Assumption-based argumentation for the minimal concession strategy
Available from www.di.unipi.it
Page 1
Assumption-based argumentation for the minimal concession strategy
Assumption-based argumentation for the
minimal concession strategy⋆
Maxime Morge and Paolo Mancarella
Dipartimento di Informatica, Universita` di Pisa
Largo Pontecorvo, 3 I-56127 Pisa, Italy
{morge,paolo}di.unipi.it,
http://maxime.morge.org
http://www.di.unipi.it/~paolo
Abstract. Several recent works in the area of Artificial Intelligence fo-
cus on computational models of argumentation-based negotiation. How-
ever, even if computational models of arguments are used to encompass
the reasoning of interacting agents, this logical approach does not come
with an effective strategy for agents engaged in negotiations. In this pa-
per we propose a realisation of the Minimal Concession (MC) strategy
which has been theoretically validated. The main contribution of this
paper is the integration of this intelligent strategy in a practical applica-
tion by means of assumption-based argumentation. We claim here that
the outcome of negotiations, which are guaranteed to terminate, is an
optimal agreement (when possible) if the agents adopt the MC strategy.
1 Introduction
Negotiations occur in electronic procurement, commerce, health and government,
amongst individuals, companies and organisations. In negotiations, the aim for
all parties is to “make a deal” while bargaining over their interests, typically
seeking to maximise their “good” (welfare), and prepared to concede some as-
pects, while insisting on others. Negotiations are time consuming, emotionally
demanding and emotions may affect the quality of the outcomes of negotiations.
These issues can be addressed by delegating (at least partially) negotiations to
a multiagent system responsible for (or helping with) reaching agreements
(semi-)automatically [1]. Within this approach, software agents are associated
with stakeholders in negotiations. As pointed out by [2] (resp. [3]), there is a need
for a solid theoretical foundation for negotiation (resp. argumentation-based ne-
gotiation) that covers algorithms and protocols, while determining which strate-
gies are most effective under what circumstances.
Several recent works in the area of Artificial Intelligence focus on computa-
tional models of argumentation-based negotiation [4–9]. In these works, argu-
mentation serves as a unifying medium to provide a model for agent-based nego-
⋆ This work is supported by the Sixth Framework IST programme of the EC, under
the 035200 ARGUGRID project.
minimal concession strategy⋆
Maxime Morge and Paolo Mancarella
Dipartimento di Informatica, Universita` di Pisa
Largo Pontecorvo, 3 I-56127 Pisa, Italy
{morge,paolo}di.unipi.it,
http://maxime.morge.org
http://www.di.unipi.it/~paolo
Abstract. Several recent works in the area of Artificial Intelligence fo-
cus on computational models of argumentation-based negotiation. How-
ever, even if computational models of arguments are used to encompass
the reasoning of interacting agents, this logical approach does not come
with an effective strategy for agents engaged in negotiations. In this pa-
per we propose a realisation of the Minimal Concession (MC) strategy
which has been theoretically validated. The main contribution of this
paper is the integration of this intelligent strategy in a practical applica-
tion by means of assumption-based argumentation. We claim here that
the outcome of negotiations, which are guaranteed to terminate, is an
optimal agreement (when possible) if the agents adopt the MC strategy.
1 Introduction
Negotiations occur in electronic procurement, commerce, health and government,
amongst individuals, companies and organisations. In negotiations, the aim for
all parties is to “make a deal” while bargaining over their interests, typically
seeking to maximise their “good” (welfare), and prepared to concede some as-
pects, while insisting on others. Negotiations are time consuming, emotionally
demanding and emotions may affect the quality of the outcomes of negotiations.
These issues can be addressed by delegating (at least partially) negotiations to
a multiagent system responsible for (or helping with) reaching agreements
(semi-)automatically [1]. Within this approach, software agents are associated
with stakeholders in negotiations. As pointed out by [2] (resp. [3]), there is a need
for a solid theoretical foundation for negotiation (resp. argumentation-based ne-
gotiation) that covers algorithms and protocols, while determining which strate-
gies are most effective under what circumstances.
Several recent works in the area of Artificial Intelligence focus on computa-
tional models of argumentation-based negotiation [4–9]. In these works, argu-
mentation serves as a unifying medium to provide a model for agent-based nego-
⋆ This work is supported by the Sixth Framework IST programme of the EC, under
the 035200 ARGUGRID project.
Page 2
tiation systems, in that it can support: the reasoning and decision-making pro-
cess of agents [4], the inter-agent negotiation process to reach an agreement [5],
the definition of contracts emerging from the negotiation [9, 6, 8] and, finally, the
resolution of disputes and disagreements with respect to agreed contracts [7].
However, even if computational models of arguments are used to encompass the
reasoning of interacting agents, few works are concerned by the strategy of agents
engaged in negotiations and its properties. A first attempt in this direction is
the Minimal Concession (MC) strategy proposed by [6]. However, the latter does
not show how to fill the gap between the argumentation-based decision-making
mechanism and its realisation for computing this negotiation strategy. More-
over, some assumptions are too strong with respect to our real-world scenario,
e.g. the fact the agents know the preferences and the reservation values of the
other agents. In this paper we propose a realisation of the MC strategy which
has been practically validated. Actually, our strategy has been tested within
industrial scenarios [10, 11] from which we extract an intuitive and illustrative
example. Moreover, we show here that negotiations are guaranteed to termi-
nate. The negotiation outcome emerges from the interleaved decision-making
processes of agents specified by the MC strategy. We claim that this outcome
is an optimal agreement when it is possible. Argumentation logic is used to
support the intelligent strategy of negotiating agents, to guide and empower
negotiation amongst agents and to allow them to reach agreements. With the
support of assumptions-based argumentation, agents select the “optimal” utter-
ances to fulfil the preferences/constraints of users and the requirements imposed
by the other agents. The main contribution of this paper is the integration of
our intelligent strategy in a practical application by means of assumptions-based
argumentation.
The paper is organised as follows. Section 2 introduces the basic notions of
assumption-based argumentation in the background of our work. Section 3 intro-
duces the walk-through example. Section 3 outlines the dialogue-game protocol
we use. Section 5 defines our framework for decision making. Section 6 presents
our realisation of the MC strategy. Section 7 highlights some properties of our
protocol and our strategy. Section 8 discusses some related works. Section 9
concludes with some directions for future work.
2 Assumption-based argumentation
Assumption-based argumentation [12] (ABA) is a general-purpose computa-
tional framework which allows to reason with incomplete information, whereby
certain literals are assumptions, meaning that they can be assumed to hold as
long as there is no evidence to the contrary. Moreover, ABA concretise Dung’s
abstract argumentation [13] (AA). Actually, all the semantics used in AA, which
capture various degrees of collective justifications for a set of arguments, can be
applied to ABA.
An ABA framework considers a deductive system augmented by a non-empty
set of assumptions and a (total) mapping from assumptions to their contraries. In
2
cess of agents [4], the inter-agent negotiation process to reach an agreement [5],
the definition of contracts emerging from the negotiation [9, 6, 8] and, finally, the
resolution of disputes and disagreements with respect to agreed contracts [7].
However, even if computational models of arguments are used to encompass the
reasoning of interacting agents, few works are concerned by the strategy of agents
engaged in negotiations and its properties. A first attempt in this direction is
the Minimal Concession (MC) strategy proposed by [6]. However, the latter does
not show how to fill the gap between the argumentation-based decision-making
mechanism and its realisation for computing this negotiation strategy. More-
over, some assumptions are too strong with respect to our real-world scenario,
e.g. the fact the agents know the preferences and the reservation values of the
other agents. In this paper we propose a realisation of the MC strategy which
has been practically validated. Actually, our strategy has been tested within
industrial scenarios [10, 11] from which we extract an intuitive and illustrative
example. Moreover, we show here that negotiations are guaranteed to termi-
nate. The negotiation outcome emerges from the interleaved decision-making
processes of agents specified by the MC strategy. We claim that this outcome
is an optimal agreement when it is possible. Argumentation logic is used to
support the intelligent strategy of negotiating agents, to guide and empower
negotiation amongst agents and to allow them to reach agreements. With the
support of assumptions-based argumentation, agents select the “optimal” utter-
ances to fulfil the preferences/constraints of users and the requirements imposed
by the other agents. The main contribution of this paper is the integration of
our intelligent strategy in a practical application by means of assumptions-based
argumentation.
The paper is organised as follows. Section 2 introduces the basic notions of
assumption-based argumentation in the background of our work. Section 3 intro-
duces the walk-through example. Section 3 outlines the dialogue-game protocol
we use. Section 5 defines our framework for decision making. Section 6 presents
our realisation of the MC strategy. Section 7 highlights some properties of our
protocol and our strategy. Section 8 discusses some related works. Section 9
concludes with some directions for future work.
2 Assumption-based argumentation
Assumption-based argumentation [12] (ABA) is a general-purpose computa-
tional framework which allows to reason with incomplete information, whereby
certain literals are assumptions, meaning that they can be assumed to hold as
long as there is no evidence to the contrary. Moreover, ABA concretise Dung’s
abstract argumentation [13] (AA). Actually, all the semantics used in AA, which
capture various degrees of collective justifications for a set of arguments, can be
applied to ABA.
An ABA framework considers a deductive system augmented by a non-empty
set of assumptions and a (total) mapping from assumptions to their contraries. In
2
Page 3
order to perform decision making, we consider here the generalisation of the orig-
inal assumption-based argumentation framework and its computational mecha-
nism, whereby multiple contraries are allowed [14].
Definition 1 (ABA). An assumption-based argumentation framework
is a tuple ABF = 〈L,R,Asm, Con〉 where:
– (L,R) is a deductive system where
• L is a formal language consisting of countably many sentences,
• R is a countable set of inference rules of the form r: α ← α1, . . . , αn
(n ≥ 0) where α ∈ L is called the head of the rule (denoted by head(r)),
and the conjunction α1, . . . , αn is called the body of the rule (denoted
body(r)), with n ≥ 0 and αi ∈ L for each i ∈ [1, n];
– Asm ⊆ L is a non-empty set of assumptions. If x ∈ Asm, then there is no
inference rule in R such that x is the head of this rule;
– Con: Asm→ 2L is a (total) mapping from assumptions into set of sentences
in L, i.e. their contraries.
In the remainder of the paper, we restrict ourselves to finite deduction systems,
i.e. with finite languages and finite set of rules. For simplicity, we also restrict
ourselves to flat frameworks [12], in which assumptions do not occur as conclu-
sions of inference rules.
We adopt here the tree-like structure for arguments proposed in [15] and we
adapt it for ABA.
Definition 2 (Argument). Let ABF = 〈L,R,Asm, Con〉 be an ABA frame-
work. An argument a¯ deducing the conclusion c ∈ L (denoted conc(a¯)) sup-
ported by a set of assumptions A in Asm (denoted asm(a¯)) is a tree where the
root is c and each node is a sentence of L. For each node :
– if the node is a leaf, then it is either an assumption in A or ⊤1;
– if the node is not a leaf and it is α ∈ L, then there is an inference rule
α← α1, . . . , αn in R and,
• either n = 0 and ⊤ is its only child,
• or n > 0 and the node has n children, α1, . . . , αn.
We write a¯ : A ⊢ α to denote an argument a¯ such that conc(a¯) = α and asm(a¯) =
A. The set of arguments built upon ABF is denoted by A(ABF).
Our definition corresponds to the definition of tight argument in [16]. Arguments
can be built by reasoning backwards as in the dialectical proof procedure pro-
posed in [16] and extended in [14]. It is worth noticing that all the rules and
assumptions of our arguments are useful to deduce their conclusion even if we
do not explicitly enforce the minimality of the premises as in [17]. Moreover,
we do not enforce the consistency of the premises but this property will arise
in the arguments computed by the dialectical proof procedure due to the attack
relation.
In an assumption-based argumentation framework, the attack relation amongst
arguments comes from the contraries which capture the notion of conflicts.
1 ⊤ denotes the unconditionally true statement.
3
inal assumption-based argumentation framework and its computational mecha-
nism, whereby multiple contraries are allowed [14].
Definition 1 (ABA). An assumption-based argumentation framework
is a tuple ABF = 〈L,R,Asm, Con〉 where:
– (L,R) is a deductive system where
• L is a formal language consisting of countably many sentences,
• R is a countable set of inference rules of the form r: α ← α1, . . . , αn
(n ≥ 0) where α ∈ L is called the head of the rule (denoted by head(r)),
and the conjunction α1, . . . , αn is called the body of the rule (denoted
body(r)), with n ≥ 0 and αi ∈ L for each i ∈ [1, n];
– Asm ⊆ L is a non-empty set of assumptions. If x ∈ Asm, then there is no
inference rule in R such that x is the head of this rule;
– Con: Asm→ 2L is a (total) mapping from assumptions into set of sentences
in L, i.e. their contraries.
In the remainder of the paper, we restrict ourselves to finite deduction systems,
i.e. with finite languages and finite set of rules. For simplicity, we also restrict
ourselves to flat frameworks [12], in which assumptions do not occur as conclu-
sions of inference rules.
We adopt here the tree-like structure for arguments proposed in [15] and we
adapt it for ABA.
Definition 2 (Argument). Let ABF = 〈L,R,Asm, Con〉 be an ABA frame-
work. An argument a¯ deducing the conclusion c ∈ L (denoted conc(a¯)) sup-
ported by a set of assumptions A in Asm (denoted asm(a¯)) is a tree where the
root is c and each node is a sentence of L. For each node :
– if the node is a leaf, then it is either an assumption in A or ⊤1;
– if the node is not a leaf and it is α ∈ L, then there is an inference rule
α← α1, . . . , αn in R and,
• either n = 0 and ⊤ is its only child,
• or n > 0 and the node has n children, α1, . . . , αn.
We write a¯ : A ⊢ α to denote an argument a¯ such that conc(a¯) = α and asm(a¯) =
A. The set of arguments built upon ABF is denoted by A(ABF).
Our definition corresponds to the definition of tight argument in [16]. Arguments
can be built by reasoning backwards as in the dialectical proof procedure pro-
posed in [16] and extended in [14]. It is worth noticing that all the rules and
assumptions of our arguments are useful to deduce their conclusion even if we
do not explicitly enforce the minimality of the premises as in [17]. Moreover,
we do not enforce the consistency of the premises but this property will arise
in the arguments computed by the dialectical proof procedure due to the attack
relation.
In an assumption-based argumentation framework, the attack relation amongst
arguments comes from the contraries which capture the notion of conflicts.
1 ⊤ denotes the unconditionally true statement.
3
Page 4
Definition 3 (Attack relation). An argument a¯: A ⊢ α attacks an argument
b¯: B ⊢ β iff there is an assumption x ∈ B such that α ∈ Con(x). Similarly, we
say that the set S¯ of arguments attacks b¯ when there is an argument a¯ ∈ S¯ such
that a¯ attacks b¯.
According to the two previous definitions, ABA is clearly a concrete instantiation
of AA where arguments are deductions and the attack relation comes from the
contrary relation. Therefore, we can adopt Dung’s calculus of opposition [13].
Definition 4 (Semantics). Let AF = 〈A(ABF), attacks 〉 be our argumenta-
tion framework built upon the ABA framework ABF = 〈L,R,Asm, Con〉. A set of
arguments S¯ ⊆ A(ABF) is:
– conflict-free iff ∀a¯, b¯ ∈ S¯ it is not the case that a¯ attacks b¯;
– admissible iff S¯ is conflict-free and S¯ attacks every argument a¯ such that a¯
attacks some arguments in S¯.
For simplicity, we restrict ourselves to admissible semantics.
3 Walk-through example
We consider e-procurement scenarios where buyers seek to purchase earth ob-
servation services from sellers [10]. Each agent represents a user, i.e. a service
requester or a service provider. The negotiation of the fittest image is a complex
task due to the number of possible choices, their characteristics and the prefer-
ences of the users. It makes this usecase interesting enough for the evaluation of
our strategy [11]. For simplicity, we abstract away from the real world data of
these features and we present here an intuitive scenario illustrating our strategy.
In our scenario, we consider a buyer that seeks to purchase a service s(x )
from a seller. The latter is responsible for the four following concrete instances
of services: s(a), s(b), s(c) and s(d). These four concrete services reflect the
combinations of their features (cf Fig. 1). For instance, the price of s(a) is
high (Price(a, high)), its resolution is low (Resolution(a, low)) and its deliv-
ery time is high (DeliveryTime(a, high)). According to the preferences and the
constraints of the user represented by the buyer: the cost must be low (cheap);
the resolution of the service must be high (good); and the delivery time must
be low (fast). Additionally, the buyer is not empowered to concede about the
delivery time but it can concede indifferently about the resolution or about the
cost. According to the preferences and constraints of the user represented by
the seller: the cost of the service must be high; the resolution of the service
must be low; and the delivery time must be high (slow). The seller is not
empowered to concede about the cost but it can concede indifferently about the
resolution and the delivery time. The agents attempt to come to an agreement on
the contract for the provision of a service s(x ). Taking into account some goals,
preferences and constraints, the buyer (resp. the seller) needs to interactively
solve a decision-making problem where the decision amounts to a service it can
4
b¯: B ⊢ β iff there is an assumption x ∈ B such that α ∈ Con(x). Similarly, we
say that the set S¯ of arguments attacks b¯ when there is an argument a¯ ∈ S¯ such
that a¯ attacks b¯.
According to the two previous definitions, ABA is clearly a concrete instantiation
of AA where arguments are deductions and the attack relation comes from the
contrary relation. Therefore, we can adopt Dung’s calculus of opposition [13].
Definition 4 (Semantics). Let AF = 〈A(ABF), attacks 〉 be our argumenta-
tion framework built upon the ABA framework ABF = 〈L,R,Asm, Con〉. A set of
arguments S¯ ⊆ A(ABF) is:
– conflict-free iff ∀a¯, b¯ ∈ S¯ it is not the case that a¯ attacks b¯;
– admissible iff S¯ is conflict-free and S¯ attacks every argument a¯ such that a¯
attacks some arguments in S¯.
For simplicity, we restrict ourselves to admissible semantics.
3 Walk-through example
We consider e-procurement scenarios where buyers seek to purchase earth ob-
servation services from sellers [10]. Each agent represents a user, i.e. a service
requester or a service provider. The negotiation of the fittest image is a complex
task due to the number of possible choices, their characteristics and the prefer-
ences of the users. It makes this usecase interesting enough for the evaluation of
our strategy [11]. For simplicity, we abstract away from the real world data of
these features and we present here an intuitive scenario illustrating our strategy.
In our scenario, we consider a buyer that seeks to purchase a service s(x )
from a seller. The latter is responsible for the four following concrete instances
of services: s(a), s(b), s(c) and s(d). These four concrete services reflect the
combinations of their features (cf Fig. 1). For instance, the price of s(a) is
high (Price(a, high)), its resolution is low (Resolution(a, low)) and its deliv-
ery time is high (DeliveryTime(a, high)). According to the preferences and the
constraints of the user represented by the buyer: the cost must be low (cheap);
the resolution of the service must be high (good); and the delivery time must
be low (fast). Additionally, the buyer is not empowered to concede about the
delivery time but it can concede indifferently about the resolution or about the
cost. According to the preferences and constraints of the user represented by
the seller: the cost of the service must be high; the resolution of the service
must be low; and the delivery time must be high (slow). The seller is not
empowered to concede about the cost but it can concede indifferently about the
resolution and the delivery time. The agents attempt to come to an agreement on
the contract for the provision of a service s(x ). Taking into account some goals,
preferences and constraints, the buyer (resp. the seller) needs to interactively
solve a decision-making problem where the decision amounts to a service it can
4
Page 5
buy (resp. provide). Moreover, some decisions amount to the moves they can
utter during the negotiation.
We consider the negotiation performed through the moves in Tab. 1. A move
at time t: has an identifier, mvt; it is uttered by a speaker, and the speech act is
composed of a locution and a content, which consists of an offer. With the first
moves, the seller and the buyer start with the proposals which are “optimal”
for themselves, which are s(a) and s(d) respectively. In the third step of the
negotiation, the seller can concede minimally either with s(b) or with s(c).
Arbitrarily, it suggests s(b) rather than s(c), and so implicitly it rejects s(d).
The buyer rejects s(b) since its delivery time is high, and so the buyer concedes
minimally with s(c). Finally, the seller accepts s(c).
Move Speaker Locution Offer
mv0 seller assert s(a)
mv1 buyer reply s(d)
mv2 seller concede s(b)
mv3 buyer concede s(c)
mv4 seller accept s(c)
Table 1. Negotiation dialogue
The evaluation of the services during the negotiation are represented at the
three axis of the three dimension plot represented in Fig. 1. The acceptability
space of the two participants is represented by shaded areas and depends on the
delivery time (x-axis), on the resolution (y-axis) and the price (z-axis). As said
previously, the four points of intersection reflect the combinations of their values.
The services s(a), s(b) and s(c) respect the constraints of the seller. According
to the latter, s(a) is preferred to s(b) and s(c), which are equally preferred. The
services s(d) and s(c) respect the constraints of the buyer. According to the
latter, s(d) is preferred to s(c).
DeliveryTimeRes
olut
ion
P
r
i
c
e
buyer
seller
s(a)
s(b)
s(c)
s(d)
Fig. 1. Acceptability space of participants and proposals after the move mv3.
5
utter during the negotiation.
We consider the negotiation performed through the moves in Tab. 1. A move
at time t: has an identifier, mvt; it is uttered by a speaker, and the speech act is
composed of a locution and a content, which consists of an offer. With the first
moves, the seller and the buyer start with the proposals which are “optimal”
for themselves, which are s(a) and s(d) respectively. In the third step of the
negotiation, the seller can concede minimally either with s(b) or with s(c).
Arbitrarily, it suggests s(b) rather than s(c), and so implicitly it rejects s(d).
The buyer rejects s(b) since its delivery time is high, and so the buyer concedes
minimally with s(c). Finally, the seller accepts s(c).
Move Speaker Locution Offer
mv0 seller assert s(a)
mv1 buyer reply s(d)
mv2 seller concede s(b)
mv3 buyer concede s(c)
mv4 seller accept s(c)
Table 1. Negotiation dialogue
The evaluation of the services during the negotiation are represented at the
three axis of the three dimension plot represented in Fig. 1. The acceptability
space of the two participants is represented by shaded areas and depends on the
delivery time (x-axis), on the resolution (y-axis) and the price (z-axis). As said
previously, the four points of intersection reflect the combinations of their values.
The services s(a), s(b) and s(c) respect the constraints of the seller. According
to the latter, s(a) is preferred to s(b) and s(c), which are equally preferred. The
services s(d) and s(c) respect the constraints of the buyer. According to the
latter, s(d) is preferred to s(c).
DeliveryTimeRes
olut
ion
P
r
i
c
e
buyer
seller
s(a)
s(b)
s(c)
s(d)
Fig. 1. Acceptability space of participants and proposals after the move mv3.
5
Page 6
4 One-to-one bargaining protocol
A negotiation is a social interaction amongst self-interested parties intended to
resolve a dispute by verbal means and to produce an agreement upon a course of
action. For instance, the aim for all parties is to “make a deal” while bargaining
over their interests, typically seeking to maximise their individual welfare, and
prepared to concede some aspects while insisting on others. In this section, we
briefly present our game-based social model to handle the collaborative opera-
tions of agents. In particular, we present a dialogue-game protocol for one-to-one
bargaining.
According to the game metaphor for social interactions, agents are players
which utter moves according to social rules.
Definition 5 (Dialogue-game). Let us consider L a common object language
and ACL a common agent communication language. A dialogue-game is a
tuple DG=〈P, ΩM , H, T, proto, Z〉 where:
– P is a set of agents called players;
– ΩM ⊆ ACL is a set of well-formed moves;
– H is a set of histories, the sequences of well-formed moves s.t. the speaker
of a move is determined at each stage by the turn-taking function T and the
moves agree with the protocol proto;
– T: H→ P is the turn-taking function;
– proto: H → 2ΩM is the function determining the legal moves which are
allowed to expand an history;
– Z is the set of dialogues, i.e. the terminal histories.
DG allows social interaction between agents. During a dialogue-game, players
utter moves. Each dialogue is a maximally long sequence of moves. Let us now
specify informally the elements of DG for one-to-one bargainings.
In one-to-one bargainings, there are two players, the buyer and the seller,
which utter moves each in turn.
The syntax of moves is in conformance with a common agent commu-
nication language, ACL. A move at time t: has an identifier, mvt; is uttered
by a speaker (spt ∈ P) and the speech act is composed of a locution loct and
a content contentt. The possible locutions are: assert, reply, standstill,
concede, accept and reject. The content consists of a sentence in the common
object language, L.
Given an history, the players share a dialogue state, depending on their
previous moves. Considering the step t ∈ N, the dialogue state is a tuple
DSt = 〈lloct, loffert(buyer), loffert(seller), nbsst〉 where:
– lloct is the last locution which has been uttered, possibly none;
– loffert(buyer) (resp. loffert(seller)) represents the last offer of the buyer
(resp. seller), i.e. the content of its last move;
– nbsst is the number of consecutive standstill in the last moves.
6
A negotiation is a social interaction amongst self-interested parties intended to
resolve a dispute by verbal means and to produce an agreement upon a course of
action. For instance, the aim for all parties is to “make a deal” while bargaining
over their interests, typically seeking to maximise their individual welfare, and
prepared to concede some aspects while insisting on others. In this section, we
briefly present our game-based social model to handle the collaborative opera-
tions of agents. In particular, we present a dialogue-game protocol for one-to-one
bargaining.
According to the game metaphor for social interactions, agents are players
which utter moves according to social rules.
Definition 5 (Dialogue-game). Let us consider L a common object language
and ACL a common agent communication language. A dialogue-game is a
tuple DG=〈P, ΩM , H, T, proto, Z〉 where:
– P is a set of agents called players;
– ΩM ⊆ ACL is a set of well-formed moves;
– H is a set of histories, the sequences of well-formed moves s.t. the speaker
of a move is determined at each stage by the turn-taking function T and the
moves agree with the protocol proto;
– T: H→ P is the turn-taking function;
– proto: H → 2ΩM is the function determining the legal moves which are
allowed to expand an history;
– Z is the set of dialogues, i.e. the terminal histories.
DG allows social interaction between agents. During a dialogue-game, players
utter moves. Each dialogue is a maximally long sequence of moves. Let us now
specify informally the elements of DG for one-to-one bargainings.
In one-to-one bargainings, there are two players, the buyer and the seller,
which utter moves each in turn.
The syntax of moves is in conformance with a common agent commu-
nication language, ACL. A move at time t: has an identifier, mvt; is uttered
by a speaker (spt ∈ P) and the speech act is composed of a locution loct and
a content contentt. The possible locutions are: assert, reply, standstill,
concede, accept and reject. The content consists of a sentence in the common
object language, L.
Given an history, the players share a dialogue state, depending on their
previous moves. Considering the step t ∈ N, the dialogue state is a tuple
DSt = 〈lloct, loffert(buyer), loffert(seller), nbsst〉 where:
– lloct is the last locution which has been uttered, possibly none;
– loffert(buyer) (resp. loffert(seller)) represents the last offer of the buyer
(resp. seller), i.e. the content of its last move;
– nbsst is the number of consecutive standstill in the last moves.
6
Page 7
reply
accept reject
standstill concede
assert
Fig. 2. One-to-one bargaining protocol
Fig. 2 represents our dialogue-game protocol with the help of a deterministic
finite-state automaton. A dialogue begins with a first offer when a participant
(the buyer or the seller) makes an assert. The legal responding speech act
is reply. After that, the legal responding moves are standstills, concessions, ac-
ceptations and rejections. The legal responding moves to a concession/standstill
are the same. An history is final and: i) the dialogue is a failure if it is closed by
a reject; ii) the dialogue is a success if it is closed by an accept. The strategy
interfaces with the dialogue-game protocol through the condition mechanism of
utterances for a move. For example, at a certain point in the dialogue the agent
is able to send standstill or concede. The choice of which locution and which
content to send depends on the agent’s strategy.
5 Decision making
Taking into account the goals and preferences of the user, an agent needs to solve
a decision-making problem where the decision amounts to a service it can agree
on. This agent uses argumentation in order to assess the suitability of services
and to identify “optimal” services. It argues internally to link the services, their
features and the benefits that these features guarantee under possibly incomplete
knowledge. This section presents our framework to perform decision making,
illustrated by the buyer’s decision which amounts to the service it can buy.
7
accept reject
standstill concede
assert
Fig. 2. One-to-one bargaining protocol
Fig. 2 represents our dialogue-game protocol with the help of a deterministic
finite-state automaton. A dialogue begins with a first offer when a participant
(the buyer or the seller) makes an assert. The legal responding speech act
is reply. After that, the legal responding moves are standstills, concessions, ac-
ceptations and rejections. The legal responding moves to a concession/standstill
are the same. An history is final and: i) the dialogue is a failure if it is closed by
a reject; ii) the dialogue is a success if it is closed by an accept. The strategy
interfaces with the dialogue-game protocol through the condition mechanism of
utterances for a move. For example, at a certain point in the dialogue the agent
is able to send standstill or concede. The choice of which locution and which
content to send depends on the agent’s strategy.
5 Decision making
Taking into account the goals and preferences of the user, an agent needs to solve
a decision-making problem where the decision amounts to a service it can agree
on. This agent uses argumentation in order to assess the suitability of services
and to identify “optimal” services. It argues internally to link the services, their
features and the benefits that these features guarantee under possibly incomplete
knowledge. This section presents our framework to perform decision making,
illustrated by the buyer’s decision which amounts to the service it can buy.
7
Page 8
Definition 6 (Decision framework). A decision framework is a tuple DF =
〈L,G,D,B,R,Asm, Con,P〉 such that:
– 〈L,R,Asm, Con〉 is an ABA framework as defined in Def. 1 and L = G∪D∪B
where,
• G is a set of literals in L called goals,
• D is a set of assumptions in Asm called decisions,
• B is a set of literals in L called beliefs;
– P ⊆ G × G is a strict partial order over G, called the preference relation.
In the object language L, we distinguish three disjoint components: a set of goals
representing the objectives the agent wants to be fulfilled (e.g. cheap, good or
fast); a set of decisions representing the possible services (e.g. s(d) or s(c)); a
set of beliefs, representing the characteristics of the services (e.g. Price(c, high)
or Resolution(c, low)). Decisions are assumptions. The multiple contraries
capture the mutual exclusion of alternatives. For instance, we have Con(s(d)) =
{s(a), s(b), s(c)}.
The inference rules of the buyer are depicted in Tab. 2. All variables occurring
in an inference rule are implicitly universally quantified over the whole rule. A
rule with variables is a scheme standing for all its ground instances. The buyer
is aware of the characteristics of the available services and the benefits that these
features guarantee. The inference rules of the seller are similar.
cheap← s(x ), Price(x , low)
Price(a, high)←
Price(b, high)←
Price(c, high)←
Price(d, low)←
good← s(x ), Resolution(x , high)
Resolution(a, low)←
Resolution(b, high)←
Resolution(c, low)←
Resolution(d, low)←
fast← s(x ), DeliveryTime(x , low)
DeliveryTime(a, high)←
DeliveryTime(b, high)←
DeliveryTime(c, low)←
DeliveryTime(d, low)←
Table 2. The inference rules of the buyer
We consider the preference relation P over the goals in G, which is tran-
sitive, irreflexive and asymmetric. g1Pg2 can be read “g1 is preferred to g2”.
From the buyer viewpoint, fastPcheap, fastPgood, it is not the case that
cheapPgood and it is not the case that goodPcheap.
Formally, given an argument a¯, let
dec(a¯) = asm(a¯) ∩ D
be the set of decisions supported by the argument a¯.
Decisions are suggested to reach a goal if they are supported by arguments.
Definition 7 (Decisions). Let DF = 〈L,G,D,B,R,Asm, Con,P〉 be a decision
framework, g ∈ G be a goal and D ⊆ D be a set of decisions.
8
〈L,G,D,B,R,Asm, Con,P〉 such that:
– 〈L,R,Asm, Con〉 is an ABA framework as defined in Def. 1 and L = G∪D∪B
where,
• G is a set of literals in L called goals,
• D is a set of assumptions in Asm called decisions,
• B is a set of literals in L called beliefs;
– P ⊆ G × G is a strict partial order over G, called the preference relation.
In the object language L, we distinguish three disjoint components: a set of goals
representing the objectives the agent wants to be fulfilled (e.g. cheap, good or
fast); a set of decisions representing the possible services (e.g. s(d) or s(c)); a
set of beliefs, representing the characteristics of the services (e.g. Price(c, high)
or Resolution(c, low)). Decisions are assumptions. The multiple contraries
capture the mutual exclusion of alternatives. For instance, we have Con(s(d)) =
{s(a), s(b), s(c)}.
The inference rules of the buyer are depicted in Tab. 2. All variables occurring
in an inference rule are implicitly universally quantified over the whole rule. A
rule with variables is a scheme standing for all its ground instances. The buyer
is aware of the characteristics of the available services and the benefits that these
features guarantee. The inference rules of the seller are similar.
cheap← s(x ), Price(x , low)
Price(a, high)←
Price(b, high)←
Price(c, high)←
Price(d, low)←
good← s(x ), Resolution(x , high)
Resolution(a, low)←
Resolution(b, high)←
Resolution(c, low)←
Resolution(d, low)←
fast← s(x ), DeliveryTime(x , low)
DeliveryTime(a, high)←
DeliveryTime(b, high)←
DeliveryTime(c, low)←
DeliveryTime(d, low)←
Table 2. The inference rules of the buyer
We consider the preference relation P over the goals in G, which is tran-
sitive, irreflexive and asymmetric. g1Pg2 can be read “g1 is preferred to g2”.
From the buyer viewpoint, fastPcheap, fastPgood, it is not the case that
cheapPgood and it is not the case that goodPcheap.
Formally, given an argument a¯, let
dec(a¯) = asm(a¯) ∩ D
be the set of decisions supported by the argument a¯.
Decisions are suggested to reach a goal if they are supported by arguments.
Definition 7 (Decisions). Let DF = 〈L,G,D,B,R,Asm, Con,P〉 be a decision
framework, g ∈ G be a goal and D ⊆ D be a set of decisions.
8
Page 9
– The decisions D argue for g iff there exists an argument a¯ such that conc(a¯) =
g and dec(a¯) = D.
– The decisions D credulously argue for g iff there exists an argument a¯ in
an admissible set of arguments such that conc(a¯) = g and dec(a¯) = D.
– The decisions D skeptically argue for g iff for all admissible set of argu-
ments S¯ such that for some arguments a¯ in S¯ conc(a¯) = g, then dec(a¯) = D.
We denote val(D), valc(D) and vals(D) the set of goals in G for which the set
of decisions D argues, credulously argues and skeptically argues, respectively.
Due to the uncertainties, some decisions satisfy goals for sure if they skeptically
argue for them, or some decisions can possibly satisfy goals if they credulously
argue for them. While the first case is required for convincing a risk-averse agent,
the second case is enough to convince a risk-taking agent. We focus here on risk-
taking agents.
Since agents can consider multiple objectives which may not be fulfilled all
together by a set of non-conflicting decisions, high-ranked goals must be preferred
to low-ranked goals.
Definition 8 (Preferences). Let DF = 〈L,G,D,B,R,Asm, Con,P〉 be a deci-
sion framework. We consider G, G′ two set of goals in G and D, D′ two set of
decisions in D. G is preferred to G (denoted GPG′) iff
1. G ⊇ G′, and
2. ∀g ∈ G \ G′ there is no g′ ∈ G′ such that g′Pg.
D is preferred to D′ (denoted DPD′) iff valc(D)Pvalc(D′).
The reservation value (denoted RV) is the minimal set of goals which needs to
be reached by a set of decisions to be acceptable. Formally, given a reservation
value RV, let
as = {s(o) | ∃D ∈ D such that s(o) ∈ D and valc(D)PRV}
be the services which can be accepted by the agent.
In our example, the buyer has the arguments: b¯ supporting the service s(b)
due to its resolution; c¯ supporting the service s(c) due to its delivery time; d¯1
supporting the service s(d) due to its price and d¯2 supporting the service s(d)
due to its delivery time. The set of decisions {s(d)} (resp. {s(b)}) is the only one
which skeptically argues for cheap (resp. good) while both {s(c)} and {s(d)}
credulously argue for fast. Since the buyer is not empowered to concede about
the delivery time but it can concede about the other goals, its reservation value
is {fast}. Since {s(d)} credulously argue for good and this is not the case for
{s(c)}, we have that s(d) is preferred to s(c).
6 Minimal concession strategy
Taking into account the preferences/goals of the user and the dialogue state, an
agent needs to solve some decision-making problems where the decision amounts
9
g and dec(a¯) = D.
– The decisions D credulously argue for g iff there exists an argument a¯ in
an admissible set of arguments such that conc(a¯) = g and dec(a¯) = D.
– The decisions D skeptically argue for g iff for all admissible set of argu-
ments S¯ such that for some arguments a¯ in S¯ conc(a¯) = g, then dec(a¯) = D.
We denote val(D), valc(D) and vals(D) the set of goals in G for which the set
of decisions D argues, credulously argues and skeptically argues, respectively.
Due to the uncertainties, some decisions satisfy goals for sure if they skeptically
argue for them, or some decisions can possibly satisfy goals if they credulously
argue for them. While the first case is required for convincing a risk-averse agent,
the second case is enough to convince a risk-taking agent. We focus here on risk-
taking agents.
Since agents can consider multiple objectives which may not be fulfilled all
together by a set of non-conflicting decisions, high-ranked goals must be preferred
to low-ranked goals.
Definition 8 (Preferences). Let DF = 〈L,G,D,B,R,Asm, Con,P〉 be a deci-
sion framework. We consider G, G′ two set of goals in G and D, D′ two set of
decisions in D. G is preferred to G (denoted GPG′) iff
1. G ⊇ G′, and
2. ∀g ∈ G \ G′ there is no g′ ∈ G′ such that g′Pg.
D is preferred to D′ (denoted DPD′) iff valc(D)Pvalc(D′).
The reservation value (denoted RV) is the minimal set of goals which needs to
be reached by a set of decisions to be acceptable. Formally, given a reservation
value RV, let
as = {s(o) | ∃D ∈ D such that s(o) ∈ D and valc(D)PRV}
be the services which can be accepted by the agent.
In our example, the buyer has the arguments: b¯ supporting the service s(b)
due to its resolution; c¯ supporting the service s(c) due to its delivery time; d¯1
supporting the service s(d) due to its price and d¯2 supporting the service s(d)
due to its delivery time. The set of decisions {s(d)} (resp. {s(b)}) is the only one
which skeptically argues for cheap (resp. good) while both {s(c)} and {s(d)}
credulously argue for fast. Since the buyer is not empowered to concede about
the delivery time but it can concede about the other goals, its reservation value
is {fast}. Since {s(d)} credulously argue for good and this is not the case for
{s(c)}, we have that s(d) is preferred to s(c).
6 Minimal concession strategy
Taking into account the preferences/goals of the user and the dialogue state, an
agent needs to solve some decision-making problems where the decision amounts
9
Page 10
to a move it can utter. This agent uses argumentation in order to assess the
suitability of moves and identify “optimal” moves. It argues internally to link the
current dialogue state, the legal moves (their speech acts and their contents) and
the resulting dialogue states of these moves under possibly incomplete knowledge.
This section presents how our argumentation approach realizes the Minimal
Concession (MC) strategy, illustrated by the buyer.
A dialogue strategy is a plan that specifies the moves chosen by a player to
achieve a particular goal.
Definition 9 (Strategy). Let DG=〈P, ΩM , H, T, proto, Z〉 be a dialogue-game.
A strategy of the player p ∈ P is a function that assigns a move sp(h) to each
nonterminal history h ∈ H \ Z for which T(h) = p. For each strategy profile
S = (sp)p∈P, we define the outcome O(S) of S to be: either the content of the
last move if the terminal history (that results when each player p ∈ P follows the
precepts of sp) is successful, or nothing (denoted θ) if the terminal history is a
failure.
We consider here the MC strategy which specifies the move chosen by the player
for every history when it is his turn to move.
In order to perform the MC strategy, an agent adopts a decision framework
DF = 〈L,G,D,B,R,Asm, Con,P〉. The latter, as illustrated in the previous sec-
tion, allows to perform decision making where the decision amounts to the service
it can agree on. This DF must be extended to perform the MC strategy. For this
purpose, we incorporate in the object language L:
– the goal respond (resp. optimal) in G representing the objective of the agent
which consists of responding (resp. uttering the “optimal” move);
– the decisions in D representing the possible locutions (e.g. loc(standstill)
or loc(concede)). Obviously, the multiple contraries capture the mutual ex-
clusion of the corresponding alternatives
(e.g. {loc(concede), loc(accept), loc(reject)} = Con(loc(standstill)));
– a set of beliefs in B, related to the dialogue state,
• the last locution of the interlocutor (e.g. lloc(concede)),
• the last offers of the players (e.g. loffer(seller, b) or loffer(buyer, d)),
• the previous offers of the players (e.g. poffer(seller, a)),
• the offers which have been already (and implicitly) rejected by the in-
terlocutor (e.g. rejected(d));
– a set of assumptions in Asm representing that some alternatives have not
been yet rejected (e.g. notrejected(c)), that some alternatives have not
been proposed in the last move (e.g. notloffer(seller, c)) and that a num-
ber of standstills has not been reached (e.g. notnbss(3)).
The preference relation P on the goals in G is extended in order to take into
account the new goals respond and optimal. Actually, these goals are incompa-
rable with the other ones (cheap, good, fast). By adopting the MC strategy, the
agent tries to utter the “optimal” utterances, optimal. If the agent cannot reach
this goal, then the agents responds with a legal move, optimalPrespond and
10
suitability of moves and identify “optimal” moves. It argues internally to link the
current dialogue state, the legal moves (their speech acts and their contents) and
the resulting dialogue states of these moves under possibly incomplete knowledge.
This section presents how our argumentation approach realizes the Minimal
Concession (MC) strategy, illustrated by the buyer.
A dialogue strategy is a plan that specifies the moves chosen by a player to
achieve a particular goal.
Definition 9 (Strategy). Let DG=〈P, ΩM , H, T, proto, Z〉 be a dialogue-game.
A strategy of the player p ∈ P is a function that assigns a move sp(h) to each
nonterminal history h ∈ H \ Z for which T(h) = p. For each strategy profile
S = (sp)p∈P, we define the outcome O(S) of S to be: either the content of the
last move if the terminal history (that results when each player p ∈ P follows the
precepts of sp) is successful, or nothing (denoted θ) if the terminal history is a
failure.
We consider here the MC strategy which specifies the move chosen by the player
for every history when it is his turn to move.
In order to perform the MC strategy, an agent adopts a decision framework
DF = 〈L,G,D,B,R,Asm, Con,P〉. The latter, as illustrated in the previous sec-
tion, allows to perform decision making where the decision amounts to the service
it can agree on. This DF must be extended to perform the MC strategy. For this
purpose, we incorporate in the object language L:
– the goal respond (resp. optimal) in G representing the objective of the agent
which consists of responding (resp. uttering the “optimal” move);
– the decisions in D representing the possible locutions (e.g. loc(standstill)
or loc(concede)). Obviously, the multiple contraries capture the mutual ex-
clusion of the corresponding alternatives
(e.g. {loc(concede), loc(accept), loc(reject)} = Con(loc(standstill)));
– a set of beliefs in B, related to the dialogue state,
• the last locution of the interlocutor (e.g. lloc(concede)),
• the last offers of the players (e.g. loffer(seller, b) or loffer(buyer, d)),
• the previous offers of the players (e.g. poffer(seller, a)),
• the offers which have been already (and implicitly) rejected by the in-
terlocutor (e.g. rejected(d));
– a set of assumptions in Asm representing that some alternatives have not
been yet rejected (e.g. notrejected(c)), that some alternatives have not
been proposed in the last move (e.g. notloffer(seller, c)) and that a num-
ber of standstills has not been reached (e.g. notnbss(3)).
The preference relation P on the goals in G is extended in order to take into
account the new goals respond and optimal. Actually, these goals are incompa-
rable with the other ones (cheap, good, fast). By adopting the MC strategy, the
agent tries to utter the “optimal” utterances, optimal. If the agent cannot reach
this goal, then the agents responds with a legal move, optimalPrespond and
10
Page 11
respond ∈ RV. Since this decision framework (in particular the rules) depends
on the dialogue state of the history h, we denote it by
DFh = 〈L,G,D,B,Rh,Asm, Con,P〉.
Some inference rules of the buyer are depicted in Tab. 2. The additional rules
are depicted in Tab. 3. These rules are related to the dialogue state after the
move mv2 (1-7) or the negotiation strategy (8-19). While one of the players starts
by asserting a first proposal (8), the other agent replies with a counter-proposal
(9). An agent must adopt one of these attitudes: i) either it stands still, i.e. it
repeats its previous proposal; ii) or it concedes, i.e. it withdraws to put forward
one of its previous proposal and it considers another one. In order to articulate
these attitudes, the MC strategy consists of adhering the reciprocity principle
during the negotiation. If the interlocutor stands still, then the agent will stand
still (14). Whenever the interlocutor has made a concession, it will reciprocate
by conceding as well (12). If the agent is not able to concede (e.g. there is no
other services which satisfy its constraints), the agent will standstill (13). It is
worth noticing that the third step in the negotiation has a special status, in that
the player has to concede (10). If the agent is not able to concede (e.g. there is no
other service which satisfies its constraints), the agent will standstill (11). If an
acceptable offer has been put forward by the interlocutor, the player accepts it
(17-19). When the player can no more concede, it stops the negotiation (15). It
is worth noticing that contrary to [6], our strategy does not stop the negotiation
after 3 consecutive standstills but the strategy allows to concede after them. As
we will see in the next section, this will allow a negotiation to succeed even if,
contrary to [6], an agent does not know the preferences and the reservation value
of the other agent. The inference rules of the seller are similar.
Differently from [6], we do not assume that the agents know the preferences
of their interlocutors. Therefore, we say that a decision is a minimal concession
for a speaker since there is no other service which has not been already (and
implicitly) rejected by the interlocutor and which is preferred by the speaker.
Definition 10 (Minimal concession). Let DF = 〈L,G,D,B,R,Asm, Con,P〉
be a decision framework as defined in Section 5. The service s(o) is a concession
wrt s(o′) iff there exists a set of decisions D such that s(o) ∈ D and for all D′ ⊆ D
with s(o′) ∈ D′, it is not the case that DPD′.
The service s(o) is a minimal concession wrt s(o′) iff it is a concession wrt
s(o′) and there is no s(o′′) ∈ D such that
– s(o′′) is a concession wrt s(o′), and
– there is D′′ ⊆ D with s(o′′) ∈ D′′ with D′′PD.
The minimal concessions are computed by the decision framework proposed in
this section. In our example, the buyer concedes the service s(c) after the move
mv2, since s(d) has been rejected.
The MC strategy has been implemented by means of MARGO2 [18] (Multiat-
tribute ARGumentation framework for Opinion explanation), an argumentation-
based engine for decision-making adopting the assumption-based approach of
2 http://margo.sourceforge.net
11
on the dialogue state of the history h, we denote it by
DFh = 〈L,G,D,B,Rh,Asm, Con,P〉.
Some inference rules of the buyer are depicted in Tab. 2. The additional rules
are depicted in Tab. 3. These rules are related to the dialogue state after the
move mv2 (1-7) or the negotiation strategy (8-19). While one of the players starts
by asserting a first proposal (8), the other agent replies with a counter-proposal
(9). An agent must adopt one of these attitudes: i) either it stands still, i.e. it
repeats its previous proposal; ii) or it concedes, i.e. it withdraws to put forward
one of its previous proposal and it considers another one. In order to articulate
these attitudes, the MC strategy consists of adhering the reciprocity principle
during the negotiation. If the interlocutor stands still, then the agent will stand
still (14). Whenever the interlocutor has made a concession, it will reciprocate
by conceding as well (12). If the agent is not able to concede (e.g. there is no
other services which satisfy its constraints), the agent will standstill (13). It is
worth noticing that the third step in the negotiation has a special status, in that
the player has to concede (10). If the agent is not able to concede (e.g. there is no
other service which satisfies its constraints), the agent will standstill (11). If an
acceptable offer has been put forward by the interlocutor, the player accepts it
(17-19). When the player can no more concede, it stops the negotiation (15). It
is worth noticing that contrary to [6], our strategy does not stop the negotiation
after 3 consecutive standstills but the strategy allows to concede after them. As
we will see in the next section, this will allow a negotiation to succeed even if,
contrary to [6], an agent does not know the preferences and the reservation value
of the other agent. The inference rules of the seller are similar.
Differently from [6], we do not assume that the agents know the preferences
of their interlocutors. Therefore, we say that a decision is a minimal concession
for a speaker since there is no other service which has not been already (and
implicitly) rejected by the interlocutor and which is preferred by the speaker.
Definition 10 (Minimal concession). Let DF = 〈L,G,D,B,R,Asm, Con,P〉
be a decision framework as defined in Section 5. The service s(o) is a concession
wrt s(o′) iff there exists a set of decisions D such that s(o) ∈ D and for all D′ ⊆ D
with s(o′) ∈ D′, it is not the case that DPD′.
The service s(o) is a minimal concession wrt s(o′) iff it is a concession wrt
s(o′) and there is no s(o′′) ∈ D such that
– s(o′′) is a concession wrt s(o′), and
– there is D′′ ⊆ D with s(o′′) ∈ D′′ with D′′PD.
The minimal concessions are computed by the decision framework proposed in
this section. In our example, the buyer concedes the service s(c) after the move
mv2, since s(d) has been rejected.
The MC strategy has been implemented by means of MARGO2 [18] (Multiat-
tribute ARGumentation framework for Opinion explanation), an argumentation-
based engine for decision-making adopting the assumption-based approach of
2 http://margo.sourceforge.net
11
Page 12
lloc(concede) ← (1)
nbss(0) ← (2)
poffer(seller, a) ← (3)
loffer(p, x ) ← poffer(p, x ) (4)
loffer(seller, b) ← (5)
loffer(buyer, d) ← (6)
rejected(x ) ← poffer(buyer, x ) (7)
optimal ← loc(assert), lloc(none) (8)
optimal ← loc(reply), lloc(assert) (9)
optimal ← loc(concede), s(x ),
lloc(reply), notrejected(x ), notloffer(seller, x ) (10)
respond ← loc(standstill), s(x ),
lloc(reply), loffer(buyer, x ) (11)
optimal ← loc(concede), s(x ),
lloc(concede), notrejected(x ), notloffer(seller, x ) (12)
respond ← loc(standstill), s(x )
lloc(concede), loffer(buyer, x ) (13)
optimal ← loc(standstill),
lloc(standstill), notnbss(3) (14)
optimal ← loc(concede), s(x ),
lloc(standstill), notrejected(x ),
notloffer(seller, x ), nbss(3) (15)
respond ← loc(reject), s(x ),
lloc(standstill), loffer(seller, x ),
nbss(3) (16)
optimal ← loc(accept), s(x ),
lloc(reply),
loffer(seller, x ) (17)
optimal ← loc(accept), s(x ),
lloc(concede), notrejected(x ),
loffer(seller, x ) (18)
optimal ← loc(accept), s(x ),
lloc(standstill), notrejected(x ),
loffer(seller, x ), nbss(3) (19)
Table 3. The additional inference rules of the buyer after the move mv2
12
nbss(0) ← (2)
poffer(seller, a) ← (3)
loffer(p, x ) ← poffer(p, x ) (4)
loffer(seller, b) ← (5)
loffer(buyer, d) ← (6)
rejected(x ) ← poffer(buyer, x ) (7)
optimal ← loc(assert), lloc(none) (8)
optimal ← loc(reply), lloc(assert) (9)
optimal ← loc(concede), s(x ),
lloc(reply), notrejected(x ), notloffer(seller, x ) (10)
respond ← loc(standstill), s(x ),
lloc(reply), loffer(buyer, x ) (11)
optimal ← loc(concede), s(x ),
lloc(concede), notrejected(x ), notloffer(seller, x ) (12)
respond ← loc(standstill), s(x )
lloc(concede), loffer(buyer, x ) (13)
optimal ← loc(standstill),
lloc(standstill), notnbss(3) (14)
optimal ← loc(concede), s(x ),
lloc(standstill), notrejected(x ),
notloffer(seller, x ), nbss(3) (15)
respond ← loc(reject), s(x ),
lloc(standstill), loffer(seller, x ),
nbss(3) (16)
optimal ← loc(accept), s(x ),
lloc(reply),
loffer(seller, x ) (17)
optimal ← loc(accept), s(x ),
lloc(concede), notrejected(x ),
loffer(seller, x ) (18)
optimal ← loc(accept), s(x ),
lloc(standstill), notrejected(x ),
loffer(seller, x ), nbss(3) (19)
Table 3. The additional inference rules of the buyer after the move mv2
12
Page 13
argumentation [12]. MARGO is written in Prolog and it is distributed under the
GNU GPL. MARGO is built on top of CaSAPI3 [14] (Credulous and Scepti-
cal Argumentation: Prolog Implementation), a general-purpose tool for (several
types of) assumption-based argumentation which is also written in Prolog.
7 Properties
The negotiation protocol, as well as the MC strategy, has useful properties. The
negotiations always terminate. Moreover, if both players adopt the MC strategy,
the negotiation is successful, when it is possible. Finally, the outcome is optimal.
Due to the finiteness assumption of the language, and hence the finiteness of
possible decisions, the set of histories is also finite. Hence it is immediate that
the negotiations always terminate.
Theorem 1 (Terminaison). The dialogues are finite.
Due to the finiteness assumption and the definition of the MC strategy over
the potential agreements, it is not difficult to see that such negotiations are
successful, if a potential agreement exists.
Claim 1 (Success) If both players adopt a MC strategy and a potential agree-
ment exists, then the dialogue is a success.
Differently from [6], a player will concede at a certain point even if its interlocutor
stands still since it can no more concede. Therefore, the negotiation between two
players adopting the MC strategy go throw the whole sets of acceptable services.
In our example, s(c), which fulfills the constraints of both of the participants,
is the outcome of the successful dialogue.
Differently from [6], our realisation of the MC strategy allows to reach an
agreement even if the agents do not know the preferences and the reservation
value of the other agents. However, this realisation of the MC strategy is not in
a pure symmetric Nash equilibrium.
The final agreement of the negotiation is said to be a Pareto optimal if it is
not possible to strictly improve the individual welfare of an agent without making
the other worse off. This is the case of our realisation of the MC strategy in a
one-to-one bargaining.
Claim 2 (Social welfare) If both players adopt a MC strategy and a potential
agreement exists, then the outcome of the dialogue is Pareto optimal.
The outcome is Pareto optimal since the concessions are minimal.
3 http://casapi.sourceforge.net
13
GNU GPL. MARGO is built on top of CaSAPI3 [14] (Credulous and Scepti-
cal Argumentation: Prolog Implementation), a general-purpose tool for (several
types of) assumption-based argumentation which is also written in Prolog.
7 Properties
The negotiation protocol, as well as the MC strategy, has useful properties. The
negotiations always terminate. Moreover, if both players adopt the MC strategy,
the negotiation is successful, when it is possible. Finally, the outcome is optimal.
Due to the finiteness assumption of the language, and hence the finiteness of
possible decisions, the set of histories is also finite. Hence it is immediate that
the negotiations always terminate.
Theorem 1 (Terminaison). The dialogues are finite.
Due to the finiteness assumption and the definition of the MC strategy over
the potential agreements, it is not difficult to see that such negotiations are
successful, if a potential agreement exists.
Claim 1 (Success) If both players adopt a MC strategy and a potential agree-
ment exists, then the dialogue is a success.
Differently from [6], a player will concede at a certain point even if its interlocutor
stands still since it can no more concede. Therefore, the negotiation between two
players adopting the MC strategy go throw the whole sets of acceptable services.
In our example, s(c), which fulfills the constraints of both of the participants,
is the outcome of the successful dialogue.
Differently from [6], our realisation of the MC strategy allows to reach an
agreement even if the agents do not know the preferences and the reservation
value of the other agents. However, this realisation of the MC strategy is not in
a pure symmetric Nash equilibrium.
The final agreement of the negotiation is said to be a Pareto optimal if it is
not possible to strictly improve the individual welfare of an agent without making
the other worse off. This is the case of our realisation of the MC strategy in a
one-to-one bargaining.
Claim 2 (Social welfare) If both players adopt a MC strategy and a potential
agreement exists, then the outcome of the dialogue is Pareto optimal.
The outcome is Pareto optimal since the concessions are minimal.
3 http://casapi.sourceforge.net
13
Page 14
8 Related works
Rahwan et al. [19] propose an analysis grid of strategies for agents engaged in
negotiations. According to this grid, the factors which influence our strategy are:
the goals (an optimal outcome here), the domain (represented in terms of multi-
attribute choice here), the negotiation protocol, the abilities of agents (buy/sell
services here), the values (promoted by the reciprocity principle here). While the
strategy of our agents is directly influenced by the behaviour of its interlocutor,
it is not clear how to situate this factor in the analysis grid of [19].
Few concrete strategies of agents engaged in negotiations have been pro-
posed. For instance, Sierra et al. [20] propose different strategies based on ar-
guments such as threats, rewards or appeals (e.g. to authority). More works
are concerned by dialogues with theoretical issues rather than practical issues.
In particular, some works aim at formalizing and implementing communication
strategies for argumentative agents, specifying how an agent selects a move ac-
cording to the dialogue state and the arguments it has. For instance, Amgoud and
Parsons [21] define different attitudes: an agent can be agreeable/disagreeable,
open-minded/argumentative or an elephant’s child, depending on the the le-
gal moves and their rational conditions of utterance. Differently from [21], our
strategy takes into account also the overt behaviour of the interlocutor, since
this strategy is based on the reciprocity principle. More attitudes have been
proposed in [22] (credulous, skeptical, cautious) based on the various degrees of
justification captured by these different semantics of abstract argumentation. In
this paper, we claim that, in negotiations, the different semantics allow us to
distinguish risk-taking agents and risk-averse agents. In [21, 22], some properties
of these strategies have been studied, such as the existence/determinism of the
responds of these strategies, as well as the impact of these attitudes on the re-
sult, and the termination and the complexity of the dialogue. In this paper, we
have similar results expected for the complexity. The main difference between
the work in [21, 22] and our work is the type of dialogues which are considered.
While [22] focus on theoretical dialogues, i.e. with discursive purposes, only con-
cerned by beliefs, we are interested on bilateral bargaining dialogues between
parties which aim at reaching a practical agreement, i.e a course of action.
Alternatively, Kakas et al. [23, 24] consider the argumentation-based mech-
anism for decision-making [25] implemented in GORGIAS [26] to perform the
communication strategy of agents which depends on the agent knowledge, roles,
context and possibly on dynamic preferences. The work of Kakas, Maudet and
Moraitis is guided by the requirements for communication strategies of an ex-
pressive and declarative language which is directly implementable. The Agent
Argumentation Architecture model we have proposed in [27] shares with [28] (a)
the vision of argumentative deliberation for internal agent modules and (b) the
assumption that an agent can prioritize its needs. However, this paper focus on
a simple strategy and the study of its properties in game-theoretical terms.
Adopting a game-theory perspective as well, Riveret et al. [29] model an argu-
mentation dialogue [30] as an extensive game with perfect and complete informa-
tion. While they focus on argumentation games in adjudication debates, we have
14
Rahwan et al. [19] propose an analysis grid of strategies for agents engaged in
negotiations. According to this grid, the factors which influence our strategy are:
the goals (an optimal outcome here), the domain (represented in terms of multi-
attribute choice here), the negotiation protocol, the abilities of agents (buy/sell
services here), the values (promoted by the reciprocity principle here). While the
strategy of our agents is directly influenced by the behaviour of its interlocutor,
it is not clear how to situate this factor in the analysis grid of [19].
Few concrete strategies of agents engaged in negotiations have been pro-
posed. For instance, Sierra et al. [20] propose different strategies based on ar-
guments such as threats, rewards or appeals (e.g. to authority). More works
are concerned by dialogues with theoretical issues rather than practical issues.
In particular, some works aim at formalizing and implementing communication
strategies for argumentative agents, specifying how an agent selects a move ac-
cording to the dialogue state and the arguments it has. For instance, Amgoud and
Parsons [21] define different attitudes: an agent can be agreeable/disagreeable,
open-minded/argumentative or an elephant’s child, depending on the the le-
gal moves and their rational conditions of utterance. Differently from [21], our
strategy takes into account also the overt behaviour of the interlocutor, since
this strategy is based on the reciprocity principle. More attitudes have been
proposed in [22] (credulous, skeptical, cautious) based on the various degrees of
justification captured by these different semantics of abstract argumentation. In
this paper, we claim that, in negotiations, the different semantics allow us to
distinguish risk-taking agents and risk-averse agents. In [21, 22], some properties
of these strategies have been studied, such as the existence/determinism of the
responds of these strategies, as well as the impact of these attitudes on the re-
sult, and the termination and the complexity of the dialogue. In this paper, we
have similar results expected for the complexity. The main difference between
the work in [21, 22] and our work is the type of dialogues which are considered.
While [22] focus on theoretical dialogues, i.e. with discursive purposes, only con-
cerned by beliefs, we are interested on bilateral bargaining dialogues between
parties which aim at reaching a practical agreement, i.e a course of action.
Alternatively, Kakas et al. [23, 24] consider the argumentation-based mech-
anism for decision-making [25] implemented in GORGIAS [26] to perform the
communication strategy of agents which depends on the agent knowledge, roles,
context and possibly on dynamic preferences. The work of Kakas, Maudet and
Moraitis is guided by the requirements for communication strategies of an ex-
pressive and declarative language which is directly implementable. The Agent
Argumentation Architecture model we have proposed in [27] shares with [28] (a)
the vision of argumentative deliberation for internal agent modules and (b) the
assumption that an agent can prioritize its needs. However, this paper focus on
a simple strategy and the study of its properties in game-theoretical terms.
Adopting a game-theory perspective as well, Riveret et al. [29] model an argu-
mentation dialogue [30] as an extensive game with perfect and complete informa-
tion. While they focus on argumentation games in adjudication debates, we have
14
Page 15
considered here negotiation games where arguments are not push forward, but
instead they are used to evaluate proposals. Moreover, they abstract away for the
underlying logical language, whereas we concretise the structure of arguments.
Rahwan and Larson [31] consider abstract argumentation as a game-theoretic
mechanism design problem. In this perspective, Rahwan and Larson [32] analyse
and design intuitive rational criteria for self-interested agents involved in adjudi-
cation games. These rational criteria extend the attitudes based on the different
semantics of abstract argumentation (credulous, skeptical, cautious). An agent
may aim at maximising (resp. minimising) the number of its own arguments
which will be accepted (resp. rejected or considered as undecided) by a judge.
An aggressive agent aims at maximising the number of arguments from other
agents which will be rejected by a judge. Differently from [32], we have defined
the underlying logical language, and so the agents’ preferences are on the goals.
Therefore, our agents try to maximise the number of goals which will be pro-
moted by their agreements, and high-ranked goals are preferred to low-ranked
goals.
9 Conclusions
In this paper we have presented a realisation of the minimal concession strat-
egy which applies argumentation for generating and evaluating proposals during
negotiations. According to this strategy, agents start the negotiation with their
best proposals. During the negotiation, an agent may concede or stand still. It
concedes minimally if the other agent has conceded in the previous step, or after
the optimal offers for the participants have been put forward. It stands still if
the other agent has stood still in the previous step. A concession is minimal for
a speaker since there is no other alternative which has not been already (and
implicitly) rejected by the interlocutor, and which is preferred by the speaker.
Our realisation of the minimal concession strategy has useful properties: it guar-
antees that the outcome of the negotiation, which is guaranteed to terminate,
is optimal when it is possible, even if the agents ignore the preferences and the
reservation values of the other agents.
Our negotiation model only allows the exchange of proposals and counter-
proposals. Our plan for future work is to extend it and to extend the current
strategy for exchanging, generating and evaluating arguments during negotia-
tions. The extra information carried out by these arguments will allow agents
to influence other agents’ preference model, and so it will allow to decrease the
number messages required to reach an agreement. Our negotiation model can
only handle negotiation about fixed item/service. In future works, we want to
apply our argumentation-based mechanism for integrative negotiations rather
than distributive negotiations. Contrary to distributive negotiations, all aspects
are considered in [8] for a solution that maximizes the social welfare, such as new
services to accommodate each other’s needs for a better deal. We aim at adopt-
ing this negotiation model and extend the strategy to generate and evaluate
additional sub-items.
15
instead they are used to evaluate proposals. Moreover, they abstract away for the
underlying logical language, whereas we concretise the structure of arguments.
Rahwan and Larson [31] consider abstract argumentation as a game-theoretic
mechanism design problem. In this perspective, Rahwan and Larson [32] analyse
and design intuitive rational criteria for self-interested agents involved in adjudi-
cation games. These rational criteria extend the attitudes based on the different
semantics of abstract argumentation (credulous, skeptical, cautious). An agent
may aim at maximising (resp. minimising) the number of its own arguments
which will be accepted (resp. rejected or considered as undecided) by a judge.
An aggressive agent aims at maximising the number of arguments from other
agents which will be rejected by a judge. Differently from [32], we have defined
the underlying logical language, and so the agents’ preferences are on the goals.
Therefore, our agents try to maximise the number of goals which will be pro-
moted by their agreements, and high-ranked goals are preferred to low-ranked
goals.
9 Conclusions
In this paper we have presented a realisation of the minimal concession strat-
egy which applies argumentation for generating and evaluating proposals during
negotiations. According to this strategy, agents start the negotiation with their
best proposals. During the negotiation, an agent may concede or stand still. It
concedes minimally if the other agent has conceded in the previous step, or after
the optimal offers for the participants have been put forward. It stands still if
the other agent has stood still in the previous step. A concession is minimal for
a speaker since there is no other alternative which has not been already (and
implicitly) rejected by the interlocutor, and which is preferred by the speaker.
Our realisation of the minimal concession strategy has useful properties: it guar-
antees that the outcome of the negotiation, which is guaranteed to terminate,
is optimal when it is possible, even if the agents ignore the preferences and the
reservation values of the other agents.
Our negotiation model only allows the exchange of proposals and counter-
proposals. Our plan for future work is to extend it and to extend the current
strategy for exchanging, generating and evaluating arguments during negotia-
tions. The extra information carried out by these arguments will allow agents
to influence other agents’ preference model, and so it will allow to decrease the
number messages required to reach an agreement. Our negotiation model can
only handle negotiation about fixed item/service. In future works, we want to
apply our argumentation-based mechanism for integrative negotiations rather
than distributive negotiations. Contrary to distributive negotiations, all aspects
are considered in [8] for a solution that maximizes the social welfare, such as new
services to accommodate each other’s needs for a better deal. We aim at adopt-
ing this negotiation model and extend the strategy to generate and evaluate
additional sub-items.
15
Page 16
Acknowledgements
We would like to thank the anonymous reviewers for their detailed comments
on this paper. The authors thank Phan Minh Dung for many useful discussions
on the topic of this work.
References
1. Jennings, N.R., Faratin, P., Lomuscio, A.R., Parsons, S., Sierra, C., Wooldridge,
M.: Automated negotiation: prospects, methods and challenges. International
Journal of Group Decision and Negotiation 10(2) (2001) 199–215
2. Luck, M., McBurney, P.: Computing as interaction: agent and agreement tech-
nologies. In Marik, V., ed.: Proc. of the 2008 IEEE International Conference on
Distributed Human-Machine Systems, Athens, Greece (March 2008)
3. Rahwan, I., Ramchurn, S.D., Jennings, N.R., McBurney, P., Parsons, S., Sonen-
berg, L.: Argumentation-based negotiation. The Knowledge Engineering Review
18(4) (2003) 343–375
4. Kakas, A., Moraitis, P.: Adaptive agent negotiation via argumentation. In: Proc.
5th International Joint Conference on Autonomous Agents and Multi-Agent Sys-
tems (AAMAS), Hakodate, Japan (May 2006) 384–391
5. Amgoud, L., Dimopoulos, Y., Moraitis, P.: A unified and general framework for
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Autonomous Agents and Multi-Agent Systems (AAMAS), Honolulu, Hawaii (2007)
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7. Dung, P.M., Thang, P.M.: Modular argumentation for modelling legal doctrines
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on this paper. The authors thank Phan Minh Dung for many useful discussions
on the topic of this work.
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1. Jennings, N.R., Faratin, P., Lomuscio, A.R., Parsons, S., Sierra, C., Wooldridge,
M.: Automated negotiation: prospects, methods and challenges. International
Journal of Group Decision and Negotiation 10(2) (2001) 199–215
2. Luck, M., McBurney, P.: Computing as interaction: agent and agreement tech-
nologies. In Marik, V., ed.: Proc. of the 2008 IEEE International Conference on
Distributed Human-Machine Systems, Athens, Greece (March 2008)
3. Rahwan, I., Ramchurn, S.D., Jennings, N.R., McBurney, P., Parsons, S., Sonen-
berg, L.: Argumentation-based negotiation. The Knowledge Engineering Review
18(4) (2003) 343–375
4. Kakas, A., Moraitis, P.: Adaptive agent negotiation via argumentation. In: Proc.
5th International Joint Conference on Autonomous Agents and Multi-Agent Sys-
tems (AAMAS), Hakodate, Japan (May 2006) 384–391
5. Amgoud, L., Dimopoulos, Y., Moraitis, P.: A unified and general framework for
argumentation-based negotiation. In: Proc. 6th International Joint Conference on
Autonomous Agents and Multi-Agent Systems (AAMAS), Honolulu, Hawaii (2007)
963–970
6. Dung, P.M., Thang, P.M., Toni, F.: Towards argumentation-based contract nego-
tiation. In: Proc. of the 2nd Second International Conference on Computational
Models of Argument, IOS Press (2008)
7. Dung, P.M., Thang, P.M.: Modular argumentation for modelling legal doctrines
in common law of contract. In: Proc. of The Twenty-First Annual Conference
Legal Knowledge and Information Systems (JURIX). Volume 189 of Frontiers in
Artificial Intelligence and Applications. (2008) 108–117
8. Dung, P.M., Thang, P.M., Hung, N.D.: Argument-based decision making and
negotiation in e-business: Contracting a land lease for a computer assembly plant.
In: Proc. of 9th International Workshop on Computational Logic in Multi-Agent
Systems (CLIMA), Dresden, Germany (2008)
9. Dimopoulos, Y., Moraitis, P., Amgoud, L.: Characterizing the outcomes of
argumentation-based integrative negotiation. In: Proc. of IEEE/WIC/ACM In-
ternational Conference on Intelligent Agent Technology (IAT), Sydney, Australia
(2008)
10. Stournaras, T., ed.: Concrete scenarios identification & simple use cases. Deliver-
able document D1.1 ARGUGRID (2007)
11. Bromuri, S., Urovi, V., Morge, M., Toni, F., Stathis, K.: A multi-agent system for
service discovery, selection and negotiation. In: Proc. of the 8th International Joint
Conference on Autonomous Agents and Multiagent Systems (AAMAS). (2009)
Demonstration.
12. Bondarenko, A., Toni, F., Kowalski, R.: An assumption-based framework for non-
monotonic reasoning. In Nerode, A., Pereira, L., eds.: Proc. of the 2nd International
Workshop on Logic Programming and Non-Monotonic Reasoning (LPNMR), MIT
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monotonic Reasoning (ArgNMR). (2007) 80–95
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based, admissible argumentation. Artificial Intelligence 170(2) (2006) 114–159
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Agent Theories, Architectures, and Languages (ATAL). Volume 1365 of Lecture
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ries, Architectures and Languages (ATAL) - Intelligent Agents VIII. Volume 2333
of Lecture Notes in Computer Science., Springer (2002) 190–205
22. Parsons, S., Wooldridge, M., Amgoud, L.: Properties and complexity of some
formal inter-agent dialogues. Journal of Logic and Computation 13(3) (2003)
347–376
23. Kakas, A.C., Maudet, N., Moraitis, P.: Flexible agent dialogue strategies and soci-
etal communication protocols. In: Proc. of the 3rd International Joint Conference
on Autonomous Agents and Multi-Agent Systems (AAMAS). (2004) 1434–1435
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and Multi-Agent Systems (AAMAS), ACM Press (2003) 883–890
17
monotonic reasoning, logic programming and n-person games. Artif. Intell. 77(2)
(1995) 321–357
14. Gartner, D., Toni, F.: CaSAPI: a system for credulous and sceptical argumentation.
In Simari, G., Torroni, P., eds.: Proc. of the Workshop on Argumentation for Non-
monotonic Reasoning (ArgNMR). (2007) 80–95
15. Vreeswijk, G.: Abstract argumentation systems. Artificial Intelligence 90(1-2)
(1997) 225–279
16. Dung, P.M., Kowalski, R.A., Toni, F.: Dialectic proof procedures for assumption-
based, admissible argumentation. Artificial Intelligence 170(2) (2006) 114–159
17. Amgoud, L., Cayrol, C.: On the acceptability of arguments in preference-based
argumentation. In: Proc. of the 14th Conference on Uncertainty in Artificial In-
telligence (UAI), Madison, Wisconsin, USA., Morgan Kaufmann (1998) 1–7
18. Morge, M., Mancarella, P.: The hedgehog and the fox. An argumentation-based
decision support system. In: Proc. of the Fourth International Workshop on Ar-
gumentation in Multi-Agent Systems (ArgMAS). (2007) 55–68
19. Rahwan, I., McBurney, P., Sonenberg, L.: Towards a theory of negotiation strategy
(a preliminary report). In: Proc. of the AAMAS Workshop on Game Theoretic
and Decision Theoretic Agents (GTDT), Melbourne, Australia (2003) 1–8
20. Sierra, C., Jennings, N.R., Noriega, P., Parsons, S.: A framework for
argumentation-based negotiation. In: Proc. of the 4th International Workshop on
Agent Theories, Architectures, and Languages (ATAL). Volume 1365 of Lecture
Notes in Computer Science., Provident, RI, Springer (1998) 177–192
21. Amgoud, L., Parsons, S.: Agent dialogues with conflicting preferences. In Meyer,
J.J.C., Tambe, M., eds.: Proc. of the 5th International Workshop on Agent Theo-
ries, Architectures and Languages (ATAL) - Intelligent Agents VIII. Volume 2333
of Lecture Notes in Computer Science., Springer (2002) 190–205
22. Parsons, S., Wooldridge, M., Amgoud, L.: Properties and complexity of some
formal inter-agent dialogues. Journal of Logic and Computation 13(3) (2003)
347–376
23. Kakas, A.C., Maudet, N., Moraitis, P.: Flexible agent dialogue strategies and soci-
etal communication protocols. In: Proc. of the 3rd International Joint Conference
on Autonomous Agents and Multi-Agent Systems (AAMAS). (2004) 1434–1435
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