Transcript Document

Agent Technology for e-Commerce
Chapter 9: Negotiation II
Maria Fasli
http://cswww.essex.ac.uk/staff/mfasli/ATe-Commerce.htm
Agent Technology for e-Commerce
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
Agreement
zone
£
Seller’s
surplus
Seller’s valuation:
wants to receive p
s
ps or more
Agreement price p*
Buyer wants to
decrease p*
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Buyer’s
surplus
pb
Buyer’s valuation:
wants to pay pb
or less
Seller wants to
increase p*
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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
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Axiomatic bargaining
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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):0oA  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)
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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
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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
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Strategic bargaining
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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
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
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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(-ri t)
The bargaining situation can be depicted as a sequential game
with subgames in extensive form
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Subgame 1
A
offer oA
B
reject
accept
B
Subgame 2
offer oB
A
[oA , (1-oA)]
accept
[A(1- oB), BoB]
reject
A
Subgame 3
offer oA
B
reject
B
accept
…
[AA oA, B B(1-oA)]
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
The basic alternating offers game has a subgame perfect Nash
equilibrium:
 Agent A gets (1- )/(1-   )
B
A B
 Agent B gets 1 minus (1- )/(1-   )
B
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
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The following strategies define the unique subgame perfect
equilibrium
Player A always offers
Player B always offers
and always accepts an offer
and always accepts an offer
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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 tT 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)
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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
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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
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Utility functions
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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<it<1.
Every agent i has a fixed discount rate it
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
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)
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Applications of the SNP
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
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Negotiation in different domains
Two broad categories:
 Task-oriented domains
 Worth-oriented domains
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Negotiation in task-oriented domains
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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
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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’
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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 T1T2
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
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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
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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
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A’s best deal
B’s best deal
Maximal loss from concession
Conflict deal
Maximal loss from conflict deal
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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
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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:
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
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
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Features of the Zeuthian strategy
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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
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Deception in TODs
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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
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Worth Oriented Domains
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Agents are interested in bringing about states that have the
greatest value
Agents’ goals can be achieved through joint plans
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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:
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It may be impossible for each of the agents to perform singleagent 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
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Coalitions
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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
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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
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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
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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
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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:
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
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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 LM such that:
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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
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Division of payoffs
Payoff division is important as it affects the stability of the coalition
Many coalition formation algorithms rely on game theory concepts
The Core
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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
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The Shapley value:
 Agent i is a dummy if vSi-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
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The Shapley value satisfies these conditions and sets the payoffs to
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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
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Customer coalitions
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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
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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
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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 nwholesaleMUR 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
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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 nwholesaleMURcoalition then the coalition can make a wholesale
purchase
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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
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Issues in coalition protocols
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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
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Coalition protocols
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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
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Post-negotiation protocol
1. LCS: L advertises the creation of a coalition with certain
parameters (deadline, maximum number etc.)
2. Each miM 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
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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
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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 miM 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
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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
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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
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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
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Social choice problems
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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?
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Social choice rule
A social choice setting:
 N: a set of agents (society)

: a set of feasible outcomes for the society

iN 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
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Conditions:
 A social preference ordering
should exist for all possible
inputs and should be complete and transitive over
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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
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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
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Binary protocols
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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:
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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
a
b, d, c, a
b
c
c
c
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b
b
d
d
d
c, a, b, d
c
c
a
d
c
c
c, a, d, b
a
a
b
a
b
a
a
a
b
b
d
d
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Plurality protocols
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All alternatives are compared simultaneously
The winner is the alternative with the highest number of votes
Such protocols are used in political elections
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Borda protocol
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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
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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
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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
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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
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Social welfare functions

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


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Welfare maximization
The social welfare maximization problem takes the form:
such that
Such a maximal welfare allocation is Pareto efficient
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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)
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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
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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
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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
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Abstract architecture
Proposal
history
Decision making
Query
component
Update
Knowledge base
component
Communication
component
Proposal
Negotiation history
Message
interpretation
Environment model
Message
generation
Argument
Self-model
Update
Opponent model
Proposal
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Message
Message
Response
Argument
evaluation
Argument
selector
Arguments
Argument
generator
Argumentation
component
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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
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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
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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


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And  can be proven from KB
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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

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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
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

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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
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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
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

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
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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(.)
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