Lecture 7: Reaching Agreements

Chapter 15 BargainingNegotiation may involve:Exchange of informationRelaxation of initial goalsMutual concession

#Mechanisms, Protocols, StrategiesNegotiation is governed by a mechanism or a protocol:defines the rules of encounter between the agentsthe public rules by which the agents will come to agreements. The deals that can be madeThe sequence of offers and counter-offers that can be made#Negotiation is the process of reaching agreements on matters of common interest. It usually proceeds in a series of rounds, with every agent making a proposal at every round.

Negotiation MechanismIssues in negotiation process: Negotiation Space: All possible deals that agents can make, i.e., the set of candidate deals. Negotiation Set : deals that are pareto optimal and individually rational Negotiation Protocol: rules to determine the process: how/when a proposal can be made, when a deal has been struck, when the negotiation should be terminated, and so.Negotiation Strategy: When and what proposals should be made.Agreement Deal: rule to determine when a deal has been struck.

7-3Typical Goals of NegotiationEfficiency not waste utility. Pareto OptimalStability no agent have incentive to deviate from dominant strategySimplicity low computational demands on agentsDistribution no central decision makerSymmetry (possibly) may not want agents to play different roles.#Negotiation ProtocolWho beginsTake turnssingle or multiple issuesBuild off previous offersGive feed back (or not). Tell what utility is (or not)Obligations requirements for laterPrivacy (not share details of offers with others)Allowed proposals you can make as a result of negotiation historyprocess terminates (hopefully)

#Simple ModelThe rewards to be gained from negotiation are fixed and divided between the two partiesSuppose (x, 1-x) represents the portion of the utility each person gets.If the number of rounds are fixed, a person can propose (, 1-) on the last round. Theoretically, a person would rather have than nothing.Even in multiple rounds: If you knew that the other agent wouldnt offer you more than , it would be in your best interest to accept it. (So we have a pair of Nash Equilibrium strategies)#Impatient players shrinking pieDiscount factor of (a fraction in [0,1]) is applied to the utility.At time t, the value of slice x is txThe larger value of , the more patient the player is.Typically the players will have different values for , say 1 and 2if player 1 offers player 2, 2, he can do no better than accept it.

#The following offer could be accepted in the first time step (assuming agent 1 would make the first proposal): [ (1- 2)/(1-12), 2(1-1)/(1-12)]

Example: 1 =.8, 2 = .9 yields:(.36, .64) Example: 1 =.8, 2 = .8 yields:(.56, .44)

#Negotiation Process 1Negotiation usually proceeds in a series of rounds, with every agent making a proposal at every round.Communication during negotiation:ProposalCounter ProposalAgenti concedesAgentiAgentj#9The proposals that agents make are defined by their strategy; must be drawn from the negotiation set; and must be legal as defined by the protocol. If an agreement is reached as defined by the rule, then negotiation terminates.

Example: Agreeing on a price.If agenti is going a buy a book from agentj and agenti can only afford to pay a certain price, agenti will continue to negotiate on the price until the offer from agentj is a price that agenti can pay.Negotiation Process 2Another way of looking at the negotiation process is (can talk about 50/50 or 90/10 depending on who moves the farthest):Proposals by AjProposals by AiPoint ofAcceptance/aggreement#10The proposals that agents make are defined by their strategy; must be drawn from the negotiation set; and must be legal as defined by the protocol. If an agreement is reached as defined by the rule, then negotiation terminates.

Example: Agreeing on a price.If agenti is going a buy a book from agentj and agenti can only afford to pay a certain price, agenti will continue to negotiate on the price until the offer from agentj is a price that agenti can pay.Single issue negotiationLike moneySymmetric (If roles were reversed, I would benefit the same way you would) If one task requires less time, both would benefit equally by taking less timeutility for a task is experienced the same way by whomever is assigned to that task.Non-symmetric we would benefit differently if roles were reversednegotiate about who picks up an item, but you live closer to the store#Multiple Issue negotiationCould be hundreds of issues (cost, delivery date, size, quality)Some may be inter-related (as size goes down, cost goes down, quality goes up?)Not clear what a true concession is (larger may be cheaper, but harder to store or spoils before can be used)May not even be clear what is up for negotiation (I didnt realize having a bigger office was an option) (on the jobAsk for stock options, travel compensation, work from home, 4- day work week.)

#How many agents are involved?One to oneOne to many (auction is an example of one seller and many buyers)Many to many (could be divided into buyers and sellers, or all could be identical in role like officemate)n(n-1)/2 number of pairs#Jointly Improving Direction methodIterate overMediator helps players criticize a tentative agreement (could be status quo)Generates a compromise direction (where each of the k issues is a direction in k-space)Mediator helps players to find a jointly preferred outcome along the compromise direction, and then proposes a new tentative agreement.#Various DomainsTask Oriented DomainState Oriented DomainGet to a state we both agree toWorth Oriented Domain maximize value to allTypical Negotiation ProblemsTask-Oriented Domains(TOD): each agent has set of tasks that it has to achieve. The target of a negotiation is to minimize the cost of completing the tasks by divvying them up differently.State Oriented Domains(SOD): each agent is concerned with moving the world from an initial state into one of a set of goal states. The target of a negotiation is to achieve a common goal. Main attribute: actions have side effects (positive/negative). TOD is a subset of SOD. Agents can unintentionally achieve one anothers goals. Negative interactions can also occur. Utility = worth of goal cost to achieve itWorth Oriented Domains(WOD): agents assign a worth to each potential state (via a function), which captures its desirability for the agent. The target of a negotiation is to maximize mutual worth (rather than worth to individual). Superset of SOD. Rates the acceptability of final states. Allows agents to compromise on their goals.#Negotiation Domains:Task-orientedDomains in which an agents activity can be defined in terms of a set of tasks that it has to achieve, (Rosenschein & Zlotkin, 1994)An agent can carry out the tasks without interference (or help) from other agents such as who will deliver the mailAny agent can do any task.Tasks redistributed for the benefit of all agents

#17Types of dealsConflict deal: keep the same tasks as had originallyPure divide up tasksMixed we divide up the tasks, but we decide probabilistically who should do whatAll or Nothing (A/N) - Mixed deal, with added requirement that we only have all or nothing deals (one of the tasks sets is empty)#Examples of TOD Parcel Delivery: Several couriers have to deliver sets of parcels to different cities. The target of negotiation is to reallocate deliveries so that the cost of travel for each courier is minimal. Database Queries:Several agents have access to a common database, and each has to carry out a set of queries. The target of negotiation is to arrange queries so as to maximize efficiency of database operations (Join, Projection, Union, Intersection, ) . e.g., You are doing a join as part of another operation, so please save the results for me.#Consider tasks. 1 delivers to a. 2 delivers to both. Must return home. Cant find a deal where both win. Try mixed deal.Distribution Pointcity acity b33Cost function:c()=0c({a})=6c({b})=6c({a,b)}=8Utility for agent 1 (org {a}):Utility1({a}, {b}) = 0Utility1({b}, {a}) = 0Utility1({a, b}, ) = -2Utility1(, {a, b}) = 6Utility for agent 2 (org {ab}):Utility2({a}, {b}) = 2Utility2({b}, {a}) = 2Utility2({a, b}, ) = 8Utility2(, {a, b}) = 02#What mixed deals are possible if splitting utility is our goal?#Consider deal 3 with probability({},{ab}):p means agent 1 does {} with p probability and {ab} with (1-p) probability.What should p be - to be fair to both (equal utility)(1-p)(-2) + p6 = utility for agent 1(1-p)(8) + p0 = utility for agent 2(1-p)(-2) + p6= (1-p)(8) + p0 -2+2p+6p = 8-8p => p=10/16If agent 1 does no deliveries 10/16 of the time, it is fair.

Note how a mixed deal allows us to be fair.#22Incomplete InformationDont know tasks of others in TOD.SolutionExchange missing informationPenalty for liePossible liesFalse informationHiding letters (dont admit part of your job)Lie about letters (claim work that isnt required)decoy produce if neededphantom cant produce, caught in lieNot carry out a commitment (trust: misrepresent or unreliable)

#Difficult to think aboutSo many situationsSo many kinds of liesSo many kinds of deals

Approach divide into special cases so we can draw conclusions#Subadditive Task Oriented DomainCost of whole is cost of partsfor finite X,Y in T, c(X U Y)