Reaching Agreements I. 2 Outline Motivation Mechanism Design Auctions Negotiation

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<ul><li>Slide 1</li></ul> <p>Reaching Agreements I Slide 2 2 Outline Motivation Mechanism Design Auctions Negotiation Slide 3 3 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 Slide 4 4 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! Slide 5 5 Mechanism design Protocols dont 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: 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) Slide 6 6 Auctions (1) Internet made auctions part of peoples 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 Slide 7 7 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 Slide 8 8 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 Dominant strategy: Bid a small amount higher than the current highest bid Stop when bid reaches their current valuation Winners curse: Whoever won, paid more than anyone else was prepared to pay English Auction Slide 9 9 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 No dominant strategy in general Also susceptible to winners curse Adequate for goods that must be sold quickly Flowers Fish Dutch Auction Slide 10 10 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 Slide 11 11 Vickrey auctions One-shot, second-price, sealed-bid auctions A single negotiation round when bidders submit bids Bidders cannot see each others 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: Bid truthfully Not very popular: Its not intuitive! William S. Vickrey Slide 12 12 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 2 nd highest bid Lying can also affect open-cry auctions, though: Auctioneer plants bogus bidders (shills) to inflate prices Only affects English (ascending price) auctions Slide 13 13 Negotiation (1) Negotiation is the process of several agents reaching an agreement Auctions are too simple a mechanism Negotiations may include: Exchange of information, Relaxation of initial goals, Mutual concessions, Lies or threats, etc. Agents goal: reach a consensus from an initial state of conflict Slide 14 14 Negotiation (2) Negotiating settings will have: 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 deals been struck Negotiations usually have series of rounds Agents make a proposal at every round Proposals Defined by the agents strategy Must be within the negotiation set Must be legal Slide 15 15 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 shouldnt require a central decision maker Symmetry no mechanism should treat agents differently because of inappropriate criteria Slide 16 16 Negotiation Protocols (2) Ideal: Systems that produce beneficial social behaviour Robust to outside invasion E.g. the introduction of rogue agents. Slide 17 17 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? Slide 18 18 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. Lets simplify the protocol further by using a fair coin to decide who borrows which book. Slide 19 19 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? Slide 20 20 Xeroxing Articles (4) Why shouldnt 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 shouldnt 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 Slide 21 21 Xeroxing Articles (5) It is in the agents 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. Slide 22 22 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. Slide 23 23 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 = {A 1, A 2,, A n } 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 Slide 24 24 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 T 1, T 2,, T n where for all i, 1 i n, i Ag, and T i T T i is the set of tasks for agent i. Slide 25 25 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. Slide 26 26 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? Slide 27 27 Deals Given an encounter T 1,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 D 1,D 2 such that D 1 D 2 =T 1 T 2 Each agent k commits itself to executing all tasks in D k, the cost being c (D k ) Slide 28 28 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. </p>

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