We discuss the theoretical design of algorithms for solving distributional conﬂicts within groups. We consider an algorithm to be procedural if the implementation of the outcome requires the participation of the players, or if it can even be conducted by the players themselves without computational assistance. We compare two procedures for multilateral problems of fair division; both establish envy-freeness, given the possibility of monetary compensations between players

Raith, Matthias G.

Su, Francis

English

Scholarship@Claremont

Claremont CollegesScholarship @ ClaremontAll HMC Faculty Publications and Research HMC Faculty Scholarship1-1-2000Procedural Support for Cooperative Negotiations:Theoretical Design and Practical ImplementationMatthias G. RaithUniversity of Bielefeld, GermanyFrancis SuHarvey Mudd CollegeThis Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusionin All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contactscholarship@cuc.claremont.edu.Recommended CitationM. G. Raith, F. E. Su, Procedural support for cooperative negotiations, Advances in Decision Technology and Intelligent InformationSystems, Vol. I, 31–36 (2000).appeared in: Advances in Decision Technology and Intelligent Information Systems, Volume I (eds. Kurt J. Engemann and George E. Lasker),The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Canada, 2000, pp. 31-36.Procedural Support for Cooperative NegotiationsTheoretical Design and Practical ImplementationMatthias G. RaithUniversity of Bielefeld, GermanyFrancis Edward SuHarvey Mudd College and Cornell University, USAAbstract: We discuss the theoretical design of algorithms for solving distributional con-flicts within groups. We consider an algorithm to be procedural if the implementation ofthe outcome requires the participation of the players, or if it can even be conducted bythe players themselves without computational assistance. We compare two procedures formultilateral problems of fair division; both establish envy-freeness, given the possibility ofmonetary compensations between players.1 IntroductionNegotiation is always related to distribution — either of benefits or of costs. Since thisdistributive dimension is present in every bargaining situation, negotiating parties mustinevitably deal with conflict in one way or another. Negotiation analysis is a practicallyoriented field of research that seeks to offer negotiators prescriptive advice on how to establisha desirable group decision in practice. A major goal is the development of procedures fordealing with conflicts in a constructive manner. Since negotiation always involves the divisionof some “pie,” a promising approach seems to be the analysis of problems of fair division.The theoretical development of fair-division procedures has become quite popular overthe past decade. Of particular interest for group decisions are procedures dealing with mul-tilateral distribution problems. New theoretical results show conditions for the existence ofenvy-free solutions, where an outcome is considered to be envy free if each party believesthat its share is at least as desirable as that of any other party. The mere proof of existence,however, does not yet provide the desired outcome. More helpful in this respect are con-structive proofs of envy-freeness, yielding solutions via algorithms that are implementable,e.g., as a computer algorithm.In this paper we extend the notion of a constructive proof: we consider an algorithm tobe procedural if the implementation of the group decision involves the active participation ofthe players, or if it can even be conducted by the players themselves without computationalassistance. This aspect seems to be essential for the acceptance of analytical support, be-cause, as Spector (1997) observes, practitioners are often reluctant to use support tools thatoffer solutions simply at the push of a button. What is required in his view is (procedural)assistance that guides negotiators to a mutually acceptable agreement.12 A Multilateral Fair-Division ProblemConsider the following situation: Four individuals wish to rent a house with four bedroomsfor a total rent of, say $100. Is there a possibility of allocating rooms to players and dividingthe total rent between rooms in such a way that no individual will wish to trade roomswith another? Under relatively mild assumptions concerning players’ preferences such anenvy-free allocation exists — the question is how to find it.Suppose that each player Pi, i=1, . . . , 4, is able to express her valuations of the individualrooms Rj, j=1, . . . , 4, via monetary bids, as given in Table 1 (cf. Haake, Raith, and Su, 1999).R1 R2 R3 R4P1 50 20 10 20P2 60 40 15 10P3 0 40 25 35P4 50 35 10 30Table 1: Players’ monetary valuations (bids) of roomsIn addition, if players’ preferences over money are linear, then each player Pi will preferthe room Rj which offers her the maximal discount, given by the difference between herindividual bid and the actual price of the room.3 An Interactive Choice ProcedureA possible procedure for allocating rooms and splitting the rent is to assign prices to theindividual rooms that sum to the total rent, and then let each player choose the room shelikes best. For example, if all rooms are priced equally at $25, then P1, P2, and P4 will allwish to have R1, while P3 would choose R2. With only one player allowed in each room,this price distribution is sure to create envy. However, if a pricing scheme can be found suchthat each room is desired by a different player, then the allocation will be envy-free.The interactive fair-division procedure developed by Su (1999) is based on a constructiveproof of the combinatorial lemma given by Sperner (1928), reformulated to find an envy-free pricing scheme. The algorithm sequentially offers each player a specific pricing schemeand then lets this player choose her favorite alternative. For example if P1 is offered thepricing scheme [0,0,0,100], her best choice will be R1, because this maximizes her discount.Under the Sperner approach, each player’s choice of an alternative determines which pricingscheme is offered next and to which player. The interactive procedure consistently worksits way towards envy-freeness, and it provably converges on an envy-free pricing schemefor any given level of precision with which players can determine the value of rooms. Forour example above, the pricing scheme [45,25,10,20] induces P1, P2, P3, and P4 to chooseR1, R2, R3, and R4, respectively. Subtracting room prices from players’ valuations, given2in Table 1, shows that these choices give players maximum discounts for the given pricingscheme.Implemented on a computer, the Sperner choice procedure operates in the form ofan artificial mediator. The mediation procedure can be employed using the web-based“Fair-Division Calculator” (http://www.math.hmc.edu/˜ su/fairdivision/calc/). Par-ties can actively take part in the process and are allowed to make choices to their individualbenefit. The Fair Division Calculator plays the part of the mediator by offering pricingschemes in a manner that will lead the group to an envy-free allocation, provided that par-ticipants’ choices are consistent and truthful. If a player behaves inconsistently, either byaccident or due to a change of preferences, the mediator can react by pointing to the inconsis-tency or by accepting the modified preferences, thus ignoring previous (inconsistent) choices.Strategic choices, on the other hand, cannot be unmasked as long as they are consistent.However, players will find it quite difficult to manipulate the procedure, because the otherplayers’ preferences are never fully revealed. Indeed, if the choices of the other players arekept confidential up to the final round, then a player, when offered a pricing scheme, willnever know whether the next choice will be her last.Viewed as a mediation process, the main difficulty with the Sperner choice procedure isthat the operations of the mediator are largely incomprehensible to the group. Although eachplayer has a free choice of alternatives and thereby determines the direction of the process,she will generally have a problem understanding the logic behind the evolution of pricingschemes. Players must completely rely on the artificial mediator to arrive at an envy-freeoutcome. Without this trust, the choice procedure may not be acceptable for the group.4 A Mediating Compensation ProcedureAcceptability of a live mediation procedure typically requires additional features that relatethe process to the players involved. To be acceptable, a mediation procedure should be in-tuitive, meaning that the implementation of an outcome must accord to the players’ way ofreasoning. In addition, the procedure should be plausible, meaning that the individual stepsmust match the players’ way of arguing. And finally, the procedure should be manageable,meaning that the required calculations must correspond to the players’ computational abil-ities. With the compensation procedure developed by Haake, Raith, and Su (1999), playersare able to see how the outcome evolves through the interaction of their preferences. Theycan, therefore, understand the mediation process, and even conduct it themselves.The compensation procedure is initialized by having players individually and simultane-ously submit monetary bids for the individual rooms. All bids, disclosed together, then formthe basis of the mediation process leading to envy-freeness.The first step of the mediation procedure is to assign rooms to players, such that thesum of players’ bids is maximized. In our example, this utilitarian allocation is achievedby assigning R1, R2, R3, and R4 to players P1, P2,P3, and P4, respectively (in Table 1,the diagonal assignment). The utilitarian assignment ensures that no sub-group of playerscan mutually gain by trading rooms. Consequently, there can be no two-way or cyclical3envy, since this could be eliminated via a mutually beneficial trade. However, a utilitarianassignment may still leave individual players envious. As Table 1 shows, P1 is satisfied withR1, but P2 and P4 prefer R1 as well, while P3 would rather have R2. As any envious playercan verify, though, no player is willing to enter a trade with her.The second step of the procedure is to compensate all envious players by an amountsufficient to eliminate their envy. The most plausible starting point is to begin with thoseplayers whose maximum envy is directed towards a non-envious player. A non-enviousplayer always exists, because if all players were envious, there would be efficient tradingopportunities. As Table 1 shows, P1 is the non-envious player, and P2 and P4 need to becompensated for their envy; P3 envies an envious player and can, therefore, be taken careof in a later round. By adding $20 to the value of R2 and R4, P2 and P4 are not enviousof P1 anymore. Indeed, P2 is now envy-free, but, as the left-hand panel of Table 2 shows,P4 now envies P2, and P3 is even more envious of P2 than before. In the second round P3and P4 are, therefore, compensated by adding $35 to R3 and an additional $5 to R4. As theright-hand panel of Table 2 shows, all players are now satisfied with their assigned rooms.R1 R2 R3 R4P1 50 40 10 40P2 60 60 15 30P3 0 60 25 50P4 50 55 10 50comp. 0 20 0 20R1 R2 R3 R4P1 50 40 45 45P2 60 60 50 35P3 0 60 60 55P4 50 55 45 55comp. 0 20 35 25Table 2: Players’ most preferred rooms after one and two rounds of compensationsAs Haake, Raith, and Su (1999) formally show, after k rounds of compensation at least k+1 players will be envy-free. Envy-freeness for 4 players thus requires at most 3 compensationrounds; in our example only two are necessary. Note that, even if players do not understandthe formal proof of this claim, they can verify its validity at every step of the procedure.After envy-freeness is achieved, the group must bear the cost of compensations, $80, plusthe rent for the house, $100. If the total cost is shared equally, each player pays $45. Net ofcompensations, the final envy-free prices for the rooms are [45,25,10,20].Although the compensation procedure can generally be conducted without computa-tional assistance, larger groups may wish to have precise guidance as the mediation processbecomes longer. Moreover, the utilitarian assignment becomes increasingly difficult to findwithout analytical support. Implemented on a computer, the compensation procedure pro-vides the complete mediation process, based only on players’ initial valuations of rooms —the compensation procedure can be employed using the Fair Division Calculator (FDC).However, in contrast to the Sperner choice procedure in which the FDC works its way toenvy-freeness by interacting with the players, the FDC does not operate as a mediator underthe compensation procedure. Instead, it supplies the mediation process that can be used bya mediator or the group itself as a map to envy-freeness.45 Decentralized Procedural SupportAdapting group interaction to the support environment is a common feature of many com-puterized support systems. However, if the system imposes too many restrictions on thegroup decision process, users may find it too artificial and, therefore, be reluctant to use itin practice. Practitioners often find their flexibility constrained by the way they are forced tointeract with the system. The challenge in designing a practicable support system, therefore,lies in the development of analytical techniques that complement the group’s interaction ina “natural” way.As a web-based application the Fair Division Calculator can be employed from any remotelocation. Equipped with a variety of different mediation procedures, the FDC provides fullanalytical mediation support. Depending on the amount of information that parties arewilling to reveal, the FDC can assist by offering the group a workable mediation process, orit can be part of the process and operate as an artificial mediator.Since the FDC offers group support via a single user interface, decentralized group inter-action requires additional support facilities, allowing parties to interact with each other fromremote locations. This has been accomplished by integrating the FDC into a negotiationplatform under the the internet system ARTUS (http://artus.wiwi.uni-bielefeld.de/).ARTUS provides an infrastructure for group decision making over the Internet in the formof virtual tables. The system includes options for defining the method and structure ofmultilateral interaction, and it records the complete interaction for security, documentation,and evaluation (for a detailed documentation see Raith and Wilker, 1998).Due to its accessibility via the internet and its variable user interfaces, ARTUS can beadapted to many different forms of decentralized group interaction, with or without analyticalsupport. A mediation process via ARTUS allows the participation of a natural mediator,equipped with all the psychological skills necessary for guiding parties in a conflict situation,and assisted by the analytical skills of a support system such as the Fair Division Calulator.Group support can thus be integrated naturally in an artificial environment.ReferencesHaake, C.J., M.G. Raith, F.E. Su (1999): “Bidding for Envy-Freeness,” University of Biele-feld, Institute of Mathematical Economics, WP 311Raith, M.G., H. Wilker (1998): “ARTUS: The Adaptable Round Table with a User-SpecificSurface,” University of Bielefeld, Institute of Mathematical Economics, WP 298Spector, B.I. (1997): “Analytical Support to Negotiations: An Empirical Assessment,”Group Decision and Negotiation, 6, 421-436Sperner, E (1928): “Neuer Beweis fu¨r die Invarianz der Dimensionszahl und des Gebietes,”Abh. Math. Sem., Univ. Hamburg, 6, 265-272Su, F.E. (1999): “Rental Harmony: Sperner’s Lemma in Fair Division,” American Mathe-matical Monthly, 106, 922-9345

Procedural Support for Cooperative Negotiations: Theoretical Design and Practical Implementation

Keck Graduate Institute

Claremont Colleges
Scholarship @ Claremont
All HMC Faculty Publications and Research HMC Faculty Scholarship
1-1-2000
Procedural Support for Cooperative Negotiations:
Theoretical Design and Practical Implementation
Matthias G. Raith
University of Bielefeld, Germany
Francis Su
Harvey Mudd College
This Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusion
in All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contact
scholarship@cuc.claremont.edu.
Recommended Citation
M. G. Raith, F. E. Su, Procedural support for cooperative negotiations, Advances in Decision Technology and Intelligent Information
Systems, Vol. I, 31–36 (2000).
appeared in: Advances in Decision Technology and Intelligent Information Systems, Volume I (eds. Kurt J. Engemann and George E. Lasker),
The International Institute for Advanced Studies in Systems Research and Cybernetics, Windsor, Canada, 2000, pp. 31-36.
Procedural Support for Cooperative Negotiations
Theoretical Design and Practical Implementation
Matthias G. Raith
University of Bielefeld, Germany
Francis Edward Su
Harvey Mudd College and Cornell University, USA
Abstract: We discuss the theoretical design of algorithms for solving distributional con-
flicts within groups. We consider an algorithm to be procedural if the implementation of
the outcome requires the participation of the players, or if it can even be conducted by
the players themselves without computational assistance. We compare two procedures for
multilateral problems of fair division; both establish envy-freeness, given the possibility of
monetary compensations between players.
1 Introduction
Negotiation is always related to distribution — either of benefits or of costs. Since this
distributive dimension is present in every bargaining situation, negotiating parties must
inevitably deal with conflict in one way or another. Negotiation analysis is a practically
oriented field of research that seeks to offer negotiators prescriptive advice on how to establish
a desirable group decision in practice. A major goal is the development of procedures for
dealing with conflicts in a constructive manner. Since negotiation always involves the division
of some “pie,” a promising approach seems to be the analysis of problems of fair division.
The theoretical development of fair-division procedures has become quite popular over
the past decade. Of particular interest for group decisions are procedures dealing with mul-
tilateral distribution problems. New theoretical results show conditions for the existence of
envy-free solutions, where an outcome is considered to be envy free if each party believes
that its share is at least as desirable as that of any other party. The mere proof of existence,
however, does not yet provide the desired outcome. More helpful in this respect are con-
structive proofs of envy-freeness, yielding solutions via algorithms that are implementable,
e.g., as a computer algorithm.
In this paper we extend the notion of a constructive proof: we consider an algorithm to
be procedural if the implementation of the group decision involves the active participation of
the players, or if it can even be conducted by the players themselves without computational
assistance. This aspect seems to be essential for the acceptance of analytical support, be-
cause, as Spector (1997) observes, practitioners are often reluctant to use support tools that
offer solutions simply at the push of a button. What is required in his view is (procedural)
assistance that guides negotiators to a mutually acceptable agreement.
1
2 A Multilateral Fair-Division Problem
Consider the following situation: Four individuals wish to rent a house with four bedrooms
for a total rent of, say $100. Is there a possibility of allocating rooms to players and dividing
the total rent between rooms in such a way that no individual will wish to trade rooms
with another? Under relatively mild assumptions concerning players’ preferences such an
envy-free allocation exists — the question is how to find it.
Suppose that each player Pi, i=1, . . . , 4, is able to express her valuations of the individual
rooms Rj, j=1, . . . , 4, via monetary bids, as given in Table 1 (cf. Haake, Raith, and Su, 1999).
R1 R2 R3 R4
P1 50 20 10 20
P2 60 40 15 10
P3 0 40 25 35
P4 50 35 10 30
Table 1: Players’ monetary valuations (bids) of rooms
In addition, if players’ preferences over money are linear, then each player Pi will prefer
the room Rj which offers her the maximal discount, given by the difference between her
individual bid and the actual price of the room.
3 An Interactive Choice Procedure
A possible procedure for allocating rooms and splitting the rent is to assign prices to the
individual rooms that sum to the total rent, and then let each player choose the room she
likes best. For example, if all rooms are priced equally at $25, then P1, P2, and P4 will all
wish to have R1, while P3 would choose R2. With only one player allowed in each room,
this price distribution is sure to create envy. However, if a pricing scheme can be found such
that each room is desired by a different player, then the allocation will be envy-free.
The interactive fair-division procedure developed by Su (1999) is based on a constructive
proof of the combinatorial lemma given by Sperner (1928), reformulated to find an envy-
free pricing scheme. The algorithm sequentially offers each player a specific pricing scheme
and then lets this player choose her favorite alternative. For example if P1 is offered the
pricing scheme [0,0,0,100], her best choice will be R1, because this maximizes her discount.
Under the Sperner approach, each player’s choice of an alternative determines which pricing
scheme is offered next and to which player. The interactive procedure consistently works
its way towards envy-freeness, and it provably converges on an envy-free pricing scheme
for any given level of precision with which players can determine the value of rooms. For
our example above, the pricing scheme [45,25,10,20] induces P1, P2, P3, and P4 to choose
R1, R2, R3, and R4, respectively. Subtracting room prices from players’ valuations, given
2
in Table 1, shows that these choices give players maximum discounts for the given pricing
scheme.
Implemented on a computer, the Sperner choice procedure operates in the form of
an artificial mediator. The mediation procedure can be employed using the web-based
“Fair-Division Calculator” (http://www.math.hmc.edu/˜ su/fairdivision/calc/). Par-
ties can actively take part in the process and are allowed to make choices to their individual
benefit. The Fair Division Calculator plays the part of the mediator by offering pricing
schemes in a manner that will lead the group to an envy-free allocation, provided that par-
ticipants’ choices are consistent and truthful. If a player behaves inconsistently, either by
accident or due to a change of preferences, the mediator can react by pointing to the inconsis-
tency or by accepting the modified preferences, thus ignoring previous (inconsistent) choices.
Strategic choices, on the other hand, cannot be unmasked as long as they are consistent.
However, players will find it quite difficult to manipulate the procedure, because the other
players’ preferences are never fully revealed. Indeed, if the choices of the other players are
kept confidential up to the final round, then a player, when offered a pricing scheme, will
never know whether the next choice will be her last.
Viewed as a mediation process, the main difficulty with the Sperner choice procedure is
that the operations of the mediator are largely incomprehensible to the group. Although each
player has a free choice of alternatives and thereby determines the direction of the process,
she will generally have a problem understanding the logic behind the evolution of pricing
schemes. Players must completely rely on the artificial mediator to arrive at an envy-free
outcome. Without this trust, the choice procedure may not be acceptable for the group.
4 A Mediating Compensation Procedure
Acceptability of a live mediation procedure typically requires additional features that relate
the process to the players involved. To be acceptable, a mediation procedure should be in-
tuitive, meaning that the implementation of an outcome must accord to the players’ way of
reasoning. In addition, the procedure should be plausible, meaning that the individual steps
must match the players’ way of arguing. And finally, the procedure should be manageable,
meaning that the required calculations must correspond to the players’ computational abil-
ities. With the compensation procedure developed by Haake, Raith, and Su (1999), players
are able to see how the outcome evolves through the interaction of their preferences. They
can, therefore, understand the mediation process, and even conduct it themselves.
The compensation procedure is initialized by having players individually and simultane-
ously submit monetary bids for the individual rooms. All bids, disclosed together, then form
the basis of the mediation process leading to envy-freeness.
The first step of the mediation procedure is to assign rooms to players, such that the
sum of players’ bids is maximized. In our example, this utilitarian allocation is achieved
by assigning R1, R2, R3, and R4 to players P1, P2,P3, and P4, respectively (in Table 1,
the diagonal assignment). The utilitarian assignment ensures that no sub-group of players
can mutually gain by trading rooms. Consequently, there can be no two-way or cyclical
3
envy, since this could be eliminated via a mutually beneficial trade. However, a utilitarian
assignment may still leave individual players envious. As Table 1 shows, P1 is satisfied with
R1, but P2 and P4 prefer R1 as well, while P3 would rather have R2. As any envious player
can verify, though, no player is willing to enter a trade with her.
The second step of the procedure is to compensate all envious players by an amount
sufficient to eliminate their envy. The most plausible starting point is to begin with those
players whose maximum envy is directed towards a non-envious player. A non-envious
player always exists, because if all players were envious, there would be efficient trading
opportunities. As Table 1 shows, P1 is the non-envious player, and P2 and P4 need to be
compensated for their envy; P3 envies an envious player and can, therefore, be taken care
of in a later round. By adding $20 to the value of R2 and R4, P2 and P4 are not envious
of P1 anymore. Indeed, P2 is now envy-free, but, as the left-hand panel of Table 2 shows,
P4 now envies P2, and P3 is even more envious of P2 than before. In the second round P3
and P4 are, therefore, compensated by adding $35 to R3 and an additional $5 to R4. As the
right-hand panel of Table 2 shows, all players are now satisfied with their assigned rooms.
R1 R2 R3 R4
P1 50 40 10 40
P2 60 60 15 30
P3 0 60 25 50
P4 50 55 10 50
comp. 0 20 0 20
R1 R2 R3 R4
P1 50 40 45 45
P2 60 60 50 35
P3 0 60 60 55
P4 50 55 45 55
comp. 0 20 35 25
Table 2: Players’ most preferred rooms after one and two rounds of compensations
As Haake, Raith, and Su (1999) formally show, after k rounds of compensation at least k+
1 players will be envy-free. Envy-freeness for 4 players thus requires at most 3 compensation
rounds; in our example only two are necessary. Note that, even if players do not understand
the formal proof of this claim, they can verify its validity at every step of the procedure.
After envy-freeness is achieved, the group must bear the cost of compensations, $80, plus
the rent for the house, $100. If the total cost is shared equally, each player pays $45. Net of
compensations, the final envy-free prices for the rooms are [45,25,10,20].
Although the compensation procedure can generally be conducted without computa-
tional assistance, larger groups may wish to have precise guidance as the mediation process
becomes longer. Moreover, the utilitarian assignment becomes increasingly difficult to find
without analytical support. Implemented on a computer, the compensation procedure pro-
vides the complete mediation process, based only on players’ initial valuations of rooms —
the compensation procedure can be employed using the Fair Division Calculator (FDC).
However, in contrast to the Sperner choice procedure in which the FDC works its way to
envy-freeness by interacting with the players, the FDC does not operate as a mediator under
the compensation procedure. Instead, it supplies the mediation process that can be used by
a mediator or the group itself as a map to envy-freeness.
4
5 Decentralized Procedural Support
Adapting group interaction to the support environment is a common feature of many com-
puterized support systems. However, if the system imposes too many restrictions on the
group decision process, users may find it too artificial and, therefore, be reluctant to use it
in practice. Practitioners often find their flexibility constrained by the way they are forced to
interact with the system. The challenge in designing a practicable support system, therefore,
lies in the development of analytical techniques that complement the group’s interaction in
a “natural” way.
As a web-based application the Fair Division Calculator can be employed from any remote
location. Equipped with a variety of different mediation procedures, the FDC provides full
analytical mediation support. Depending on the amount of information that parties are
willing to reveal, the FDC can assist by offering the group a workable mediation process, or
it can be part of the process and operate as an artificial mediator.
Since the FDC offers group support via a single user interface, decentralized group inter-
action requires additional support facilities, allowing parties to interact with each other from
remote locations. This has been accomplished by integrating the FDC into a negotiation
platform under the the internet system ARTUS (http://artus.wiwi.uni-bielefeld.de/).
ARTUS provides an infrastructure for group decision making over the Internet in the form
of virtual tables. The system includes options for defining the method and structure of
multilateral interaction, and it records the complete interaction for security, documentation,
and evaluation (for a detailed documentation see Raith and Wilker, 1998).
Due to its accessibility via the internet and its variable user interfaces, ARTUS can be
adapted to many different forms of decentralized group interaction, with or without analytical
support. A mediation process via ARTUS allows the participation of a natural mediator,
equipped with all the psychological skills necessary for guiding parties in a conflict situation,
and assisted by the analytical skills of a support system such as the Fair Division Calulator.
Group support can thus be integrated naturally in an artificial environment.
References
Haake, C.J., M.G. Raith, F.E. Su (1999): “Bidding for Envy-Freeness,” University of Biele-
feld, Institute of Mathematical Economics, WP 311
Raith, M.G., H. Wilker (1998): “ARTUS: The Adaptable Round Table with a User-Specific
Surface,” University of Bielefeld, Institute of Mathematical Economics, WP 298
Spector, B.I. (1997): “Analytical Support to Negotiations: An Empirical Assessment,”
Group Decision and Negotiation, 6, 421-436
Sperner, E (1928): “Neuer Beweis fu¨r die Invarianz der Dimensionszahl und des Gebietes,”
Abh. Math. Sem., Univ. Hamburg, 6, 265-272
Su, F.E. (1999): “Rental Harmony: Sperner’s Lemma in Fair Division,” American Mathe-
matical Monthly, 106, 922-934
5


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