Manuscript 15.6.2004

E-learning for Mathematical Models of Negotiation Analysis

An E-learning Approach for Teaching Mathematical Models of Negotiation Analysis

Harri Ehtamo, Raimo P. Hämäläinen, Ville Koskinen* Helsinki University of Technology

Systems Analysis Laboratory P.O. Box 1100, FIN-02015 HUT, Finland Tel. 358-9-451 3054, fax 358-9-451 3096

ehtamo@hut.fi, raimo@hut.fi, ville.koskinen@hut.fi

* Corresponding author

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Abstract

We describe a web-site containing material and tools for learning mathematical models of negotiation analysis and discuss students’ experiences of its use. The site is part of our general e-learning decision making site, www.dm.hut.fi.

The negotiation analysis section provides an introduction to the theory and gives online practice in negotiation support. The material consists of theory sections, case studies and assignments. It also includes quizzes for self-evaluation and video clips that illustrate the use of the Joint Gains negotiation support system.

Models of negotiation analysis are interesting from the e-learning perspective because negotiations always are interactive in nature. The Joint Gains is an interactive negotiation support system for multi player multi issue negotiation problems and it is intended for real-life negotiations. Here, we apply the Joint Gains as a tool for active learning in role-playing experiments.

“Introduction to game theory and negotiation” learning module was evaluated in a mathematical modeling web-course. The experiences were encouraging and mainly positive; the students are willing to work in similar learning environments in the future.

Key words: Negotiation Analysis, Decision Analysis, Negotiation Support, e-Learning, Game Theory 1. Introduction

The web is a natural and promising platform for supporting negotiations. Nevertheless,

people are not yet familiar with web-tools available to support their decision making. To

promote the emergence of e-negotiations, we have created e-learning material to teach e-

negotiation methods for the university students. Particularly our focus is on teaching

mathematical models of negotiation analysis that are prescriptive models of negotiation for

generating acceptable compromise outcomes (Raiffa 1982). Negotiation analysis has its

roots in game theory and in decision analysis; see, e.g., the discussions on the subject in

Sebenius (1992) and in Raiffa, Richardson and Metcalfe (2002, p. 1).

Software systems can be developed for supporting negotiations. They provide

possibilities for exchanging messages between negotiating parties and they may also

implement mathematical methods in negotiation analysis, see, e.g., Rangaswamy and Shell

(1997) and Anson and Jelassi (1990). Many of these systems can be used in a distributed

mode, which allows the negotiating parties to negotiate, e.g., over the Internet, in separate

physical locations.

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In this paper, we present a way to introduce negotiation support systems (NSSs) for

students. We let them to practice the use of an NSS in role-playing exercises and thus gain

insight in how it could be applied in real-life problems. The role-playing exercises provide

possibilities for “learning by doing”, which is a concept originally introduced by Dewey

(1938). Learning by doing has been proven to be a useful way of learning negotiation skills

because the nature of the negotiations is very practical and it has been often claimed in

literature that the best way to learn negotiation is to do it; for pedagogical arguments on

this see, e.g., Susskind and Corburn (2000).

There are many studies on teaching negotiations by face to face role-plays for university

students and real negotiators, see, e.g., Winham (2002). Some recent studies have also

focused on assessing possibilities of using computers for teaching negotiation and e-

negotiation skills for university students (Köszegi and Kersten 2003; Saunders and

Lewicki 2000). According to these studies, computer systems can provide an effective way

for testing, evaluating and reinforcing acquired knowledge on negotiations. Hämäläinen et

al. (2001) have also experiences on applying computer systems for teaching negotiation

skills but with different aims. Their starting point was to learn more about a lake-river

regulation policy problem. They let some university students to make role-playing

experiments with an NSS, the Joint Gains software (Kettunen et al. 1999). The

experiences indicated that the role-plays provide a way to explore and learn the objectives

of different parties and to get practical feedback about suitability of a particular NSS for

applications without burdening the real decision makers. Similar observations have been

made in a workshop on environmental negotiations at Caspian Sea area (Meerts 2003).

Students of international relations had face to face role-playing experiments, which

provided much insight, e.g., on the complexities of the negotiation problem at hand,

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coalition building and power between the parties and possible coalitions. Thus role-plays

can be useful for education and particularly, NSSs can be used to illustrate methods in

negotiation analysis.

Our students use the Joint Gains in role-playing experiments. The Joint Gains is

intended for solving negotiation problems online over the web and it implements an

interactive multiple criteria negotiation method. The role-plays with the river-lake

regulation policy problem by Hämäläinen et al. (2001) also indicated that the role-players

need clear instructions. They need to understand the method behind the NSS to see that it

is helpful to work with such a software. Our e-learning material consists of theory sections

including relevant references to the literature, case studies and software assignments,

which are complemented with multimedia presentations such as video clips, animations

and colorful graphics where necessary. It also contains quizzes for self-evaluation and

analytical assignments. The learning material is primarily planned for students in

operations research and management science (OR/MS) but also other engineering students

can work with it as well.

Teachers can use our learning material for introducing analytical NSSs and

mathematical models of negotiation problems in their own courses, e.g., on mathematical

modeling or on possible applications of NSSs, such as, political or environmental decision

making, international affairs, e-business, etc. (Hämäläinen et al. 2001, Sebenius 2002,

Kersten 2003). The role of the teacher is not to act only as a lecturer but also as an

instructor, who guides the students to work with the material more independently than

traditionally and answers the students’ questions, e.g., by e-mail or in instructed e-learning

sessions. Since the learning material and the Joint Gains can be used completely over the

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web with Java enabled web-browser, the teachers need not to take care for technical

arrangements and maintenance.

The e-learning material can be used to form learning modules which consist of selected

parts of the material and correspond to a few hours lecture plus the exercises. We have

formed an e-learning module “introduction to game theory and negotiation”; see the web-

site (Ehtamo, Hämäläinen and Koskinen 2002). We present the experiences of its use in a

web-course on mathematical modeling in Section 6. The material could also be used to

create other modules for decision makers and mediators that are preparing themselves for

real-life negotiations and possibly for the use of the Joint Gains NSS. These possibilities

are discussed in Section 7. Section 2 reviews some web-material related to negotiation

analysis and Sections 3, 4 and 5 present the contents and the structure of our e-learning

module.

2. E-Learning Negotiation Analysis on the Web

There is e-learning material on negotiation analysis and on related fields such as game

theory, decision analysis and mathematical modeling available in the Internet. For

example, MENTOR project was initiated at the University of Strathclyde already in 1992.

The project aimed to “improve the effectiveness and the efficiency of teaching and

learning OR/MS through the use of multimedia computer based learning materials”

(Thornbury et al. 1996). The results showed that it is beneficial to use computers for

teaching mathematical modeling, since models and methods can be illustrated and

visualized through animated simulations and interactive exercises (Ball and Thornbury

2002). More recently there has been much work on developing e-learning materials and

techniques in the field of mathematical modeling. For instance, our e-learning material has

been developed as part of the OR-World project (Suhl and Kassanke 2000), and

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International Federation of Operations Research Societies (IFORS) maintains tutOR-site

that is a collection of e-learning modules (Sniedovich 2002).

Kersten (2002) has developed the first e-learning course on multi-criteria based

negotiations: “Negotiations and e-negotiations: management and support” -course and

Köszegi and Kersten (2003) have presented experiences of its use. The course consists of

an electronic textbook presenting theory, which focuses on basic concepts of economics,

game theory and social psychology. It also contains some case studies and related role-

playing assignments, which involve the students to negotiate both with an NSS and face to

face directly. Our notions on e-learning of mathematical models of negotiation analysis are

quite similar to those presented by Köszegi and Kersten. Our module and their course have

been developed independently and they both emphasize learning by doing and take

advantage of the electronic media to produce complete learning modules that can be used

in combination with face to face sessions.

The materials we have developed are relatively similar, but our site has a narrower

focus. We emphasize the mathematical modeling approach to negotiations. The special

feature on our site is the use of the Joint Gains software, which is publicly available on the

web. It is a general purpose software, which allows the users to create their own

customized negotiation cases in it. Thus its use is not limited to the cases created by

system administrators as is the case with the INSPIRE (Kersten and Noronha 1999) used

in Kersten’s e-learning course.

INSPIRE uses a standard case, which describes a simple two party buyer-seller problem.

The case has been used for teaching e-negotiations by organizing negotiation sessions

where students use the system anonymously to solve the buyer-seller problem; see, e.g.,

Kersten et al. (2003) and Kersten et al. (2002). The negotiation sessions include the

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tournament International Competition for Online Dispute Resolution, where six different

NSSs are used for e-learning e-negotiations (Davis 2003). The participating students form

local teams and solve a negotiation case by negotiating with another team by using an NSS

of their choice.

There are four NSSs, which do not implement any particular mathematical method,

available in the tournament: SimpleNS (Interneg Group 2003), MeetingOne (2003),

WebNS (1999) and Negoisst (Schoop et al. 2003). These systems provide tools for

communication through exchange of text messages over the Internet between the

negotiating parties. Additionally, MeetingOne and WebNS allow videoconferencing.

Other two systems, INSPIRE and SmartSettle, instead implement mathematical

negotiation models. They help the parties to describe their preferences by constructing

additive value functions. The parties use the value functions in negotiation for evaluating

their offers and the other party’s counteroffers. Finally, when the parties reach a settlement

through submitting consecutive offers, these systems can be used to compute a Pareto

optimal solution (Thiessen, Loucks and Stedinger 1998, Kersten and Noronha 1999).

There are also other similar NSSs using additive value functions, e.g., Negotiation

Assistant (Rangaswamy and Shell 1997) or MEDIATOR (Surrat 1997). Unlike these

systems, our Joint Gains software provides aid for reaching Pareto points starting from

initial points and it only needs local preference information from the parties to proceed.

Therefore the Joint Gains does not assume, for example, the additive value function

model; for details see Section 4.

Harvard University Press e-learning division (2001) has published an e-learning

program “Yes! The On-Line Negotiator” based on the book by Fisher and Ury (1981). It is

only commercially available and it contains slideshows summarizing the theory,

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presenting some case problems and related quizzes. The slideshows summarize the

concept of principled negotiation (Fisher and Ury 1981), which emphasizes the

importance of co-operation between the negotiating parties, who should work together side

by side and focus on their common problem and each others interests and objectives. This

joint problem solving idea is also in a central role in our e-learning material.

There is a lot of e-learning material available on game theory. For instance, Al Roth

(1995) has an experimental economics site, which contains articles and textbooks on the

theory and applications of game theory in electronic format. There are also many

interactive applets on the web which let the students play against the computer different

games, such as variants of the prisoners’ dilemma game, see, e.g., (Daniels 2003, Shor

2001).

Negotiation support also uses decision analysis to help decision makers in their

individual evaluations. There are general sites referring to web-material on decision

analysis; see, e.g., “courses and syllabi” on the Decision Analysis Society site (2003) or on

the Decisionarium site (Hämäläinen 2004), which provides access, e.g., to the Web-

HIPRE value tree software (Hämäläinen and Mustajoki 1999, Mustajoki and Hämäläinen

2000). In the case of negotiations, the Web-HIPRE software could be applied for

evaluating offers and counteroffers. Related to decision analysis, Hämäläinen and Dietrich

(2002) have presented the first complete e-learning module on value tree analysis.

3. Module Contents

In the “introduction to game theory and negotiation” e-learning module (Ehtamo,

Hämäläinen and Koskinen 2002), we teach mathematical models of negotiation analysis

through practical examples. First, we describe the basic concepts in game theory by two

classical examples: the prisoners’ dilemma game and the problem of the commons. For

different variants of these games and for further reading, the students are referred to Luce

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and Raiffa (1957), Myerson (1997), and Gibbons (1992). The games used on our site are

relatively simple but they are also rich enough to illustrate the central concepts, such as

Nash equilibrium solution and Pareto optimality. The examples emphasize that the Nash

equilibrium solution is a rational result for the players even if there are jointly preferred

Pareto points. The latter do not have the equilibrium property and hence reaching them

provides co-operation.

We then discuss negotiation analysis that can be used to give prescriptive aid for

negotiating parties to make joint decisions in co-operation (Raiffa, Richardson and

Metcalfe 2002). We present a rough classification of the methods in negotiation analysis

depending on whether the parties’ value functions are elicited or not and whether the

parties make concessions or not; see, Teich, Wallenius and Wallenius (1994), and Ehtamo

and Hämäläinen (2001) for further discussion. If the parties’ preferences are modeled

through value functions, it is possible to use various, e.g., axiomatic, models to choose fair

Pareto solutions for the negotiating parties. Nevertheless, it is usually difficult to elicit

explicitly value functions. In this case, interactive methods, which do not require the

elicitation of the value functions, can be used. When making concessions, the parties give

separate initial offers and narrow differences between them by subsequent offers and

counteroffers until they reach each other. Instead of concession making, the parties may

also search for joint gains. In this case, they start the negotiation from a joint initial point

and search for new jointly preferred points.

As a detailed example of interactive joint gains searching methods we describe the

jointly improving direction method. The method is originally presented for two-party two-

issue negotiation problems by Ehtamo, Verkama and Hämäläinen (1999). Ehtamo,

Kettunen and Hämäläinen (2001) have generalized it to include multiple parties and

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multiple issues; for an “easy to read” -version of the method see Ehtamo and Hämäläinen

(2001). The method formalizes mathematically the single negotiation text procedure by

Raiffa (1982, Chapter 14). The Joint Gains software implements the jointly improving

direction method and it acts as a mediator for the negotiating parties.

4. The Jointly Improving Direction Method

In the e-learning material, we present the jointly improving direction method by using

verbal and simple geometrical reasoning through an example where it is applied to find

Pareto points for the problem of the commons. Here, we present the method briefly to

illustrate its interactive nature. For simplicity, imagine that there are two continuous

issues, x1 and x2, and two negotiating parties, 1 and 2. We assume that the parties’ value

functions over the issues are concave and differentiable, although we do not assume that

their explicit form is known.

The mediator generates step-by-step new jointly preferred intermediate points for the

parties. To produce a new intermediate point, the mediator directs the parties through the

following three steps:

1. Identification of the parties’ most preferred directions at the intermediate point.

2. Determination of a fair compromise direction based on the most preferred

directions.

3. Determination of a new jointly preferred intermediate point in the compromise

direction.

At step 1, the parties criticize the intermediate point. The party lets the mediator know

that she wants to have, e.g., more issue x1 and less issue x2. Thus the mediator knows into

which quadrant in the (x1,x2)-plane the party wants to move from the intermediate point,

see Figure 1. Then the mediator draws a circle around the intermediate point and lets the

party to choose her most preferred point in the circle arc in the quadrant in question. In

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practice, the mediator chooses some discrete points in the circle and helps the party to

choose the best point by stating a series of pairwise comparison tasks of the form “Which

one of these points do you prefer more, A or B?”. The number of these comparisons can be

decreased by choosing the discrete points cleverly. This can be done by using a suitable

line search method.

The mediator draws a line segment from the intermediate point through the most

preferred point in the circle. This direction is called most preferred and it approximates the

gradient direction of the party’s value function. If the party’s value function is concave, all

the directions, which form an angle strictly smaller than 90° with the gradient, are

improving directions for the party. A direction is called improving if by taking a

sufficiently small step on it party’s value function increases. By taking the intersection of

the parties’ improving directions, the mediator can produce the set of all jointly improving

directions, see Figure 2.

- - - - Figures 1 and 2 are about here - - - -

At step 2, the mediator chooses one fair jointly improving direction as the compromise

direction. For instance, in the case of two parties it is defined as the direction bisecting the

angle between parties’ most preferred directions. If there are more than two parties a

mathematical programming problem needs to be solved; for details on this, see, Ehtamo,

Kettunen and Hämäläinen (2001).

At step 3, the mediator chooses a new intermediate point by taking a suitable step in the

compromise direction. The step must not be too long to guarantee that the new point is

jointly preferred. It must not be either too short because too short steps will produce very

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little gain for the parties. Hence the mediator chooses a step length which is the minimum

of the distances the parties would prefer to move in the compromise direction. The

mediator identifies party’s most preferred step length by choosing some discrete points in

the compromise direction and again using some line search method as at step 1; see Figure

3.

- - - - Figures 3 and 4 are about here - - - -

By repeating the steps 1, 2 and 3 iteratively, the mediator guides the parties to a Pareto

point, see Figure 4, where the negotiation process is depicted in the issue space and in the

utility space. By varying the initial point, the process can be used to produce several Pareto

points, after which the parties may vote or make concessions among these Pareto points.

5. Module Description

Previous sections presented what we teach for the students. This section, on the other

hand, describes how we teach them. Our e-learning module includes only selected parts of

our negotiation analysis e-learning material and it is primarily designed for the students of

OR/MS but also other engineering students can use it. Learning module means an

independent whole, which corresponds to a few hours lecture and assignments in a

traditional university course. We can form complete courses by sequencing learning

modules into larger entities, which we refer to as learning paths. A learning path may

contain material from different sources, e.g., it could combine the learning module

described here, more details and more interactive assignments on game theory from Al

Roth’s material (1995) and social viewpoints from the “Negotiations and e-negotiations:

management and support” course (Kersten 2002).

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We follow a generic e-learning module structure originally developed for the value tree

analysis e-learning module at the Systems Analysis Laboratory (Hämäläinen and Dietrich

2002), see Figure 5. In the following, we discuss the elements of the learning module,

which support different learning objectives and present the topic from different

viewpoints. Each module has a front page, see Figure 6, which contains motivating

introduction to the module and states explicitly what the students are expected to learn.

There is a link list at the end of the front page, which guides the students to navigate in the

material included in the module.

- - - - Figures 5 and 6 are about here - - - -

The online quizzes and the assignments are elements that include interactive parts of the

learning material. The theory sections and the case descriptions can be compared to an

ordinary introductory textbook but they are designed to be on-screen readable. It is a well-

known problem that reading electronic textbooks on a computer screen can be difficult,

see, e.g., Hobbs (2002), Weitl et al. (2002), Ball and Thornbury (2002). This is mainly due

to two reasons. First, students’ perception tires out when studying new information on a

computer screen. Second, only low amount of information can be shown on a computer

screen at a time, which tends the students to lose the overview. We have written the theory

in a format of a story telling about two friends, Harold and William. This story is

complemented with frequent headings and introductory overview sections that point out

the thread of the story and the core concepts of the theory.

We decided to include only basic, high school level, mathematical definitions and

analysis in the theory. Most of the presentation is based on colorful graphs and their

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interpretations. Further mathematical details were left to be found from articles and

textbooks given in further reading sections.

The theory is divided into subsections each of which consists of one HTML-page. The

table of contents of the theory is presented for the students in a navigation frame on the left

side of the body text to help the navigation and sharpen the overview. As an example,

Figure 7 illustrates a part of the theory section presenting the prisoners’ dilemma game.

The theory sections are also available as a PDF-document for printing.

- - - - Figure 7 is about here - - - -

Online quizzes are web-forms stored in the Quiz Star server (ALTec 1997). They

contain multiple choice questions regarding the theory. Their main purpose is to act as a

motivating self-evaluation tool by which the students can interactively test the knowledge

they have acquired. The quizzes summarize the core concepts of the theory and thus they

also sharpen students’ overview on the topic through presenting simple games and

negotiation situations. After filling in and submitting a quiz a student gets immediately a

response pointing out the correct and incorrect answers. In the case of possible incorrect

answers, the student should refer to the theory and try refilling and submitting the quiz.

Cases are simple problems encountered in real life. In this learning module, the students

study a description of a case, namely, buyer-seller problem. That problem represents a

typical case in e-commerce, where a buyer and a seller negotiate about price and delivery

time. The case acts as an example connecting the theory to real-life applications.

The module contains two types of assignments: analytical and software assignments.

The analytical ones ask the students to apply mathematical tools they have learned. In the

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software assignment, the students complete role-playing exercises and write a brief report

on their experiences. They solve the buyer-seller problem by the Joint Gains software

which implements the jointly improving direction method; see Section 3. The students first

create a negotiation case by defining the negotiating parties, a buyer and a seller, and the

issues they negotiate about, i.e., price and time, see Figure 8. After creating the case, the

students take their roles, start the negotiation and answer the pairwise comparison tasks.

Figure 9 shows how the students interact with the mediating software by answering the

questions and interact with each other directly by using an online chat for verbal

communication in the Joint Gains.

The assignments are delivered both as HTML and MS Word documents for the

students. Those who are able to use MS Word can apply the assignment document as a

report template and fill their answers directly in it. Besides the questions, the assignment

document contains detailed instructions so that the students need not to open a separate

window for writing a report, for reading the assignment and for reading the instructions.

There are also some video clips that are recordings demonstrating the use of the Joint

Gains at a “click the OK-button” -level. The main purpose of the clips is to reduce the

need for personal instruction and communication between the teacher and students by e-

mail or face to face directly. The clips are mainly intended to help the students who

consider themselves unfamiliar with computers and encourage them to start working with

the software assignment.

After completing the module, the students evaluate it by filling in an online

questionnaire about their subjective experiences. The evaluations are accomplished with

the Opinions Online software (Hämäläinen and Kalenius 1999), which is an online-

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platform for voting, surveys and group decision making developed at the Systems Analysis

Laboratory.

6. Experiences of Use

The following conclusions are based on the use of the learning module in November

2002 in a web-course on mathematical modeling organized by the Finnish Virtual

University (2003). The course consisted of eleven learning sessions and our module was

one of them.

There were nine one or two student groups from different Finnish universities who

completed our learning module. The students were mainly graduate students in industrial

engineering, systems engineering, physics or other engineering. They considered

themselves quite experienced users of web and they had some familiarity on e-learning

from the earlier learning sessions of the course but not on an e-learning format similar to

ours. The course was not compulsory for the students. We measure the students’ skills

based on their performance in the assignments. There is not a way to assess how much the

students actually learned during the session.

Nine of our students evaluated the learning module by filling in an online questionnaire

form. The results of the student evaluation were positive. Some of the students stated in

the free-form feedback that our module provided refreshing activities. They found our e-

learning format convenient despite the fact that it was something new for them. Most of

the students stated that they are willing to work in similar e-learning environments in the

future and that they could also recommend their experiences for their fellow students; see

the results in Table 1. This kind of positive attitude has been reported in literature also

earlier, see, e.g., Benbunan-Fich and Hilz (2002), and Spiceland and Hawkins (2002), and

it may well reflect the fact that the learning format was new for most of the students.

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- - - - Table 1 is about here - - - -

The lack of face to face interaction between students and teacher, and among the

students, is widely discussed problem in e-learning literature, see, e.g., articles by Wesley

(2002), Dufner et al. (2002), and Aggarval and Legon (2003). Our students also found the

lack of face to face communication as a problem; see Table 2, which presents students’

opinions about the main benefits and disadvantages in e-learning. Nevertheless, the

students were able to work with our learning module completely independently; they did

not communicate with a human instructor either personally, through e-mail or a newsgroup

system. This is probably due to two reasons. First, the students had an option to work

together with a pair and second, the instructions in our material were intentionally very

detailed, e.g., through the use of the video clips.

- - - - Table 2 is about here - - - -

The students succeeded well in the analytical assignments but they had more problems

with the software assignment. Seven groups out of nine had two negotiation sessions

starting from two different initial points. Hence, 14 negotiation sessions were completed in

total. The negotiation converged reasonably well towards a Pareto optimal solution only in

three sessions. In the other sessions, the students realized that there was something wrong

with the convergence but they were unable to explain the reasons. Later, the analysis of the

negotiation sessions indicated that the students experiencing problems had entered

irrational answers in the Joint Gains software during the negotiations. Hence, the students

were suffering from the lack of a personal instructor who could have verified that they

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actually understand their roles. Moreover, four of our students negotiated alone by playing

the roles of both parties, even if we recommended them to form two person groups. This

makes role-playing harder since the students may easily confuse the roles they should

represent.

It was somewhat surprising to note that only four groups out of nine even took a look at

the optional quizzes and only two groups answered each of them. The quizzes have been

considered useful in literature. For instance, Arvan et al. (1998) have observed that

students enjoy taking quizzes and especially answering them again and again until they get

the right answers. Weitl et al. (2002) also consider that the quizzes play a crucial role in e-

learning because they allow the students to have some online feedback on their learning

and some relaxing cognitive activities. In our case, the quizzes were unpopular probably

because they were intended to let the students to evaluate their learning if they wish to.

This was not, however, considered a problem by our students as the students’ opinions in

Table 2 show.

Systematical analysis and comparison between different subgroups of the students, such

as male and female, is not judicious in our case because the number of the students was

such small. Nevertheless, we may highlight one interesting pattern in the results related to

on-screen readability. Almost every student printed out the material. Those two students,

who did not consider the theory sections useful, did not print anything on paper. Hence, it

is indeed necessary to offer possibilities for printing out the material easily and that the

foremost role of the Internet is to act as a tool for material dissemination in case of the

theory sections.

The overall structure of the other learning sessions in the mathematical modeling web-

course was different from that of ours. For example, they consisted of video lectures,

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lecture slides and assignments. Yet, most of the students reported that they are relatively

indifferent between the format of the other learning sessions and that of our module, as

shown by the results in Table 3. Hence, they did not miss the video lectures. One could

interpret this so that different formats of learning have their own advantages and

disadvantages. According to the opinions of our students, the greatest advantage in e-

learning is the freedom of learning almost everywhere and any time, see Table 2. This

freedom has the other side of the coin, too. Namely, e-learning requires strong self-

motivation from the students and in this respect e-learning does not compare to more

traditional forms of learning see, e.g., Spiceland and Hawkins (2002). For instance, two

groups attending the web-course did not complete the software assignment in our module.

- - - - Table 3 is about here - - - -

7. Discussion

Our aim is to use the e-learning module in the web-course on mathematical modeling

also in future to provide new ideas on mathematical models on negotiation problems and

e-negotiations for university students. Our material has been developed mainly for OR/MS

students but also other university students could use it as well. For instance, students of

environmental or political decision making could use it to have new ideas on how

environmental and political problems can be modeled and mediated systematically.

Hämäläinen et al. (2001) have presented successful role-playing experiments with the

Joint Gains software in a lake-river system regulation problem. Their experiments show

that the role-players learn more and more about their objectives and preferences during the

Joint Gains negotiations. Besides this the students could also use the NSS for structuring

and restructuring the problem and testing different models of the negotiation problem at

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hand. For instance, they could first solve simple models with few issues and few parties to

gain experimental feedback about the model and then test if adding or excluding parties or

issues would be relevant. Hence, this kind of learning process is also a good way to learn

the suitability of different NSSs for different negotiation problems.

Our e-learning material could be useful also for experts in e-business. E-business

negotiations are becoming more and more important because companies outsource their

non-core activities and increasingly work with other companies in co-operation; see, e.g.,

Hoover et al. (2001). There have been many studies on electronic procurement

negotiations, which typically cover transactions between companies, customers and

companies, or company departments. These negotiations are discussed in literature ranging

from simple price negotiations, see, e.g., Kraus (2001, Chapter 2), to complex multi

attribute negotiations on price, quantity, product features, quality considerations, terms of

delivery, etc.; see, e.g., Barbuceanu and Lo (2003), and Rebstock, Thun and Tafreschi

(2003).

Another fruitful way to teach university students through role-plays is to instruct them

to invent their own cases instead of only working with ready-made ones. This is how we

have used the Joint Gains in a postgraduate seminar in applied mathematics on negotiation

analysis in spring 2001. The seminar students invented their own cases and they solved a

case both by the Joint Gains and through face to face negotiations. The cases included

simple two party two issue negotiations but some student groups also invented more

complicated ones. For instance, one case was a three party negotiation on hiring a football

player from one team to another. The football player and the two teams negotiated on the

length of the contract, player’s salary and the compensation the hiring team gets from the

other team. In another case involving multiple issues and multiple parties, university

20

students, the head of a university department and a lecturer were reorganizing a course.

They negotiated on amount of lectures, home assignments and demonstration exercises.

Most of the seminar students reported that the Joint Gains was a useful tool for supporting

their negotiations. They tested various different initial points and they were able to

produce jointly preferred points. They reported that the negotiations with the Joint Gains

were very strictly structured. This was not, however, considered a drawback but a benefit;

the students realized that they did not keep on the subject during the face to face

negotiations and the discussions easily led to unessential points.

Meerts (2002) suggests that it is beneficial use role-plays and their analysis in teaching

students who already have some real-life negotiation experiences. Therefore our e-learning

material could seem even more useful for teaching the mathematical modeling approach

and the use of the Joint Gains for real decision makers directly. The decision makers do

not, however, necessarily have time to learn the use of NSSs, theory behind them and

assess their suitability for solving their negotiation problems. Therefore, negotiation

analysis experts, who have practical understanding and experience on negotiation support,

are needed. In real-life negotiations, the role of these experts is to learn the problem by

using one or more promising NSSs, choose a suitable system and finally assist the

decision-makers with its use.

21

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Captions Figure 1 The most preferred point in the quadrant of the circle is identified by successive questions and it gives an approximation of the gradient direction Figure 2 Jointly improving directions Figure 3 Searching for the most preferred point in the compromise direction Figure 4 The Joint Gains helps the parties produce successive jointly preferred intermediate points Figure 5 Overall view of the learning module Figure 6 Learning module front page Figure 7 An example of a theory section presenting the prisoners’ dilemma game Figure 8 Creating a case in the Joint Gains Figure 9 Negotiating with the Joint Gains Table 1 Students’ willingness to work in and recommend this type of e-learning format Table 2 Students’ opinions about the main benefits and disadvantages in e-learning Table 3 Student feedback Figures

B

A

Issue x1

Issu

e x 2

Intermediatepoint

B

A

Issue x1

Issu

e x 2

Intermediatepoint

Figure 1 The most preferred point in the quadrant of the circle is identified by successive questions

and it gives an approximation of the gradient direction

Issue x1

Issu

e x 2

Gradient direction for party 1

Gradient direction for party 2

Jointly improving directions

Improving directions for party 1

Improving directions for party 2

Issue x1

Issu

e x 2

Gradient direction for party 1

Gradient direction for party 2

Jointly improving directions

Improving directions for party 1

Improving directions for party 2

Figure 2 Jointly improving directions

28

Issue x1

Issu

e x 2

A

B

Compromise direction

Intermediatepoint

Issue x1

Issu

e x 2

A

B

Compromise direction

Intermediatepoint

Figure 3 Searching for the most preferred point in the compromise direction

Utility of party 1

Util

ity o

f par

ty 2

Pareto frontier

Issue x1

Issu

e x 2

Pareto points

Utility of party 1

Util

ity o

f par

ty 2

Pareto frontier

Issue x1

Issu

e x 2

Pareto points

Figure 4 The Joint Gains helps the parties produce successive jointly preferred intermediate points

Theory•HTML

pages

+ motivation, detailed instructions, 2 to 6 hour sessions

Cases•slide shows•video clips

Assignments•analyticalassignments

•role-plays withthe Joint Gains

Student Evaluation •Opinions

Online

Quizzes•web-forms•automatically

graded

Figure 5 Overall view of the learning module

29

Figure 6 Learning module front page

Figure 7 An example of a theory section presenting the prisoners’ dilemma game

30

Figure 8 Creating a case in the Joint Gains

Online chatOnline chatOnline chatOnline chat

Figure 9 Negotiating with the Joint Gains

31

Tables Table 1 Students’ willingness to work in and recommend this type of e-learning format

Table 2 Students’ opinions about the main benefits and disadvantages in e-learning

Table 3 Student feedback