Reaching Agreements-Multiagent Systems-Lecture Slides, Slides of Multiagent Systems

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LECTURE 7: Reaching Agreements 7-1 docsity.com Reaching Agreements • How do agents reaching agreements when they are self interested? • In an extreme case (zero sum encounter) no agreement is possible — but in most scenarios, there is potential for mutually beneficial agreement on matters of common interest • The capabilities of negotiation and argumentation are central to the ability of an agent to reach such agreements 7-2 docsity.com Auctions • An auction takes place between an agent known as the auctioneer and a collection of agents known as the bidders • The goal of the auction is for the auctioneer to allocate the good to one of the bidders • In most settings the auctioneer desires to maximize the price; bidders desire to minimize price 7-5 docsity.com Auction Parameters • Goods can have • private value • public/common value • correlated value • Winner determination may be • first price • second price • Bids may be • open cry • sealed bid • Bidding may be • one shot • ascending • descending 7-6 docsity.com English Auctions • Most commonly known type of auction: • first price • open cry • ascending • Dominant strategy is for agent to successively bid a small amount more than the current highest bid until it reaches their valuation, then withdraw • Susceptible to: • winner’s curse • shills 7-7 docsity.com Vickrey Auctions • Vickrey auctions are: • second-price • sealed-bid • Good is awarded to the agent that made the highest bid; at the price of the second highest bid • Bidding to your true valuation is dominant strategy in Vickrey auctions • Vickrey auctions susceptible to antisocial behavior 7-10 docsity.com Lies and Collusion • The various auction protocols are susceptible to lying on the part of the auctioneer, and collusion among bidders, to varying degrees • All four auctions (English, Dutch, First-Price Sealed Bid, Vickrey) can be manipulated by bidder collusion • A dishonest auctioneer can exploit the Vickrey auction by lying about the 2nd-highest bid • Shills can be introduced to inflate bidding prices in English auctions 7-11 docsity.com Negotiation • Auctions are only concerned with the allocation of goods: richer techniques for reaching agreements are required • Negotiation is the process of reaching agreements on matters of common interest • Any negotiation setting will have four components: • A negotiation set: possible proposals that agents can make • A protocol • Strategies, one for each agent, which are private • A rule that determines when a deal has been struck and what the agreement deal is • Negotiation usually proceeds in a series of rounds, with every agent making a proposal at every round 7-12 docsity.com Heterogeneous, Self-motivated Agents The systems: • are not centrally designed • do not have a notion of global utility • are dynamic (e.g., new types of agents) • will not act “benevolently” unless it is in their interest to do so 7-15 docsity.com The Aim of the Research • Social engineering for communities of machines • The creation of interaction environments that foster certain kinds of social behavior 7-16 The exploitation of game theory tools for high-level protocol design docsity.com Broad Working Assumption • Designers (from different companies, countries, etc.) come together to agree on standards for how their automated agents will interact (in a given domain) • Discuss various possibilities and their tradeoffs, and agree on protocols, strategies, and social laws to be implemented in their machines 7-17 docsity.com Phone Call Competition Example • Customer wishes to place long-distance call • Carriers simultaneously bid, sending proposed prices • Phone automatically chooses the carrier (dynamically) 7-20 AT&T MCI Sprint $0.20 $0.18 $0.23 docsity.com Best Bid Wins • Phone chooses carrier with lowest bid • Carrier gets amount that it bid 7-21 AT&T MCI Sprint $0.20 $0.18 $0.23 docsity.com Attributes of the Mechanism Distributed Symmetric  Stable  Simple  Efficient 7-22 AT&T MCI Sprint $0.20 $0.18 $0.23 Carriers have an incentive to invest effort in strategic behavior “Maybe I can bid as high as $0.21...” docsity.com Domain Theory • Task Oriented Domains  Agents have tasks to achieve  Task redistribution • State Oriented Domains  Goals specify acceptable final states  Side effects  Joint plan and schedules • Worth Oriented Domains  Function rating states’ acceptability  Joint plan, schedules, and goal relaxation 7-25 docsity.com Postmen Domain 7-26 Post Office a c d e / 2 1 / / / / TOD b f docsity.com Database Domain 7-27 Common Database “All female employees with more than three children.” 2 1 TOD “All female employees making over $50,000 a year.” docsity.com The Multi-Agent Tileworld 7-30 2 2 2 2 5 5 3 4 A B tile hole obstacle agents WOD docsity.com TODs Defined • A TOD is a triple <T, Ag, c> where • T is the (finite) set of all possible tasks • Ag = {1,…,n} is the set of participating agents • c = (T)  + defines the cost of executing each subset of tasks • An encounter is a collection of tasks <T1,…,Tn> where Ti  T for each i  Ag 7-31 docsity.com Building Blocks  Domain • A precise definition of what a goal is • Agent operations • Negotiation Protocol • A definition of a deal • A definition of utility • A definition of the conflict deal • Negotiation Strategy • In Equilibrium • Incentive-compatible 7-32 docsity.com The Negotiation Set Illustrated utility for agent deals on this line B from B to C are Pareto optimal, hence in the negotiation set utility of conflict A this circle delimits the deal for i E space of all possible deals conflict deal = utility for agent j utility of conflict deal for j docs Negotiation Protocols • Agents use a product-maximizing negotiation protocol (as in Nash bargaining theory) • It should be a symmetric PMM (product maximizing mechanism) • Examples: 1-step protocol, monotonic concession protocol… 7-36 docsity.com The Monotonic Concession Protocol Rules of this protocol are as follows… • 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 is at least as good or better than its proposal • 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 it proposed at time u • If neither agent makes a concession in some round u > 0, then negotiation terminates, with the conflict deal 7-37 docsity.com Nash Equilibrium Again… • The Zeuthen strategy is in Nash equilibrium: under the assumption that one agent is using the strategy the other can do no better than use it himself… • This is of particular interest to the designer of automated agents. It does away with any need for secrecy on the part of the programmer. An agent’s strategy can be publicly known, and no other agent designer can exploit the information by choosing a different strategy. In fact, it is desirable that the strategy be known, to avoid inadvertent conflicts. 7-40 docsity.com Building Blocks  Domain • A precise definition of what a goal is • Agent operations  Negotiation Protocol • A definition of a deal • A definition of utility • A definition of the conflict deal • Negotiation Strategy • In Equilibrium • Incentive-compatible 7-41 docsity.com Deception in TODs • Deception can benefit agents in two ways: • Phantom and Decoy tasks Pretending that you have been allocated tasks you have not • Hidden tasks Pretending not to have been allocated tasks that you have been 7-42 docsity.com Hiding Letters 7-45 They then agree that agent 2 delivers to f and e (hidden) a c b h f d g e Post Office / / / (1) 1 2 e b 2 1 f docsity.com Another Possibility for Deception They will agree to flip a coin to decide who goes to b and who goes to c 7-46 a c b Post Office / / b, c 2 1 b, c 1, 2 1, 2 docsity.com Phantom Letter They agree that agent 1 goes to c 7-47 b, c, d Post Office 2 1 b, c a c b / / 1, 2 1, 2 d / 1 (phantom) docsity.com Phantom Letters with Mixed Deals They will agree on the mixed deal where A has 3/4 chance of delivering all letters, lowering his expected utility 7-50 a c b b, c, d Post Office 2 / 1 / b, c 1, 2 1, 2 d / 1 (phantom) docsity.com Sub-Additive TODs TOD < T, Ag, c > is sub-additive if for all finite sets of tasks X, Y in T we have: c(X  Y)  c(X) + c(Y) 7-51 docsity.com Sub-Additivity 7-52 c(X  Y)  c(X) + c(Y) X Y docsity.com Incentive Compatible Mechanisms 7-55 Sub-Additive a c b / / 1, 2 1, 2 d / (phantom) 1 (hidden) a c b h f d g e / / / (1) 1 2 Theorem: For all encounters in all sub-additive TODs, when using a PMM over all-or-nothing deals, no agent has an incentive to hide a task. Hidden Pure L L A/N T T/P Mix L T/P Phantom docsity.com Incentive Compatible Mechanisms • Explanation of the up-arrow: If it is never beneficial in a mixed deal encounter to use a phantom lie (with penalties), then it is certainly never beneficial to do so in an all-or-nothing mixed deal encounter (which is just a subset of the mixed deal encounters) 7-56 Hidden Pure L L A/N T T/P Mix L T/P Phantom docsity.com Decoy Tasks 7-57 Sub-Additive Hidden Pure L L A/N T T/P Mix L T/P Phantom L L L Decoy Decoy tasks, however, can be beneficial even with all-or-nothing deals / / / / / / 1 1 1 1 2 2 1 Decoy lies are simply phantom lies where the agent is able to manufacture the task (if necessary) to avoid discovery of the lie by the other agent. docsity.com Concave TODs TOD < T, Ag, c > is concave if for all finite sets of tasks Y and Z in T , and X  Y, we have: c(Y  Z) – c(Y)  c(X  Z) – c(X) 7-60 Concavity implies sub-additivity docsity.com Concavity The cost Z adds to X is more than the cost it adds to Y. (Z - X is a superset of Z - Y) 7-61 X Y Z docsity.com Concave TODs The Database Domain and Fax Domain are concave (not the Postmen Domain, unless restricted to trees). 7-62 / / / / / / 1 1 1 1 2 2 1 X Z This example was not concave; Z adds 0 to X, but adds 2 to its superset Y (all blue nodes) docsity.com Modularity c(X  Y) = c(X) + c(Y) – c(X  Y) 7-65 X Y docsity.com Modular TODs The Fax Domain is modular (not the Database Domain nor the Postmen Domain, unless restricted to a star topology). 7-66 Even in modular TODs, hiding tasks can be beneficial in general mixed deals docsity.com Three-Dimensional Incentive Compatible Mechanism Table 7-67 Sub-Additive Pure A/N Mix Concave Pure A/N Mix H L L T T L T P L T T D H L L T T/P L T/P P L L L D Modular Pure A/N Mix H L T T T L T P T T T D docsity.com Conclusions • To maintain efficiency over time of dynamic multi-agent systems, the rules must also be stable • The use of formal tools enables the design of efficient and stable mechanisms, and the precise characterization of their properties 7-70 Stability Formal Tools docsity.com Argumentation • Argumentation is the process of attempting to convince others of something • Gilbert (1994) identified 4 modes of argument: 1. Logical mode “If you accept that A and that A implies B, then you must accept that B” 2. Emotional mode “How would you feel if it happened to you?” 3. Visceral mode “Cretin!” 4. Kisceral mode “This is against Christian teaching!” 7-71 docsity.com Logic-based Argumentation Basic form of logical arguments is as follows: Database | (Sentence, Grounds) where: • Database is a (possibly inconsistent) set of logical formulae • Sentence is a logical formula known as the conclusion • Grounds is a set of logical formulae such that: 1. Grounds f Database; and 2. Sentence can be proved from Grounds 7-72 docsity.com