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Lecture 3: Negotiation
Reaching Agreements
SIF8072
Distributed Artificial Intelligence
and
Intelligent Agents
http://www.idi.ntnu.no/~agent/
30 January 2003
Lecturer: Sobah Abbas Petersen
Email: [email protected]
Lecture Outline
1. Recap Auctions
2. Negotiation
•
Mechanisms, protocols, strategies
•
Negotiation domains (task-oriented and worthoriented)
•
Monotonic Concession Protocol
•
Zeuthen Strategy
3. Coordination – The Contract Net Protocol
2
References
•
Curriculum: Wooldridge: ”Introduction to
MAS”,
–
Negotiation: Chapter 7
–
Coordination, Contract Net Protocol: Chapter 9
•
Recommended Reading (Not curriculum):
–
J. Rosenschein and G. Zlotskin, Rules of Encounter, MIT Press, 1994, ISBN 9
780262 181594,
•
–
Chapters 1, 2 and 3
R. Davis and R. G. Smith, Negotiation as a Metaphor for Distributed Problem
Solving, (A. H. Bond and L. Gasser eds.) Readings in Distributed Artificial
Intelligence, Morgan Kaufmann Publishers, 1988, p. 333-356.
3
Negotiation
•
”The process of several
agents searching for an
agreement”
e.g. about price.
 Reaching consensus
”Rules of Encouter” by
Rosenchein and Zlotskin, 1994
4
Recap - Auctions
auctioneer
bidders
• An Auction takes place between an auctioneer and a collection of
bidders.
• In most settings, the auctioneer desires to maximise the price;
bidders desire to minimise the price.
• Types of Auctions:
Price
bidder
– English auction
– Dutch auction
– First-price sealed bids
auctioneer
– Vickrey (Second-price sealed bids)
• Useful for allocating goods. But too simple for many other settings.
5
Recap - Limitations of Auctions
•
Only concerned with the allocation of goods;
•
Not adequate for settling agreements that
concerns matters of mutual interest.
 Negotiation
6
Negotiation Example 1
Consider two companies A and B decide to form an alliance to
develop a software product for the shipbuilding industry.
Company A has the shipbuilding market and knowledge in that
domain. Company B is a software company that specialises in
CAD systems and CAE. They negotiate to agree upon the
financial assets, the skills and technology contributed by each
company, how much of the new product each company will
own and who will market the product and provide first-line
support for the product.
7
Negotiation Example 2
Consider two agents, each controlling a
telecommunications network with associated
resources such as communication lines,
microwave links, routing computers, short and
long-term storage devices. The load that each
agent has to handle varies over time. The agents
negotiate about resource sharing.
8
Negotiation
• May involve:
– Exchange of information
– Relaxation of initial goals
– Mutual concession
9
Mechanisms, Protocols, Strategies
• Negotiation is governed by a mechanism or a
protocol:
– defines the ”rules of encounter” between the agents
– the public rules by which the agents will come to
agreements.
• Given a particular protocol, how can a particular strategy be
designed that individual agents can use?
10
Mechanisms Design
• Mechanism design is the design of protocols for governing
multi-agent interactions.
• Desirable properties of mechanisms are:
– Convergence/guaranteed success
– Maximising social welfare
– Pareto efficiency
– Individual rationality
– Stability
– Simplicity
– Distribution
11
Negotiation Components
•
Any negotiation setting will have 4 components:
1. Negotiation set: represents the space of possible
proposals that agents can make
2. Protocol: defines the legal proposals that agents can
make
3. Collection of strategies: (one for each agent)
determines what proposals the agent will make
4. Rule: to determine when an agreement has been
reached
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Negotiation Process 1
•
Negotiation usually proceeds in a series of
rounds, with every agent making a proposal at
every round.
•
Communication during negotiation:
Proposal
Counter Proposal
Agenti concedes
Agenti
Agentj
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Negotiation Process 2
•
Another way of looking at the negotiation
process is:
Proposals by Ai
Point of
Acceptance/
aggreement
Proposals by Aj
14
Complex Negotiations
•
Some attributes that make the negotiation process
complex are:
–
–
Multiple attributes:
•
Single attribute (price) – symmetric scenario.
•
Multiple attributes – several inter-related attributes, e.g. buying a car.
The number of agents and the way they interact:
•
One-to-one, e.g. single buyer and single seller .
•
Many-to-one, e.g. multiple buyers and a single seller, auctions.
•
Many-to-many, e.g. multiple buyers and multiple sellers.
15
Negotiation Domains:
Task-oriented
• ”Domains in which an agent’s activity can be defined in
terms of a set of tasks that it has to achieve”, (Rosenschein &
Zlotkin, 1994)
• An agent can carry out the tasks without interference from
other agents
• All resources are available to the agent
• Tasks redistributed for the benefit of all agents
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Task-oriented Domain: Example
Imagine you have 3 children, each of whom needs to be delivered to 3
different schools each morning. Your neighbour has 4 children who
also need to be taken to school. Delivery of each child is a task.
Assume that one of your children and one of your neighbour’s children
both go to the same school. It obviously makes sense for both children
to be taken together and only you or your neighbour needs to make the
trip.
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Task-oriented Domain: Definition
• Can be defined as a triple:
– T,Ag,c
• T: finite set of all possible tasks
• Ag: set of negotiating agents
• C: cost of executing each subset of tasks
• How can an agent evaluate the utility of a specific deal?
– Utility represents how much an agent has to gain from the deal.
– Since an agent can achieve the goal on its own, it can compare the cost of
achieving the goal on its own to the cost of its part of the deal.
• If utility<0, it is worse off than performing tasks on its own.
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Deals in Task-oriented Domains
•
Conflict deal: if agents fail to reach an agreement:
–
where no agent agrees to execute tasks other than its own.
•
•
utility = 0
A deal that is not dominated by any other deal is pareto
optimal.
•
A deal is individual rational if it weakly dominates the
conflict deal.
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Negotiation Set in Task-oriented
Domains
Utility for agent i
Negotiation set:
(pareto optimal+
B
Individual rational)
A
Utility of conflict
Deal for agent i
E
Conflict deal
C
The circle delimits the
space of all possible
deals
D
Utility for agent j
Utility of conflict
Deal for agent j
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Let’s take a minute……
• Give an example in the Task-oriented domain?
• Discuss with your neighbour(s) about this domain
and how you can agree upon sharing the tasks.
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The Monotonic Concession Protocol
(MCP) 1
•
Negotiation proceeds in rounds
•
On round 1, agents simultaneously propose a deal from
the negotiation set.
•
Agreement is reached if one agent finds that the deal
proposed by the other agent is atleast as good or better
than its proposal.
Ai best deal
Aj best deal
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The Monotonic Concession Protocol 2
•
If no agreement is reached, then negotiation proceeds to
another round of simultaneous proposals.
•
In round u+1, no agent is allowed to make a proposal
that is less preferred by the other agent than the deal
proposed at time u.
•
If neither agent concedes, then negotiation terminates
with a conflict deal.
23
The Monotonic Concession Protocol 3
•
Advantages:
–
Symmetrically distributed (no agent plays a special role)
–
Ensures convergence
–
It will not go on indefinitely
•
Disadvantages:
–
Agents can run into conflicts
–
Inefficient – no quarantee that an agreement will be reached
quickly
24
Key Questions
3 key questions to be answered:
1.
What should an agent’s first proposal be?
It’s most preferred deal.
2.
On any given round, who should concede?
The agent least willing to risk conflict.
3.
If an agent concedes, then how much should it concede?
Just enough to change the balance of risk.
25
The Risk Factor
One way to think about which agent should concede is to
consider how much each has to loose by running into
conflict at that point.
How much
am I willing
to risk a
conflict?
Maximum loss from conflict
Maximum loss from concession
Conflict deal
Ai best deal
Aj best deal
26
The Zeuthen Strategy
•
Uses the risk evaluation strategy
•
Suppose you have conceded a lot. Then:
–
Your proposal is now close to conflict deal.
–
You are more willing to risk conflict.

An agent will be more willing to risk conflict if the
difference in utility between its current proposal and the
conflict deal is low.
•
Degree of willingness to risk a conflict can be defined
as:
Riskt
i=
utility i loses by conceding and accepting j’s offer
utility i loses by not conceding and causing conflict
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About MCP and Zeuthen Strategies
•
Advantages:
–
Simple and reflects the way human negotiations work.
–
Stability – in Nash equilibrium – if one agent is using the strategy, then
the other can do no better than using it him/herself.
•
Disadvantages:
–
Computationally expensive – players need to compute the entire
negotiation set.
–
Communication burden – negotiation process may involve several
steps.
28
Negotiation Domains:
Worth-oriented
• ”Domains where agents assign a worth to each potential
state (of the environment), which captures its desirability
for the agent”, (Rosenschein & Zlotkin, 1994)
• agent’s goal is to bring about the state of the environment with highest
value
• we assume that the collection of agents have available a set of joint
plans – a joint plan is executed by several different agents
29
Worth-oriented Domain: Example
2 agents are trying to set up a meeting. The first agent wishes to meet
later in the day while the second wishes to meet earlier in the day. Both
prefer today to tomorrow. While the first agent assigns highest worth to
a meeting at 16:00hrs, s/he also assigns progressively smaller worths to
a meeting at 15:00hrs, 14:00hrs….
By showing flexibility and accepting a sub-optimal time, an agent can
accept a lower worth which may have other payoffs, (e.g. reduced
travel costs).
100
Worth function for first
agent
Ref: Rosenschein & Zlotkin, 1994
0
9
12
16
30
Worth-oriented Domain: Definition
• Can be defined as a tuple:
– E,Ag,J,c
• E: set of possible envirinment states
• Ag: set of possible agents
• J: set of possible joint plans
• C: cost of executing the plan
31
Worth-oriented Domains and
Multiple Attributes
• If you want to pay for some software, then you might consider several
attributes of the software such as the price, quality and support –
multiple set of attributes.
• You may be willing to pay more if the quality is above a given limit,
i.e. you can’t get it cheaper without compromising on quality.
 Pareto Optimal – Need to find the price for acceptable quality and
support (without compromising on some attributes).
32
How can we calculate Utility?
• Weighting each attribute
– Utility = {Price*60 + quality*15 + support*25}
• Rating/ranking each attribute
– Price : 60, quality : 20, support : 20
– INSPIRE uses rating
• Using constraints on an attribute
– Price[5,100], quality[0-10], support[1-5]
– Try to find the pareto optimum
33
Utility Graphs 1
• Each agent concedes in
every round of negotiation
Utility
• Eventually reach an
agreement
Agentj
Point of acceptance
Agenti
time
No. of negotiations
34
Utility Graphs 2
Utility
•No agreement
Agentj
Agentj finds offer unacceptable
Agenti
time
No. of negotiations
35
Let’s take a minute……
• Give an example in the Worth-oriented domain?
• Discuss with your neighbour(s) the kinds of
attributes that will play a role in the negotiation
process.
36
Argumentation 1
•
The process of attempting to convince others of
something.
•
Why argument-based negotiations:
–
Limitations of game-theoretic approaches
•
Positions cannot be justified – Why did the agent pay so much
for the car?
•
Positions cannot be changed – Initially I wanted a car with a
sun roof. But I changed preference during the buying process.
37
Argumentation 2
•
4 modes of argument:
1.
Logical - ”If you accept that A and A implies B,
then you must accept that B”
2. Emotional - ”How would you feel if it happened
to you?”
3.
Visceral - One argumentation participant stamps
their feet and show the strength of their feelings
4.
Kisceral - Appeals to the intuitive
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Negotiation - Summary
• Task-oriented domains:
• Monotonic Concession Protocol
• Could result in a conflict deal
• Zeuthen strategy – takes into account the risk of running into a
conflict
• Risk – distance between current position and conflict deal
• Worth-oriented domains
100
• Multiple set of attributes
• Pareto optimality
• Argumentation
Worth function
0
9
12
16
39
Coordination
”The process by which an agent reasons about its
local actions and the (anticipated) actions of
others to try and ensure that the community acts
in a coherent manner.”
Jennings,1996
40
References - Curriculum
•
Wooldridge: ”Introduction to MAS”,
–
•
Chapter 9
N. R. Jennings. ”Coordination Techniques for
Distributed Artificial Intelligence”, in: G. M. P. O'Hare,
N. R. Jennings (eds). Foundations of Distributed
Artificial Intelligence, John Wiley & Sons, 1996, pp.
187-210.
41
Coordination Example
Consider an interaction between two robots, A and B,
operating in a warehouse. The robots have been designed
by different companies, and they are stacking and
unstacking boxes to remove certain goods that have been
stored in the building. They need to coordinate their
actions to share the work load and to avoid knocking
into each other and dropping the boxes.
42
Reasons for Coordination
•
Preventing anarchy or chaos
•
Dependencies between agents’ actions.
•
Need to meet global constraints
•
No individual has sufficient competence, resources or
information to solve the entire problem.
•
Efficiency
43
Cooperative Distributed Problem
Solving (CDPS)
CDPS studies how a loosely-coupled network of problem
solvers can work together to solve problems that are
beyond their individual capabilities. Each problem solving
node is capable of sophisticated problem solving and can
work independently, but the problems faced by the nodes
cannot be solved without cooperation.
44
Benevolent and Self-interested Agents
• Important to distinguish between
– Benevolent agents
• Share the same goal - our best interest is their best interest.
• No potential for conflicts
 Problem-solving in benevolent systems => CDPS
– Self-interested agents
• Agents will act to further their own interests, possibly at the expense of
others
• Potential for conflicts
 Self-interested agents => MAS
45
Success Criteria for a MAS
• 2 criteria to assess the success of a MAS:
– Coherence: How well the (multi-agent) system behaves as a unit.
• May be measured in terms of solution quality, resource usage, etc.
– Coordination: The degree to which agents can avoid extraneous
activity such as synchronisation and alignment of activities.
• Indicator – Conflicts between agents where agents
destructively interfere with one another.
46
Coordinated System
• In a perfectly coordinated system:
• Agents may not need to explicitly communicate,
they may be mutually predictable.
• May maintain good models of each other.
• Agents will not accidently hit each other’s subgoals
while trying to achieve a common goal.
47
Main issues in CDPS
• Problem decomposition for distribution
• Synthesis of sub-problem results to obtain the solution
• Optimisation of the problem-solving activities of the agents
• Techniques for the coordination of the agents’ activities
48
The 3 Stages of CDPS
1.
Problem
decomposition
Ref: Smith & Davis, 1980
2.
Subproblem
solution
3.
Answer
synthesis
49
Task and Result Sharing
• Task sharing:
Task 1
– when a problem is decomposed
into subproblems and allocated
Task 1.1
Task 1.2
Task 1.3
to different agents.
• Result sharing:
– When agents share information
A1
A2
A3
relevant to their subproblems.
50
Task Sharing
The Contract Net Protocol (CNET)
•
Negotiation can be used as a metaphor for Distributed
Problem Solving

If an agent cannot achieve an assigned task using local
resources/expertise, it will decompose the task into
subtasks and try to find other agents with the necessary
resources/expertise that are willing to perform the
subtasks.
Ref: Davis and Smith, 1988
51
Basic Notions of CNET
•
A decentralised market structure is assumed
•
Agents can take 2 roles:
–
Manager
–
Contractor
•
Basic mechanism:
–
Manager announces tasks
–
Potential contractors submit a bid
–
Manager evaluates the bids and awards subtask to the contractor
with the ”best” bid
52
CNET Description
I have a
problem!
manager
announcement
(b) Task Announcement
(a) Recognising the problem
manager
manager
bids
(c) Bidding
Potential
contrators
Award task
Potential
contrator
(d) Award Contract
53
About CNET
•
Suitable for domains that can be viewed in terms
of tasks
•
Disadvantages
–
Doesn’t detect conflicts
–
Assumes benevolent and non-antagonistic agents
–
Communication intensive
54
Next Lecture - Coordination
•
Curriculum:
–
Wooldridge: ”Introduction to MAS”,
•
–
•
Chapters 9
N. R. Jennings. ”Coordination Techniques for Distributed
Artificial Intelligence”, in: G. M. P. O'Hare, N. R. Jennings
(eds). Foundations of Distributed Artificial Intelligence, John
Wiley & Sons, 1996, pp. 187-210.
Recommended Reading (Not curriculum):
–
See http://www.idi.ntnu.no/~agent/curriculum/
•
Durfee, 1999
•
Nwana et. al., 1996
•
Davis and Smith, 1988
55