more in accord with the spirit of fuzzy set theory, would be the assignment of a degree of subsethood of xR in Sz. One approach to achieve that objective is to define the binary fuzzy inclusion relation Inc for any two fuzzy sets A and B in X as follows: Inc( A, B) =
1 min(1 − A( x) + B ( x),1), n x∈X
∑
with n the cardinality of X (De Baets and Van de Walle, 1994). Using this definition of fuzzy inclusion, we easily obtain the following definitions for the remaining compositions:
xi ( R ` S ) z j =
xi ( R a S ) z j =
1 n
∑ min(1 − x R( y) + Sz i
j ( y ),1);
y∈Y
1 ∑ min(1 + xi R( y) − Sz j ( y),1); n y∈Y
with n the cardinality of Y, while for the square product it still holds that xi (R □ S) zj = xi (R S) zj ∩ xi (R S) zj, with the intersection usually modelled by the minimum operator, i.e., xi (R □ S) zj = min(xi (R S) zj, xi (R S) zj). The sub-composition can be interpreted as giving the mean degree to which the fuzzy afterset xiR is contained in the fuzzy foreset Szj, and similar for the super-composition. 5. EXAMPLES IN THE DIAMOND EMARKET In this section, we apply the non-symmetrical relational compositions to derive relevant matching information for participants in the diamond emarket. As in any electronic marketplace, we are basically dealing with three entities, namely Buyers, Sellers and Products. Sellers offer Products (diamonds) for sale, while Buyers are interested in buying the diamonds. The following examples illustrate how non-symmetrical compositions can be constructed, and the wealth of information that can be derived from such compositions.
5.1. Example 1 Let R be a relation from the set of Products (diamonds) P to the set of Buyers B, and let aRb carry the meaning that diamond a is of interest to buyer b. Then, S = Rt is a relation from the set of Buyers to the set of Products, with bSc meaning that buyer b is interested in diamond c. The R-afterset of a diamond a, aR, is the subset of B consisting of those buyers that are interested in diamond a. Similarly, Sc or the S-foreset of diamond c is the subset of B consisting of those buyers interested in diamond c. One easily verifies that the relational compositions R° S, R < S, R > S, and R S are all binary relations in the set of diamonds P. The various compositions will allow us to derive information on how different diamonds generate matching interests among buyers. In this case, the relational compositions carry the following meaning: •
a(R ° S)c: there exists at least one buyer interested in both diamonds a and c;
•
a(R < S)c: diamond a is of interest to every buyer who is interested in diamond c, while the opposite is not necessarily true;
•
a(R > S)c: diamond c is of interest to every buyer who is interested in diamond a, while the opposite is not necessarily true;
•
a(R S)c: every buyer who is interested in diamond a, is also interested in diamond c, and vice versa.
5.2. Example 2 Let R be a relation from the set of Buyers B to the set of Sellers S, and assume that aRb means that buyer a is interested in negotiating with seller b on a particular diamond. Then, S = Rt is a relation from S to B: bSc iff seller b has been approached to negotiate with buyer b on a particular diamond. The relational compositions R° S, R < S, R > S, and R S now are all binary relations in the set of Buyers B. The various compositions will allow us to derive information on how different buyers generate matching negotiation requests.
In this case, the relational compositions carry the following meaning: •
a(R ° S)c: there exists at least one diamond for which the buyers a and c are requesting to initiate a negotiation;
•
a(R < S)c: whatever diamonds buyer c is interested to start a negotiation on, buyer a is also interested, while the opposite is not necessarily true;
•
a(R > S)c: whatever diamonds buyer a is interested to start a negotiation on, buyer c is also interested, while the opposite is not necessarily true;
•
a(R S)c: represents a symmetrical matching of buying interests: whatever buyer a is interested to negotiate on, also interests buyer c, and vice versa.
5.3. Numerical example We define two relations: the relation O (offer) from S to P, and the relation CO (counter-offer or demand) from B to P, and assume we have exactely three sellers in S, three diamonds in P and three buyers in B. Assume now that all sellers want to sell the three diamonds together as a 'package deal', with each of the diamonds in the deal having a unique and different (monetary) value for each of the sellers. The buyers are interested in buying such a 'package', and each of them values the diamonds differently, e.g. based on their girlfirends' tastes. The question here is to whom the sellers should sell, or from whom the buyers should buy. We assume that a buyer will be interested in buying a diamond when his value is larger than a seller's value (and thus considers the diamond as relatively cheap). Conversely, a seller will be interested in selling a diamond when his monetary value of the diamond is smaller than the value attached to that diamond by the buyer (and who thus is relatively eager to buy). Let the offer relation O from S to P be defined as
0.8 0.6 0.4 O = 0.3 1 0.5 , 0.7 0.9 1
and the counter-offer relation CO from B to P as
1 0.7 0.6 CO = 0.5 1 0.3 . 0.8 0.5 0.2 This leads to the following compositions:
1 0.86 0.9 O < CO t = 0.9 0.93 0.73, 0.8 0.7 0.6 expressing the degree to which the 'package deal' a seller offers is wanted by a buyer;
0.83 0.76 0.9 O > CO = 0.83 0.93 0.96 , 1 0.83 0.96 t
expressing the degree to which the 'package deal' a buyer wants is offered by a seller. From the subcomposition, we learn that seller 1 (S1) should be selling to B1 (buyer 1), S2 to B2, and S3 also should try to sell to B1. Conversely, from the supercomposition we see that it might be in the best interest of B1 to talk to S2 – indeed, B1 values diamond 1 in the package very high (value of 1), which the seller values very low (only 0.3) : a true bargain. Similarly, B2 should talk to S1 and B3 to S2 as well. Clearly, this will create some interesting negotiation dynamics! 6. CONCLUSIONS AND FUTURE WORK Matching information provides an important cue to market participants whether to actively engage in a negotiation on a particular product or not. Without this information, decisions to engage in negotiation may be taken randomly, increasing the likelihood of prematurely abandoned negotiations. We have shown how non-symmetric matching information can be obtained from carefully constructed relational compositions, and we have illustrated how these constructions indeed reveal useful information to the market participants. We are currently planning experiments to assess how this information is used
by the market participants to improve their online negotiations. REFERENCES 1. Bandler, W. and L. Kohout, “Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and artificial systems”, in Fuzzy Sets: Theory and Application to Policy Analysis and Information Systems (Wang, S.K. and Wang, P.P., eds.), Plenum Press, New York and London 1980, pp. 341 – 367. 2. Bandler, W., Keravnou, E. and W. Bandler, "Automatic documentary information retrieval by means of fuzzy relational products", in TIMS/Studies in Management Sciences 20 (1984), 383 – 404. 3. De Baets, B. and B. Van de Walle, “Dependencies among alternatives and criteria in MCDM problems”, Proceedings of CIFT'94, Fourth International Workshop on Current Issues in Fuzzy Technologies (1994), 80 – 85. 4. Faratin, P., Sierra, C., and Jennings, N. R ," Using similarity criteria to make negotiation trade-offs", in 4th International Conference on MultiAgent Systems (ICMAS'00), Boston, MA, USA, 10-12 July 2000, pp. 119 – 126. 5. Legg Mason Wood Walker, Inc., “B2B eCommerce Industry Analysis”, 2000, 65 pp. 6. Maes, Pattie, Guttman, R. H. and Moukas, A.G., "Agents that buy and sell: Transforming Commerce as we Know It", Communications of the ACM, 42(3) (1999), 81 – 91. 7. Ströbel, Michael, "Effects of Electronic Markets on Negotiation Processes"Proceedings of the ECIS 2000 Conference, Vienna Austria. 8. Turban, Efraim, Lee, Jae, Kind, David, Chung, H. Michael, Electronic Commerce. A Managerial Perspective. Prentice Hall. Upper Saddle River, NJ. USA, 1999. 9. Van de Walle, B., Sven Heitsch and Peyman Faratin, “Coping with one-to-many multi-criteria negotiations in an electronic marketplace”, Proceedings of the eNegotiations Workshop at the 17th International Database and Expert Systems Applications Workshop DEXIA’01 (Munchen, September 2001), pp. 747 – 751. 10. Van de Walle, B., “A relational analysis of the decision makers’ preferences”, International Journal of Intelligent Systems (Special Issue on Preference Modeling), 2002, forthcoming.
