Negotiation
Martin Beer,
School of Computing & Management
Sciences,
Sheffield Hallam University, Sheffield,
United Kingdom
m.beer@shu.ac.uk
Introduction
• Principles of Negotiation
– Game Theoretic Approaches
•
•
•
•
•
Evaluation Criteria
Voting
Auctions
General Equilibrium Markets
Contract Nets
– Heuristic-based Negotiation
– Argumentation-based Negotiation
Principles of Negotiation
• Negotiation = Interaction amongst
Agents based on communication for
the purpose of coming to an
agreement
• Distributed conflict resolution
• Decision Making
• Proposal
accepted, refined,
criticized or refuted
Principles of Negotiation
Coordination
Collectively
Motivated Agents
Common Goals
Coordination to achieve
Common goal
Distributed Search
through a space of
possible solutions
Self-interested Agents
Own Goals
Coordination for
Coherent Behaviour
Negotiation Includes
• A communication language
• A negotiation Protocol
• A decision Process by which an agent
decides upon its
– Position
– Concessions
– Criteria for agreement etc.
Negotiation Strategies
• Negotiation can take a number of
different forms
– Single or multi-party negotiation
– May include a single shot message by
each party or a conversation with several
messages going back and forth
Negotiation Techniques
• Game Theoretic Negotiation
– Evaluation Criteria
– Voting
Auctions
– General Equilibrium Market Mechanisms
– Contract Nets
• Heuristic-based Negotiation
• Argument-based negotiation
Game Theoretic Negotiation
• Evaluation Criteria
– Criteria to evaluate negotiation protocols among selfinterested agents
– Agents are supposed to behave rationally
– Rational behavior = an agent prefers a greater utility
(payoff) than a smaller one
– Payoff maximization
• Individual payoffs
• Group payoffs
• Social welfare
– Social Welfare
• The sum of agents’ utilities (payoffs) in a given solution
• Measures the global good of the agents
• Problem: How do we compare utilities?
Utility
• Utility is the means by which we
optimise the results of the negotiation
• Utility often equates to price, this may
not always be the case. It may be
– Speed of response
– “closeness”
– Some combination of functions etc.
• Any function that can be readily
computed can be used.
Pareto Efficiency
• A solution x
– i.e. a payoff vector p(x1, … xn) is Pareto
efficient (i.e. Pareto optimal) if there is no
other solution x’ such that at least one
agent is better off in x’ than in x and no
agent is worse off in x’ than in x.
• Measures global good
– Does not require utility comparison
• Social Welfare Pereto Efficiency
Individual Rationality (IR)
• IR of an agent participation = The
agent’s payoff in the negotiated solution
is no less than the payoff that the agent
would get by not participating in the
negotiation
• A mechanism is IR if the participation is
IR for all agents
Stability
•
A protocol is stable if once the agents arrived at a
solution they do not deviate from it
Dominant Strategy
–
The agent is best off using a specific strategy no matter
what strategies the other agents use
Nash Equilibrium
–
–
The strategy profile S*A = < S*1 …. S*n >
For each I, S*I is the agent’s best strategy given that the
other agents use strategies
< S*1 …. S*i-1 ,S*i+1 …. S*n >P
–
Problems
•
•
•
No Nash Equilibrium
Multiple Nash Equilibria
Guarantees stability only in the beginning of the game
Prisoners Dilemma
• Two prisoners are collectively charged with a
crime and held in separate cells, with no way
of meeting or communicating.
• They are told that:
– If one confesses and the other does not, the
confessor will be freed, and the other will be jailed
for three years
– If both confess, then each will be jailed for two
years
• Both prisoners know that if neither confesses,
then they will each be jailed for one year.
Prisoner’s Dilemma – Possible
Outcomes
Note – 4 is immediate
release
Player j
Cooperate Defect
Player i
Cooperate 4,4
1,4
Defect
3,3
4,1
Prisoner’s Dilemma – Strategic
Considerations
• The individual rational action is to defect
• This guarantees a payoff of at least 2 whereas
cooperating guarantees a payoff of at most 1
• Logic Says that this is not the best alternative – if
both cooperate the payoff is 3
• This is the fundamental problem with multi-agent
systems
• It appears to imply that cooperation will not occur with
self-interested agents
• Can we get over this?
Yes – by repeating the problem many times
Computational Efficiency
• To achieve perfect rationality
– The number of options to consider is too big
– Sometimes no algorithm finds the optimal solution
• Bounded Rationality
– Limits the time/computation for options
consideration
– Prunes the search space
– Imposes restrictions on the types of spaces
Voting
• Truthful Voters
– Rank feasible social outcomes based on agents’
individual ranking of those outcomes
– A – set of n agents
– O – set of m feasible outcomes
– Each agent has a preference relation
<I : O x O, asymmetric and transitive
• Social Choice Rule
– Input: the agent preference relations (<1, …. <n)
– Output: elements of O sorted according to the
input – gives the social preferences relation <*
Properties of the Social Choice
Rule
• A social preference ordering <* should exist for all
possible inputs (individual preferences)
• <* should be defined for every pair (o,o’) O
• <* should be asymmetric & transitive over O
• The outcomes should be Pareto efficient
If "I A, o<I o’ then o <* o’
• The scheme is independent of irrelevant alternatives
If "I A, < and <‘ satisfy o <I o’ and o <’I o’ then the social
ranking of o and o’ is the same in these two situations
• No agent should be a dictator in the sense that
o <I o’ implies o<* o’ for all preferences of the other agents
Arrow’s Impossibility Theorem
• No Social choice rule satisfies all of the six conditions
listed on the last slide
• Alternatives
– Binary Protocol
•
•
•
•
Alternatives are voted pair-wise
The chosen alternative depends on the agenda
That is the order of the pairings
This is the method used in parliamentary debates
– Borda Protocol
• Assigns an alternative |O| points for the highest preference, |O|
-1 points for the second and so on …..
• The counts are summed across the voters and the alternative
with the highest count becomes the social choice
• Winner turns loser and loser turns winner if the lowest ranked
alternative is removed
Auctions - Theory
• The auctioneer wants to sell an item at the highest possible
payment and the bidders want to acquire the item at the lowest
possible price
• A centralised protocol includes
– One auctioneer
– Several bidders
• The auctioneer introduces the item for sale, which can be a
combination of other items, or have multiple attributes
• Bidders make offers. This may be repeated for several times,
depending on the auction type
• The auctioneer determines the winner
• Auction Characteristics
–
–
–
–
Simple protocols
Centralised
Allows collusion “behind the scenes”
May favour auctioneer
Auction Settings
• Private Value Auctions
– The value to a bidder agent depends on its private
preferences
– Assumed to be known exactly
• Common Value Auctions
– The good’s value depends entirely on other
agents’ valuation
• Correlated Value Auctions
– The good’s value depends on internal and
external valuations
English (First-price Open Cry)
Auction
– Each bidder announces openly its bid
– When no bidder is willing to raise anyone, the auction ends
– The highest bidder wins the item at the price of the bid
• Strategy
– In private value auctions the dominant strategy is to always
bid a small amount more than the current highest bid and
stop when the private value is reached
– In correlated value auctions the bidder increases the price at
a constant rate or at a rate it thinks appropriate
First-Price Sealed-Bid Auction
• Each bidder submits one bid without knowing
the other’s bids
• The highest Bidder wins the item and pays
the amount of their bid
• Strategy
– No dominant strategy
– Bid less than its true valuation but it is dependant
on the other agents bids which are not known
Dutch (descending) Auction
• The auctioneer continuously lowers the
price until one of the bidders takes the
item at the current price
• Strategy
– Strategically equivalent to the first-price
sealed-bid auction
– Efficient for real time
Vickery (Second-Price Sealed Bid)
Auctions
• Each bidder submits one bid without
knowing the others’ bids
• The highest bidder wins but pays the
price of the second bid
• Strategy
– The bidder dominant strategy is to bid its
true valuation
All-Pay Auctions
• Each participating bidder has to pay the
amount of their bid (or some other
amount) to the auctioneer
Problems with Auction Protocols
• They are not collusion proof
• Lying Auctioneer
– Problem with Vickery Auction
– Problem with English Auction – use skills that bid in the
auction to increase bidders’ valuation of the item
– The auctioneer bids the highest second price to obtain its
reservation price – may lead to the auctioneer keeping the
item
– Common value auctions suffer from the winner’s curse:
agents should bid less than their valuation prices (as winning
the auction means its valuation is too high)
– Interrelated auctions – the bidder may lie about the value of
an item to get a combination of items at its valuation price
General Equilibrium Markets
• General Equilibrium Theory =A macroeconomic
theory
• A set of goods available at different prices
• Two types of agents – Consumers & Producers
• The producer’s profits are profits are divided among
the consumers according to predetermined
proportions that need not be equal
• The producers’ profits are divided among consumers
according the shares they ‘own’
• Prices may change and the agents may change their
consumption and production plans but
– Actual production and consumption only occur when the
market has reached a general equilibrium
Contract Nets
• General Equilibrium Market Mechanisms use
– Global prices
– A centralised mediator
• Drawbacks
–
–
–
–
Not all prices are global
Bottleneck of the mediator
Mediator – point of failure
Agents have no direct control over the agents to which they
send information
• Need a more distributed solution
• Task allocation via negotiation – Contract Net
– A kind of bridge between game theoretic negotiation and
heuristic-based one
– Formal model for making bids and awarding decisions
Contract Net
• Protocol
– The agents suggest contracts to each other and make their
accepting/rejecting decisions based on marginal cost
calculations
– The agent can take the roles of both Contractor and
Contractee
– It can also contract out tasks that it received earlier via
another contract
– The agents do not know the tasks and cost functions of other
agents
– Task allocation improves with each step - hill climbing in the
space of task allocations where the high-metric of the hill is
social welfare
– It is an anytime algorithm
• Contracting can be terminated anytime
• The worth of each agent’s solution increases monotonically 
Social Function increases monotonically
Contract Net
• Problem
– Task allocation stuck in a local equilibrium = no contract net
is individually rational and the task allocation is not globally
optimal
• Possible solution
– Different contract types
•
•
•
•
O – one task
C – cluster contracts
S – swap contracts
M – multi-agent contracts
– For each of the four contract types there exists task
allocations \for which there is an IR contract under one type
but no IR contracts under the other three types
– Under all four contract types there are initial task allocations
for which no IR sequence of contracts will lead to the optimal
solution (social welfare)
Contract Net
• Main differences as compared to game theoretic
negotiation
– An agent may reject an IR contract
– An agent may accept a non-IR contract
– The order of accepting IR contracts may lead to different pay
offs
– Each contract is made by evaluating just a single contract
instead of doing look ahead in the future
• Untruthful Agents
– An agent may lie about its marginal costs
– An agent may lie about what tasks it ahs
• Hide tasks
• Phantom tasks
• Decoy tasks
– Sometimes lying may be beneficial
Heuristic-based Negotiation
• Produce good rather than optimal solution
• Heuristic-based negotiation
– Computational approximations of game theoretic
techniques
– Informal negotiation models
• No central mediator
• Utterances are private between negotiating
agents
• The protocol does not prescribe an optimal
course of action
• Central concern: the agent’s decision making
heuristically during the course of negotiation
Argumentation-based Negotiation
• Arguments used to persuade the party to
accept a negotiation proposal
• Different types of agents
• Each Argument type defines preconditions for
its usage. If the preconditions are met, then
the agent may use the argument
• The agent needs a strategy to decide which
argument to use
• Most of the times assumes the BDI model
Argumentation-based Negotiation
• Strategies
– Appeal to past promise
– Promise a future reward
– Appeal to self interest
– Threat