Reaching Agreements I
Outline
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Motivation
Mechanism Design
Auctions
Negotiation
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Why is this important? (1)
• In societies of self-interested agents who
– communicate and
– cooperate
reaching agreements is an obvious problem…
• We daily interact with other agents
– Some of these are zero-sum encounters!
– The only way we profit is at the expense of our opponent
• The ability to reach agreements is a fundamental capability
of intelligent autonomous agents
• Agreements can be reached via
– Negotiation
– Argumentation
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Why is this important? (2)
• Negotiations: governed by mechanism (or protocol)
• Protocols define the “rules of encounter” between agents
– Different protocols offer different benefits/guarantees
– Protocol/mechanism design is very important!
• Given a protocol,
– Are there strategies agents can use to maximise the welfare of all
involved?
– Will agents have incentives to deviate from strategies that
maximise global welfare?
• This might be because the agent will get more!
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Mechanism design
• Protocols don’t happen by accident
– They must be designed!
• Protocols must be free of
– Deadlocks (everyone is waiting for everyone else)
– Livelocks (messages never stop being sent)
• Protocols ideally must have the following properties:
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Guaranteed success (agreement is eventually reached)
Maximising social welfare (i.e., all should benefit)
Paretto efficiency (no other outcome would be better)
Individual rationality (following the protocol is best for all)
Distribution (no single point of failure)
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Auctions (1)
• Internet made auctions part of people’s lives
– eBay and others
• Online auctions are very simple interactions
– Easy to automate them!
• Auctions involve
– A single auctioneer who is trying to sell a good
– A collection of bidders who are trying to get the good
• Goal of an auction is
– For the auctioneer to allocate the good to one of the bidders
• In traditional auctions
– Auctioneer wishes to maximise the price of good
– Bidders desire to minimise the price of the good
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Auctions (2)
Several factors affect protocol and strategy
• The goods auctioned
– Public/common value: a typical £10 note is worth £10
– Private value: £10 note autographed by your favourite artist
• Winner determination
– First-price auctions
– Second-price auctions
• Bids being known to all concerned
– Open cry auctions
– Sealed bid auctions
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English Auction
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First-price, open cry, ascending auctions
1. Auctioneer suggests reservation price for good
• If no-one bids more than the reservation price, the good is allocated to
the auctioneer for that amount
2. Bids are invited from bidders
• Bidders must bid more than the current highest bid
• All bidders can see bids being made
3. When no agent is willing to raise the bid, good is allocated to the
bidder that has made the current highest bid
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Dominant strategy:
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Bid a small amount higher than the current highest bid
Stop when bid reaches their current valuation
Winner’s curse:
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Whoever won, paid more than anyone else was prepared to
pay…
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Dutch Auction
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Open cry, descending auctions
1. Auctioneer offers good at high value
2. Auctioneer continually lowers offer price by some value
• This stops when a bidder makes a bid equal to current offer price
3. Good is allocated to the bidder that made offer
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No dominant strategy in general
Also susceptible to winner’s curse
Adequate for goods that must be sold quickly
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Flowers
Fish
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First-price sealed-bid auctions
• One-shot auctions
– The simplest of all auctions
• General mechanism
– A single round: bidders submit to auctioneer their bids
• There are no subsequent rounds
– Good awarded to bidder that made the highest bid
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Vickrey auctions
• One-shot, second-price, sealed-bid auctions
– A single negotiation round when bidders submit bids
• Bidders cannot see each other’s bids
– Good awarded to bidder with highest bid
• However, the winner does not pay what it bid!
• The winner pays the second highest bid…
• Dominant strategy:
• Not very popular:
– It’s not intuitive!
William S. Vickrey
– Bid truthfully
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Lies and collusions
• All auctions presented are vulnerable to collusion:
– Bidders agree beforehand on the price (very low)
– One of the bidders gets the good
– The colluders re-sell the good at higher value
• Lying can also be an issue in sealed-bid auctions
– Auctioneer in Vickrey auction may lie about 2nd highest bid
• Lying can also affect open-cry auctions, though:
– Auctioneer plants bogus bidders (shills) to inflate prices…
– Only affects English (ascending price) auctions
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Negotiation (1)
• Negotiation is the process of several agents reaching an
agreement
– Auctions are too simple a mechanism…
• Negotiations may include:
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Exchange of information,
Relaxation of initial goals,
Mutual concessions,
Lies or threats, etc.
• Agents’ goal: reach a consensus from an initial state of
conflict
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Negotiation (2)
• Negotiating settings will have:
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A negotiation set: space of possible proposals agents make
A protocol: legal proposals agents can make
A collection of strategies: which proposals agents will make
A rule to determine when a deal’s been struck
• Negotiations usually have series of rounds
– Agents make a proposal at every round
• Proposals
– Defined by the agent’s strategy
– Must be within the negotiation set
– Must be legal
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Negotiation Protocols (1)
• A negotiation protocol describes the rules of the game
• Characteristics of a good protocol:
– Efficiency — agreements must be such that no agent could derive
more from a different agreement without some other agent
deriving less from it (Pareto Optimality)
– Stability — no agent should have an incentive to deviate from the
protocol. Particularly important in open systems; i.e. systems
where new agents arrive/leave the community
– Simplicity — the protocol should minimise the computational
demands on the agents involved
– Distribution — the interaction rules shouldn’t require a central
decision maker
– Symmetry — no mechanism should treat agents differently
because of inappropriate criteria
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Negotiation Protocols (2)
• Ideal:
– Systems that produce beneficial social behaviour
– Robust to outside invasion
• E.g. the introduction of rogue agents.
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Xeroxing Articles (1)
• Two researchers want to Xerox chapters of books in a
library.
• There is a cost associated with borrowing a book, but once
borrowed any chapters can be Xeroxed.
• If they both want to copy chapters from the same book
only one need pay for borrowing the book.
• How do they decide which one pays for which book to be
borrowed?
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Xeroxing Articles (2)
• Consider this mechanism:
– Each of the researchers declare which books they need to borrow
from the library.
– Any book that only one researcher needs will not be part of the
agreement.
– Responsibility for borrowing the remaining books is decided upon
and these become the common set.
– Both agents have access to the common set of books once
borrowed.
– Let’s simplify the protocol further by using a fair coin to decide
who borrows which book.
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Xeroxing Articles (3)
• What is the best strategy for an agent to adopt?
– Should the agent declare extra books?
– Should fewer books than those required be declared?
– Is there any incentive for an agent to diverge from declaring his
true set of books?
• In this example, declaring the true set of books required is
the dominant strategy — but why?
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Xeroxing Articles (4)
• Why shouldn’t an agent hide a book?
– If it would have been in the common set, the researcher has lost
the opportunity to share the cost
– If it was declared, the researcher would have a 50% chance of not
paying for it; now it is 100%
• Why shouldn’t an agent declare a book that is not needed?
– If it appears in the common set, the researcher has a 50% chance
of having to pay for a book that is not required
– If it does not, there is neither harm nor benefit
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Xeroxing Articles (5)
• It is in the agent’s best interests to declare its true set of
books — the protocol is stable.
• N.B.: It is not the use of the fair coin that guarantees us
most of the desirable properties of the protocol.
– The use of the fair coin gives symmetry, but it guarantees neither
stability nor efficiency.
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Xeroxing Articles (6)
• Suppose agents can use borrowed books that are not in
the common set.
• If an agent can guess the books that the other requires, it
has the incentive to hide the fact that it needs books from
the common set.
• Then, the the set of common books is only a subset
(possibly empty) of the true set of common books.
• This will lead to inefficient solutions.
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Task-Oriented Domains
• We define the domain of negotiation in terms of tasks to
be distributed.
• A task domain is a triple
T, Ag, c 
where:
– T is the set of all possible tasks
– Ag = {A1, A 2,…, An} is the set of participating agents.
– c is a function c :(T ) + defining the cost of executing each
subset of tasks in T
The cost function must be:
• Monotonic: adding tasks never decreases the cost
• The cost of doing nothing is zero, that is c ({ }) = 0
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Encounters
• Sample task domain:
– Car pool with tasks of driving to a set of schools
• A specific encounter in this domain:
– The set of schools that I need to visit and the set of schools my
neighbour must visit.
• Formally:
An encounter within task domain T, Ag, c  is an ordered
list
T1,T 2,…,Tn 
where for all i, 1  i  n, i  Ag, and Ti  T
– Ti is the set of tasks for agent i.
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Example: Delivery Domain
• Agents have to deliver containers to warehouses
– Warehouses represented as weighted graph G = (V,E )
• Agents start from a central point and may exchange
containers at no cost prior to delivery.
• Task Set: all addresses (vertices V) in the graph
• Cost Function: cost of a set of addresses is
– Length of minimal path starting at the central point and
– Visiting all those addresses.
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A Negotiation Mechanism
• The space of possible deals:
– The set of all possible distribution of tasks that involves no
redundancy.
• The negotiation process:
– Given a set of deals…
what is the process that agents can use to converge to
agreement on a single deal?
• The negotiation strategy:
– Given a set of deals and a negotiation process…
what strategy should an individual agent adopt when
participating in the process?
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Deals
• Given an encounter T1,T 2 in a 2-agent task domain T,
{1,2}, c  a pure deal is the redistribution of tasks among
the agents.
• Formally:
a pure deal  is an ordered list D1,D 2 such that
D1  D2 =T1T 2
– Each agent k commits itself to executing all tasks in Dk, the cost
being c (Dk)
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Deals in the Delivery Domain
• Consider the delivery domain:
– Agents 1 and 2 have deliveries to warehouse a
– Agent 2 has a delivery to warehouse b
• Deals:
– {a},{b} — agent 1 delivers all containers to a and agent 2
delivers all to b
– {a,b},{} — agent 1 delivers all containers to warehouses a and
b
– {},{a,b} — agent 2 delivers all containers to a and b
– {a},{a,b} — agent 1 delivers containers to a while agent 2
delivers to a and b.
– {a,b},{b} — agent 1 delivers containers to a and b and agent 2
delivers to b.
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