agent technology for e-commerce chapter 9: negotiation ii maria fasli

Agent Technology for e-Commerce

Chapter 9: Negotiation II

Maria Faslihttp://cswww.essex.ac.uk/staff/mfasli/ATe-Commerce.htm

2Chapter 9


Bargaining

A bargaining situation: two or more agents have a common interest and could reach a mutually beneficial agreement, but have a conflict of interest about which one to reach

Seller’s surplus

Buyer’s surplus

Agreement zone

ps pb

£

Seller’s valuation:wants to receiveps or more

Buyer’s valuation:wants to pay pb

or less

Agreement price p*

Buyer wants to decrease p*

Seller wants to increase p*

3Chapter 9


Bargaining power

The bargaining power of the participating agents in a bargaining situation is determined by a number of factors

Impatience Risk of breakdown Outside options Inside options Commitment tactics Asymmetric information

4Chapter 9


Axiomatic bargaining

Axiomatic bargaining theory assumes no equilibrium Axiomatic models of bargaining yield solutions that satisfy a set

of desired properties – the axioms of the bargaining solution

Example Two agents A and B need to divide a cake of size The set of possible agreements that they can reach is:

={(oA,oB):0oA and oB= -oA

The agents’ utilities are:

UA (oA)= uA and UB (oB)= uA

If the agents fail to reach a deal, then a default solution is implemented and they gain utility (dA, dB)

5Chapter 9


Nash Bargaining Solution

The Nash Bargaining Solution (NBS) of this bargaining situation is the allocation of utilities (uA, uB) which solves:

o*=max(uA- dA) (uB- dB) subject to (uA dA) and (uB dB)

The NBS is the only bargaining solution that satisfies the following: Pareto efficiency Symmetry Invariance Independence of irrelevant alternatives

6Chapter 9


Returning to the example:

uA= oA and uB= oB = (1- oA ) The NBS is the sharing rule that maximizes the Nash product:

(oA - dA) (oB - dB) The NBS is at:

uA=[+dA-dB]/2 and uB=[+dB-dA]/2

uA=dA +[-dA-dB]/2 and uB=dB +[-dB-dA]/2 As a result the two agents split the difference: the agents first

agree to take a part of the cake equal to their di and then they split the remaining cake equally between themselves

7Chapter 9


Strategic bargaining

In strategic models of bargaining, the bargaining solution emerges as the equilibrium of a sequential game in which the parties take turns in making offers and counteroffers

Two agents A and B bargain about the partition of a cake Offers are made at discrete points in time An offer is a number 0 and At each moment in time each agent makes an offer to the other; if

the other accepts, the game ends, otherwise the game continues with the other agent now making an offer

8Chapter 9


The bargaining process is not frictionless: agents are impatient and they would rather agree on the same deal today rather than tomorrow. This is expressed as a discount factor =exp(-ri)

If the agents reach a deal at time point t then agent i’s payoff is oiexp(-rit)

The bargaining situation can be depicted as a sequential game with subgames in extensive form

9Chapter 9


A

offer oA

B

accept

[oA , (1-oA)]

reject B

offer oB

A

accept

[A(1- oB), BoB]

rejectA

offer oA

B

accept

[AA oA, B B(1-oA)]

rejectB

Subgame 1

Subgame 2

Subgame 3

…

10Chapter 9


The basic alternating offers game has a subgame perfect Nash equilibrium:

Agent A gets (1-B)/(1- A B)

Agent B gets 1 minus (1-B)/(1- A B)

The unique subgame perfect Nash equilibrium satisfies two properties

No delay: whenever an agent has to make an offer, the equilibrium offer is accepted by the other agent

Stationarity: in equilibrium, a player makes the same offer whenever it has to make an offer

11Chapter 9


The following strategies define the unique subgame perfect equilibrium

Player A always offers

and always accepts an offer

Player B always offers

and always accepts an offer

12Chapter 9


The Strategic Negotiation Protocol

Based on Rubinstein’s protocol of alternating offers N agents A={a1,….,an} need to agree on a given issue They can take actions at certain times T={0,1,..} In each period tT of the negotiation if an agreement hasn’t

been reached, the agent whose turn is to make an offer at time t will suggest a possible solution

Each of the other agents responds by accepting (Yes), refusing (No), or opting out of the negotiation (Opt)

13Chapter 9


If all the agents choose Yes then the negotiation ends and the solution/offer is implemented

If at least one of the agents opts out, then the negotiation ends and a default solution is implemented

If no agent has opted out, but at least one has refused the offer, the negotiation proceeds to cycle t+1 and the next agent makes a counteroffer

An agent that responds to an offer is not aware of the other agents’ responses in the current negotiation period

14Chapter 9


Assumptions:

1. Rationality

2. Agents avoid opting out

3. Agreements are honoured

4. No long-term commitments

5. Common knowledge. Assumptions 1-4 are common knowledge

15Chapter 9


Utility functions

An agent has a utility function over all possible outcomes o The time and resources spent on the negotiation process affect

this utility

Types of utility functions: Fixed losses/gains per time unit: ui(o,t)=ui (o,0)+tci

Time constant discount rate: ui (o,t)= it · ui(o,0) where 0<i

t<1. Every agent i has a fixed discount rate i

t

16Chapter 9


Models with a financial system with an interest rate r:

Finite-horizon models with fixed losses per time unit:

ui(o,t) = ui (o,0)(1-t/k)-tc for t k

(applicable when it is known in advance that the outcome is valid for k periods)

17Chapter 9


The SNP is useful in situations where: Agents do not agree on any entity-oracle who may provide a

centralized solution The system is dynamic and therefore a predefined solution

cannot be imposed A centralized solution may cause a performance bottleneck There is incomplete information and no entity-oracle has all the

relevant information

Applications: data and ask allocation, negotiation over pollution issues, hostage negotiation

Applications of the SNP

18Chapter 9


Negotiation in different domains

Two broad categories: Task-oriented domains Worth-oriented domains

19Chapter 9


Task-oriented domains (TOD): an agent’s activity can be defined in terms of a set of tasks, where a task is a nondivisible job

Example A has to post letters and return a few books to the library B has to post a package and visit the library to borrow this

month’s National Geographic Both agents could benefit if they could reach an agreement

Negotiation in task-oriented domains

20Chapter 9


Task-oriented domains

A task-oriented domain can be formalized as a tuple T,A,c: T is a finite set of tasks A is the set of agents and any agent is capable of carrying out any

combination of tasks c is the cost function which takes as parameters the set of tasks;

c(T’) is independent of which agent carries the tasks in list T’

21Chapter 9


An encounter within a TOD is an ordered list of tasks T1,…,Tn such that Ti is the list of tasks allocated to agent ai

A deal = D1,D2 is an allocation of tasks T1T2

The cost of a deal to agent ai will be denoted costi() and the agent’s utility is:

ui()=c(Ti)- costi() If the agents fail to agree on a deal, a default conflict deal is

implemented and ui()=0 A Pareto efficient allocation or deal cannot be improved upon by

any of the agents without making any other agent worse off

22Chapter 9


Monotonic concession protocol

The negotiation proceeds in rounds: In round 1, both agents propose a deal from the negotiation set

simultaneously An agreement is reached and the protocol terminates when one of

the agents finds that the deal proposed by the other is at least as good or better than its own proposal

If no agreement is reached, the negotiation proceeds to the next round

23Chapter 9


In round t+1, both agents make proposals: A new proposal can be the previously made proposal by the agent

(the agent stands still), or A new proposal which gives the other agent more utility than the

proposal made in round t (the agent concedes) If none of the agents make a concession, the protocol terminates

with the conflict deal

24Chapter 9


A’s best deal B’s best deal Conflict deal

Maximal loss from concession

Maximal loss from conflict deal

25Chapter 9


The Zeuthian strategy

Three aspects: What should an agent’s first proposal be?

The best deal for that agent

Who should concede on any given round?

The agent that has more to loose if the conflict deal is imposed

If an agent concedes, how much should it concede?

As much as it is required so that the balance of risk is changed between the agent and its opponent

26Chapter 9


Measuring the degree of willingness to risk Suppose A has conceded a lot already, then the deal is very close

to the conflict deal and A does not have much to loose The extent to which an agent is more willing to risk conflict is:

As dwriski,t increases, the agent has less to lose if a conflict occurs and as a result will not be willing to concede

The agent with the lowest dwriski,t should concede

27Chapter 9


The agents will not run into conflict, i.e. the outcome reached is going to be Pareto efficient

Not in Nash equilibrium, a self-interested agent knowing that the opponent is using the Zeuthian strategy can try and exploit this

Extended Zeuthian strategy: who concedes in case both agents have the same dwriski,t is decided on the flip of a fair coin

This is now a game where the players play with mixed strategies, so there is at least on mixed strategies Nash equilibrium

But there is some positive probability that the conflict deal will be reached. So although the extended Zeuthian strategy is stable, it may yield an inefficient outcome

Not computational and communication efficient

Features of the Zeuthian strategy

28Chapter 9


Deception in TODs

Agents have to declare their tasks, and may do so insincerely An agent can declare phantom or decoy tasks in an attempt to

influence the outcome of the negotiation process. If an agent can produce a phantom task on demand then this is

called a decoy Phantom tasks that cannot be easily produced make deception

detection easier An agent can also hide tasks

29Chapter 9


Worth Oriented Domains

Agents are interested in bringing about states that have the greatest value

Agents’ goals can be achieved through joint plans

30Chapter 9


Worth-oriented domains can be formalized as a tuple S, A, J, c: S is the set of all possible states A is the set of agents J is the set of all possible joint plans c is the cost function which represents the cost of a joint plan to

an agent ai

j:s1|→s2 denotes that the execution of plan j is s1 leads to s2

If the agent were alone in the world, then its utility from bringing the world to its own ‘stand-alone optimal’ using its own plan is:

31Chapter 9


It may be impossible for each of the agents to perform single-agent plans to bring the world to a desirable state

Agents in WODs can reach a compromise by negotiating not only over what parts of their goals will be achieved, but also over the means

State-oriented domains: the worth value is associated only with the achievement of an agent’s full goal

32Chapter 9


Coalitions

A coalition is a set of agents that agree to cooperate in order to achieve a common objective

The incentives for creating/joining a coalition can be: Monetary: reduction of cost or increased profit Risk reduction (or allowing someone else to assume risk) Increase in market size or share

33Chapter 9


Coalition formation

Coalition formation can be studied in the context of characteristic function games (CFG):

A set N of agents in which each subset is called a coalition The value of a coalition S is given by a characteristic function vS

CS: the coalition structure is the set of all coalitions such that every agent belongs to one

The solution of a game with side payments is a coalition configuration which consists of a partition S of N, the coalition structure CS, and an n-dimensional payoff vector

34Chapter 9


Coalition formation in CFG games involves two activities: Coalition structure generation Division of the value of the generated coalition structure among

all agents

The two activities are intertwined

35Chapter 9


Coalition structure generation

The formation of an optimal, maximum welfare coalition structure is trivial when the coalition values are:

Super-additive: there is at least one optimal coalition structure, the grand coalition

Sub-additive: the optimal coalition structure is the one in which every agent acts on their own

When games are neither sub-additive or super-additive some coalitions are best off merging whereas others are not

36Chapter 9


The objective is to maximize the social welfare of the agents by finding an optimal coalition structure CS*:

where V(CS) is the value of a coalition structure:

37Chapter 9


The number of coalition structures CS is exponential in the number of coalitions S, the agent must search among O(nn) coalition structures to find the optimal one

The number of coalitions is

Not all coalition structures can be enumerated unless n is small Can the agents approximate the optimal coalition structure? Can they search through a subset LM such that:

38Chapter 9


Coalition structures for four agents

• The lowest two levels of the ordering (j=1 and j=2) the agents have seen all the possible coalition structures• The agents must at least inspect 2n-1 different coalition structures in order to determine a worse-case bound• If more time for computation is available more coalition structures can be inspected

39Chapter 9


Division of payoffs

Payoff division is important as it affects the stability of the coalitionMany coalition formation algorithms rely on game theory concepts

The Core

The strongest solution concept; it may be empty Agents may switch indefinitely between coalitions The Core may contain multiple solutions – the agents need to

agree on one: the nucleolus Calculating the Core is an NP-hard problem

40Chapter 9


The Shapley value: Agent i is a dummy if vSi-vS=vi for every coalition S that does not

include i Agents i and j are interchangeable if for all S with either i or j, vS

remains the same if i is replaced by j

We require a set of payoffs that satisfy: Symmetry: if i and j are interchangeable then pi=pj

Dummies: if i is a dummy, then pi=v{i}

Additivity: for two games v and w, pi in v+w is equal to pi in v plus pi in w

41Chapter 9


The Shapley value satisfies these conditions and sets the payoffs to

It always exists and is unique Pareto efficient It guarantees that individual agents and the grand coalition have

an incentive to stay with the coalition structure No guarantee that all subgroups of agents are better off in the

coalition structure than by splitting out into a coalition of their own

42Chapter 9


Customer coalitions

Suppose you want to buy a PC, you can do so at retail price If nine of your friends are interested in the same type of PC, you

can join forces and ask retailers to make you a better offer as this is a bulk purchase

What the discount is depends on the number of PCs The vendor has an incentive to lower the price, as otherwise the

sale will be lost

43Chapter 9


Supplier incentive to sell wholesale

Utility to sell wholesale:

The utility of selling n items retail:

The utility of selling n items wholesale:

Up to some number nretail, the supplier does not have an incentive to sell wholesale as marketing costs are identical

44Chapter 9


Customer incentive to buy wholesale

A customer’s utility:

ucustomer = vitem – pitem – cstorage

Maximum utility range: MUR(nmin,nmax) – utility is high while the management or storage costs remain low

If nwholesaleMUR then the customer can purchase the items at wholesale price

But the customer needs to be given incentives to buy larger quantities, i.e, the supplier needs to lower the price

45Chapter 9


In practice, individual consumers very rarely require large enough quantities so that they can purchase at wholesale prices

But by forming coalitions, consumers can increase the quantity purchased so as to be charged wholesale prices

The utility of the coalition is now MURcoalition = MURi

If nwholesaleMURcoalition then the coalition can make a wholesale purchase

46Chapter 9


Coalition protocols

The general stages involved in a coalition protocol are: Negotiation: The coalition leader/representative negotiates with

suppliers Coalition formation: The initiator/leader invites potential

members to join the coalition; possible admission constraints Leader election/voting: The members may elect a leader. Not all

protocols have this stage Payment collection: The coalition leader/representative collects

payments and pays supplier. Execution/distribution: The transaction is executed; the goods

arrive and they are distributed to the members of the coalition

47Chapter 9


Issues in coalition protocols

Coalition stability Distribution of utility and costs Trust

Negotiation stage Payment collection stage Distribution stage

Distribution of risk Risk of transaction failure Risk of coalition failure Price uncertainty

48Chapter 9


Coalition protocols

Assume a coalition leader (L), a set of suppliers S={s1,s2,…,sk} and a set of potential coalition members M={m1,m2,…,mn}

Based on the order in which the negotiation and coalition formation stages take place there are two types:

Post-Negotiation Pre-Negotiation

49Chapter 9


Post-negotiation protocol

1. LCS: L advertises the creation of a coalition with certain parameters (deadline, maximum number etc.)

2. Each miM considers whether to join the coalition and sends necessary message mi L: “Join the Coalition”

3. At the expiration of the coalition deadline/size limit, the leader enters the negotiation with the suppliers si S using its private protocol/strategy and decides on a deal

4. L collects money from group members, and arranges for the shipping and distribution of goods

50Chapter 9


Issues Trust in the coalition leader is required Shills can start coalitions

Trust can be established in a number of ways Leaders can be elected A trusted third party can be appointed to conduct the negotiations The coalition leader could be compelled to open every step of the

negotiation to the scrutiny of group members Members can vote on the suppliers’ bids – but time-consuming

51Chapter 9


Pre-negotiation protocol

1. L conducts negotiations with the suppliers S, using its private parameters.

2. L opens the coalition to potential coalition members, disclosing the details of the deal agreed

3. Each miM considers whether to join the coalition and sends necessary message mi L: “Join the Coalition”

4. After a certain period of time elapses, or the coalition gains some minimum number of members, L closes the coalition to new members and executes the transaction

52Chapter 9


Issues An insufficient number of members join the coalition The deal must be re-negotiated, resulting in a higher price and,

possibly, more members leaving the coalition

53Chapter 9


Variation: L presents not an estimated group size, but a range of sizes. The supplier bids with a step function P = Fbid(quantity) The risk in the transaction is shifted onto the coalition members

due to the price uncertainty A buyer’s decision on whether to join depends on its estimate of

the probability that the final price will be lower than its preservation:

pmax-coalition >= preservation >= pmin-coalition

A dominant strategy for a buyer would be to wait until the coalition is almost closed for new members

54Chapter 9


Distribution of costs and utility

The coalition leader can operate on: Non-Profit: ccoalition is distributed either equally among all

participants or on the sub-lot size basis. Can form on a per need basis or be stable ‘buyer's clubs’ that exist over time

For-Profit: Consolidator: Pre-negotiates a deal with the supplier given an

estimated group size, and then re-sells the items individually, keeping enough of the savings to cover ccoalition and profit

Rebater: Sells the items at retail price minus a small rebate, and keeps the rest of the savings

55Chapter 9


Social choice problems

Given a society of agents and their preferences we would like to aggregate them into a social ‘preference’

How can we go from often divergent and incompatible but individually consistent views on what is the socially best outcome, to a single and socially consistent view?

56Chapter 9


Social choice rule

A social choice setting: N: a set of agents (society) : a set of feasible outcomes for the society iN there is an asymmetric and transitive preference relation

on

Social choice rule takes as input the agents’ preference relations

and produces as output the social preferences denoted by a relation

57Chapter 9


Conditions: A social preference ordering should exist for all possible

inputs and should be complete and transitive over The outcome should be Pareto efficient The scheme should be independent of irrelevant alternatives No agent should be a dictator: no o o’ implies o o’ for all

preferences of the other agents

Arrow’s Impossibility Theorem:

There is no social choice rule that satisfies all four conditions

58Chapter 9


Voting protocols

A class of social choice rules: the third condition is relaxed Agents give input to a mechanism and the mechanism chooses

an outcome based on these inputs which is the solution imposed upon all participating agents

The aim is to enhance the general good (social welfare) Binary protocols Plurality protocols Mixed protocols

59Chapter 9


Binary protocols

Agents are asked to choose between two alternatives at a time, if there are more than two, these are compared pairwise and the winner challenges further alternatives

Condorcet protocol: each alternative is pitted against all other others and the one that defeats all others wins

They may not generate a transitive social preferences ordering:

60Chapter 9


The outcome depends on the agenda:

28% prefer c d b a

25% prefer a c d b

24% prefer b a c d

23% prefer a d c b

a, b, c, d b, d, c, a c, a, d, b

c

b

c

b

d

a

c

c

d

c

d

a

b

a

a

a

b

d

a

c

b

c, a, b, d

b

a

b

a

d

c

d

61Chapter 9


Plurality protocols

All alternatives are compared simultaneously The winner is the alternative with the highest number of votes Such protocols are used in political elections

62Chapter 9


Borda protocol

The Borda count assigns an alternative | | points whenever it is highest in some agent’s preference list | |-1 whenever it is second and so on

The alternative with the highest count becomes the social choice But, it can lead to paradoxical results if an irrelevant alternative

is removed

63Chapter 9


64Chapter 9


Mixed protocols

Some protocols combine plurality and binary protocols

Majority runoff protocol First stage: voters indicate their preferences among a set of

alternatives by casting one vote. If an alternative receives the majority of votes, this is the winner. Otherwise:

Second stage: the two most preferred alternatives run against each other

Proportional representation The full preference rankings of the voters provide for a

proportional representation

65Chapter 9


Variation of proportional representation: single transferable vote or Hare protocol:

Agents cast one vote, but indicate their preference rankings over all alternatives

Alternatives which obtain a certain percentage of votes are elected and those that fail to obtain that percentage (or the alternatives with the fewer votes) are eliminated

The votes from the eliminated alternatives are transferred to the next highest ranking alternative according to the agents’ preference rankings

The processes is repeated until an appropriate number of alternatives is elected

66Chapter 9


Issues in voting protocols

Agents may declare their preferences insincerely or vote strategically in order to increase their own gain

Those responsible for setting up the process may attempt to manipulate the proceedings

The application of different protocols to the same situation may lead to different outcomes

67Chapter 9


A function that aggregates the individual agents’ preferences into a social one is called a social welfare function

Summing up the agents’ utilities according to an allocation is such a social welfare function

The allocation o is preferred to o’ if:

Weighted sum of utilities

Social welfare functions

68Chapter 9


Welfare maximization

The social welfare maximization problem takes the form:

such that

Such a maximal welfare allocation is Pareto efficient

69Chapter 9


Argumentation

Negotiation as purported by game theory has two limitations: Proposal/offers and negotiation positions cannot be justified Proposals/offers and negotiation positions cannot be modified

These limitations can be overcome through argumentation-based negotiation

Additional information can be exchanged on top of the offers Agents enter into a dialogue and attempt to convince the others

(persuasion type of dialogue according to Walton and Krabbe)

70Chapter 9


Argumentation amongst humans: Logical mode: resembles logical or mathematical proof Emotional mode: makes use of one’s feelings, emotions and

other attitudes Visceral mode: such arguments involve physical and social

aspects Kisceral mode: makes appeal to the religious, mystical or

intuitive side of human nature

71Chapter 9


Generating persuasive arguments

Two parties: the persuader and the persuadee Persuasive arguments are used in order to change the behaviour

of the pursuadee – behaviour changes not necessarily the beliefs

Arguments may: explain the opinion of the agent on a particular proposal or

provide a critique on a proposal which explains why it is unacceptable – the negotiation space of the agent is explained

give reasons why the agent should accept a proposal – attempt to convince the other party about the validity of a proposal

72Chapter 9


To generate persuasive arguments, agents need to be able to: Represent and maintain the beliefs of other agents Select which beliefs need to be influenced and in what way Connect beliefs with behaviour Choose the most appropriate and convincing argument Offer counter-arguments Modify one’s own position as the dialogue process progresses

A complex cognitive task

73Chapter 9


Abstract architecture

Message interpretation

Message generation

Communication component

Knowledge base component

Environment model

Self-model

Opponent model

Negotiation history

Decision making component

ProposalProposalhistory

UpdateQuery

Proposal

Message

Message

Argument evaluation

Argument

Argument generator

Argument selector

Update

Argumentation component

Arguments

Response

74Chapter 9


The PERSUADER system

Domain: negotiations between union and employers The system plays the role of the mediator Three main tasks

Proposal generation Counter-proposal generation based on proposal from the

disagreeing participant Persuasive argumentation

Agents have a representation of the others’ beliefs which they update based on the proposals and arguments made during the negotiation process

75Chapter 9


The system can generate different types of arguments (in order of increasing convincing power):

Appeal to universal principle Appeal to a theme or a package of goals Appeal to authority Appeal to status quo Appeal to ‘minor standard’ Appeal to prevailing practice Appeal to precedents and counterexamples Appeal to self-interest Threats and promises

76Chapter 9


Logic-based argumentation

Generating a series of logical arguments for and against propositions, offers etc.

A logical argument is of the form :

where is a knowledge base containing facts about the world (which

may not necessarily be consistent is the sentence (offer, position etc.) that is to be proved, i.e. the

conclusion KB is a set of logical formulas that

And can be proven from KB

77Chapter 9


Given an argument (, KB) there are two types of argument against it:

Those that rebut it: argument (1, KB1) rebuts (2, KB2) if 1 attacks 2

Those that undercut it: argument (1, KB1) rebuts (2, KB2) if 1 attacks for some KB2

Attack: for any propositions and , attacks , if an only if

78Chapter 9


Classes of arguments (in order of increasing acceptability): A1: all arguments that can be made from A2: all nontrivial arguments that can be made from A3: all arguments that can be made from for propositions

for which there are no rebutting arguments A4: All arguments that may be made from for propositions

for which there are no undercutting arguments A5: All tautological arguments

79Chapter 9


Negotiation as dialogue games

Dialogue games describe interactions among agents where each agent ‘makes a move’ by making an utterance according to a set of rules

Commencement rules Locution rules Combination rules Commitment rules Termination rules

80Chapter 9


A dialogue game between buyers and sellers

The dialogue game of McBurney et al. (2003) includes 7 stages:

1. Open dialogue

2. Inform

3. Consideration set formation

4. Option selection

5. Negotiation

6. Confirmation

7. Dialogue termination

Strictly speaking stages (3) and (4) are not part of the dialogue

81Chapter 9


The simplest form of dialogue consists of all 7 stages More complex dialogues can be formed by entering some stages

multiple times subject to the following rules: The first stage must be the Open dialogue and occurs once The last stage is the Dialogue termination and occurs once Every dialogue that terminates normally involves the Open

dialogue and Dialogue termination stages The first instance of every other stage apart from the first and

last one must be preceded by an instance of the Inform stage The Confirmation stage may only be entered following an

instance of the Negotiation stage

82Chapter 9


To automate dialogues appropriate locutions are required: Open dialogue: open_dialogue(.) followed by at least one

enter_dialogue(.)

Inform: seek_info(.) and willing_to_sell(.)

Negotiation: desire_to_buy(.), prefer(.), refuse_to_buy(.) and refuse_to_sell(.)

Confirmation: agree_to_sell(.) and agree_to_buy(.)

Dialogue termination: withdraw_dialogue(.)

agent technology for e-commerce chapter 9: negotiation ii maria fasli

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