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Reaching Agreements: Reaching Agreements: NegotiationNegotiation

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Typical Competition Mechanisms

Auction: allocate goods or tasks to agents through market. Need a richer technique for reaching agreements

Negotiation: reach agreements through interaction.

Argumentation: resolve confliction through debates.

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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 Mechanism

Issues in negotiation process:• Negotiation Space: All possible deals that agents can make, i.e., t

he set of candidate deals. • Negotiation Protocol: – A rule that determines the process of a ne

gotiation: how and 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.

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Protocol

Means kinds of deals that can be made

Means sequence of offers and counter-offers

Protocol is like rules of chess game, whereas strategy is way in which player decides which move to make

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Game Theory

Computers make concrete the notion of strategy which is central to game playing

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Mechanisms Design

Mechanism design is the design of protocols for governing multi-agent

interactions.

Desirable properties of mechanisms are:

– Convergence/guaranteed success

– Maximising global welfare: sum of agent benefits are maximized

– Pareto efficiency

– Individual rationality

– Stability: no agent should have incentive to deviate from strategy

– Simplicity: low computational demands, little communication

– Distribution: no central decision maker

– Symmetry: not wwant agents to play different roles

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Attributes not universally accepted

Sometimes be tradeoffs – efficiency and stability and sometimes in conflict with each other

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Protocols

What is an elevator protocol?– Direction you face– How close to another do you stand– Are you allowed to talk to a stranger?– Where you stand (not in front of buttons, near

back)– What to do if person is running for elevator

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Negotiation Protocol

Who begins

Take turns

Build off previous offers

Obligations

Privacy

Legal proposals you can make as a result of negotiation history

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Negotiation Process 1

Negotiation usually proceeds in a series of rounds,

with every agent making a proposal at every round.

Communication during negotiation:

Proposal

Counter Proposal

Agenti concedes

Agenti Agentj

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Negotiation Process 2

Another way of looking at the negotiation

process is:

Proposals by AjProposals by AiPoint of

Acceptance/aggreement

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Typical Negotiation ProblemsTask-Oriented Domains(TOD): Domains in which an agent's activity can be defined in terms of a set of tasks that it has to achieve. The target of a negotiation is to minimize the cost of completing the tasks.

State Oriented Domains(SOD): Domains where 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)

Worth Oriented Domains(WOD): Domains where agents assign a worth to each potential state, which captures its desirability for the agent. The target of a negotiation is to maximize mutual worth.

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Single issue negotiation

Like money

Symmetric (what is more for you is less for me, both benefit equally if roles reversed) – If you get more money, I get less– If you travel less than I do, I would benefit by

switching routes with you

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Multiple Issue negotiation

Could 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 didn’t realize not having any test was an option)

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How many agents are involved?

One to one

One 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 equal)– n(n-1)/2 number of pairs

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Negotiation Domains:Task-oriented

”Domains in which an agent’s 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 from

other agents

» All resources are available to the agent

» Tasks redistributed for the benefit of all agents

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Formalization of TOD

A Task Oriented Domain(TOD) is a triple <T, Ag, c>

where:– T is a finite set of all possible tasks;

– Ag={A1, A2,…, An} is a list of participant agents;– c:(T)R+ defines cost of executing each subset of tasks.

Assumptions on cost function:1. c() = 0.2. The cost of a subset of tasks does not depend on who carries out

them. (Idealized situation)3. Cost function is monotonic, which means that more tasks, more

cost. (It can’t cost less to take on more tasks.) i. T1 T2 implies c(T1) c(T2)

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Redistribution of TasksGiven a TOD <T, {A1,A2}, c>,

An encounter (instance) within the TOD is an ordered list (T1, T2) such that for all k, Tk T. This is an original allocation of tasks that they might want to reallocate.

A pure deal on an encounter is the redistribution of tasks among agents: (D1, D2), such that

D1 D2= T1 T2

Specifically, (T1, T2) is called the conflict deal.

For each deal =(D1, D2), the cost of such a deal to agent k is Costk()=c(Dk)

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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 to 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, …) .

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Possible DealsConsider an encounter from the Parcel Delivery Domain. Suppose we have two agents. Both agents have parcels to deliver to city a and only agent 2 has parcels to deliver to city b. There are nine distinct pure deals in this encounter:

1. ({a}, {b})

2. ({b}, {a})

3. ({a,b}, )

4. (, {a,b})

5. ({a}, {a,b})

6. ({b}, {a,b})

7. ({a,b}, {a})

8. ({a,b}, {b})

9. ({a,b}, {a,b})

the conflict deal

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Utility Function for AgentsGiven an encounter (T1, T2), the utility function for each agent is defined as follow:

Utilityk()=c(Tk)-Costk()

where =(D1, D2) is a deal;

– c(Tk) is the stand-alone cost to agent k (the cost of achieving its goal with no help)

– Costk() is the cost of its part of the deal.

Note that the utility of the conflict deal is always 0.

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Parcel Delivery Domain (cont)Distribution Point

city a city b

1 1

Cost function:c()=0c({a})=1c({b})=1c({a,b)}=3

Utility for agent 1:

1. Utility1({a}, {b}) = 0

2. Utility1({b}, {a}) = 0

3. Utility1({a, b}, ) = -2

4. Utility1(, {a, b}) = 1

…

Utility for agent 2:

1. Utility2({a}, {b}) = 2

2. Utility2({b}, {a}) = 2

3. Utility2({a, b}, ) = 3

4. Utility2(, {a, b}) = 0

…

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Dominant DealsDeal dominates deal ' if is better for at least one agent and not worse for the other, i.e., is at least as good for every agent as ':

k{1,2}, Utilityk() Utilityk(')

is better for some agent than ':

k{1,2}, Utilityk()> Utilityk(')

Deal weakly dominates deal ' if at least the first condition holds.

Any reasonable agent would prefer (or go along with) over ' if

dominates or weakly dominates '.

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Negotiation Set: Space of Negotiation

A deal is called individual rational if weakly dominates the conflict deal. (no worse than what you have already)

A deal is called Pareto optimal if there does not exit another deal ' that dominates . (best deal for x without disadvantaging y)

The set of all deals that are individual rational and Pareto optimal is called the negotiation set (NS).

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Utility Function for Agents1. Utility1({a}, {b}) =0

2. Utility1({b}, {a})=0

3. Utility1({a,b}, )=-2

4. Utility1(, {a,b})=1

5. Utility1({a}, {a,b})=0

6. Utility1({b}, {a,b})=0

7. Utility1({a,b}, {a})=-2

8. Utility1({a,b}, {b})=-2

9. Utility1({a,b}, {a,b})=-2

1.Utility2({a}, {b}) =2

2.Utility2 ({b}, {a})=2

3.Utility2 ({a,b}, )=3

4.Utility2 (, {a,b})=0

5.Utility2 ({a}, {a,b})=0

6.Utility2 ({b}, {a,b})=0

7.Utility2 ({a,b}, {a})=2

8.Utility2 ({a,b}, {b})=2

9.Utility2 ({a,b}, {a,b})=0

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Individual Deals1. ({a}, {b})

2. ({b}, {a})

3. ({a,b}, )

4. (, {a,b})

5. ({a}, {a,b})

6. ({b}, {a,b})

7. ({a,b}, {a})

8. ({a,b}, {b})

9. ({a,b}, {a,b})

individualrational

({a}, {b})

({b}, {a})

(, {a,b})

({a}, {a,b})

({b}, {a,b})

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Pareto Optimal Deals1. ({a}, {b})

2. ({b}, {a})

3. ({a,b}, )

4. (, {a,b})

5. ({a}, {a,b})

6. ({b}, {a,b})

7. ({a,b}, {a})

8. ({a,b}, {b})

9. ({a,b}, {a,b})

ParetoOptimal

({a}, {b})

({b}, {a})

({a,b}, )

(, {a,b})

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Negotiation Set

Negotiation Set

({a}, {b})

({b}, {a})

(, {a,b})

Individual Rational Deals

({a}, {b})

({b}, {a})

(, {a,b})

({a}, {a,b})

({b}, {a,b})

Pareto Optimal Deals

({a}, {b})

({b}, {a})

({a,b}, )

(, {a,b})

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Negotiation Set illustrated

Create a scatter plot of the utility for i over the utility for j

Only those where both is positive are individually rational (for both) (origin is conflict deal)

Which are pareto optimal?

Utility for i

Utility for j

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Negotiation Set in Task-oriented Domains

AC

B

D

E

Utility for agent i

Utility for agent j

Utility of conflict Deal for agent i

Utility of conflict Deal for agent j

Conflict deal

The circle delimits the space of all possible deals

Negotiation set:

(pareto optimal+

Individual rational)

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The Monotonic Concession ProtocolRules of this protocol are as follows. . .

Negotiation proceeds in rounds.

On round 1, agents simultaneously propose a deal from the negotiation set. (can re-propose same one)

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.

An agent is not allowed to offer the other agent less (in term of utility ) than it did in the previous round. It can either stand still or make a concession. Assumes we know what the other agent values.

If neither agent makes a concession in some round, then negotiation terminates, with the conflict deal.

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Condition to Consent an Agreement

If one of the agents finds that the deal proposed by the other is at least as good or better than the proposal it made.

Utility1(2) Utility1(1)and

Utility2(1) Utility2(2)

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The Monotonic Concession Protocol

Advantages:

– Symmetrically distributed (no agent plays a special role)

– Ensures convergence

– It will not go on indefinitely

Disadvantages:

– Agents can run into conflicts

– Inefficient – no quarantee that an agreement will be reached

quickly

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Negotiation Strategy

Given the negotiation space and the Monotonic Concession Protocol, a strategy of negotiation is an answer to the following questions:

What should an agent’s first proposal be?

On any given round, who should concede?

If an agent concedes, then how much should it concede?

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The Zeuthen Strategy

Q: What should my first proposal be?

A: the best deal for you among all possible deals in the negotiation set. (Is a way of telling others what you value.)

Agent 1's best deal agent 2's best deal

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The Zeuthen StrategyQ: Do I need to make a concession in this round?

A: If you are not willing to risk a conflict, you should make a concession.

How much am I willing to risk a

conflict?

Agent 1's best deal agent 2's best deal

How much am I willing to risk a

conflict?

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Willingness to Risk Conflict

Suppose you have conceded a lot. Then:

– You have lost your expected utility (closer to zero).

– In case conflict occurs, you are not much worse off.

– You are more willing to risk conflict.

An agent will be more willing to risk conflict if the difference in utility between your loss in making an concession and your loss in taking a conflict deal with respect to your current offer.

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Risk Evaluation

riski= utility agent i loses by conceding and accepting agent j's offer

utility agent 1 loses by not conceding and causing a conflict

You have to calculate?• How much you will lose if you make a concession and

accept your opponent's offer?• How much you will lose if you stand still which causes a

conflict?

=Utilityi (i )-Utilityi (j )

Utilityi (i )

where i and i are the current offer of agent i and j, respectively.

Thus, riski is willingness to risk conflict (1 is perfectly willing to risk)

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The Risk Factor

One way to think about which agent should concede is

to consider how much each has to loose by running into

conflict at that point.

Ai best deal Aj best deal

Conflict deal

How much am I willing to risk a conflict?

Maximum loss from conflict

Maximum loss from concession

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The Zeuthen Strategy

Q: If I concedes, then how much should I concede?

A: Just enough to change the balance of risk. (Otherwise, it will just be your turn to concede again at the next round)

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About MCP and Zeuthen Strategies

Advantages:

– Simple and reflects the way human negotiations work.

– Stability – in Nash equilibrium – if one agent is using the strategy, then

the other can do no better than using it him/herself.

Disadvantages:

– Computationally expensive – players need to compute the entire

negotiation set.

– Communication burden – negotiation process may involve several

steps.

42Parcel Delivery Domain: recall, agent 1 delivered to a, agent 2 delivered to both a and b

Negotiation Set

({a}, {b})

({b}, {a})

(, {a,b})

First offer

(, {a,b})

({a}, {b})

Agent 1

Agent 2

Utility of agent 1

Utility1({a}, {b}) = 0

Utility1({b}, {a}) = 0

Utility1(, {a,b})=1

Utility of agent 2

Utility2({a}, {b}) =2

Utility2({b}, {a}) = 2

Utility2(, {a,b})=0

Risk of conflict

1

1

Can they reach an agreement?Who will concede?

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Conflict Deal

He should concede.

Agent 1's best deal agent 2's best deal

He should concede.

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Parcel Delivery Domain: Example 2

Distribution Point

a d

7 7

Cost function:c()=0c({a})=c({d})=7c({b})=c({c})=c({a,b})=c({c,d})=8c({b,c})=c({a,b,c})=c({b,c,d})=9c({a,d})=c({a,b,d})=c({a,c,d})=c({a,b,c,d})=10

b c1 1 1

Negotiation Set: ({a,b,c,d}, ) ({a,b,c), {d}) ({a,b}, {c,d}) ({a}, {b,c,d}) (, {a,b,c,d})

Conflict Deal: ({a,b,c,d}, {a,b,c,d})

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Parcel Delivery Domain: Example 2

No Pure Deal Agent 1's Utility Agent 2's Utility

1 ({a,b,c,d}, ) 0 10

2 ({a,b,c), {d}) 1 3

3 ({a,b}, {c,d}) 2 2

4 ({a}, {b,c,d}) 3 1

5 (, {a,b,c,d}) 10 0

Conflict deal 0 0

agent 1 agent 25 4 3 2 1

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Nash Equilibrium

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.

Generally Nash equilibrium is not applicable in negotiation setting because it requires both sides utility function.

It 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.

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Task Oriented Domain

Non-conflicting jobs

Negotiation : Redistribute tasks to everyone’s mutual benefit

Example - Postmen domain

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State Oriented Domain

Goals are acceptable final states (superset of TOD)

Have side effects - agent doing one action might hinder or help another agent. Example, on(white,gray) has side effect of clear(black).

Negotiation : develop joint plans and schedules for the agents, to help and not hinder other agents

Example – Slotted blocks world -blocks cannot go anywhere on table – only in slots (restricted resource)

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Joint plan is used to mean “what they both do” not “what they do together” – just the joining of plans. There is no joint goal!The actions taken by agent k in the joint plan are called k’s role and is written as Jk

C(J)k is the cost of k’s role in joint plan J.In TOD, you cannot do another’s task or get in their way. In TOD, coordinated plans are never worse, as you can just do your original task.With SOD, you may get in each other’s wayDon’t accept partially completed plans.

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Assumptions of SOD1. Agents will maximize expected utility (will prefer 51%

chance of getting $100 than a sure $50)2. Agent cannot commit himself (as part of current

negotiation) to behavior in future negotiation.3. Interagent comparison of utility: common utility units4. Symmetric abilities (all can perform tasks, and cost is

same regardless of agent performing)5. Binding commitments6. No explicit utility transfer (no “money” that can be used

to compensate one agent for a disadvantageous agreement)

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Achievement of Final State

Goal of each agent is represented as a set of states that they would be happy with.Looking for a state in intersection of goalsPossibilities:– Both can be achieved, at gain to both– Goals may contradict, so no mutually acceptable state– Can find common state, but perhaps it cannot be

reached with the primitive operations in the domain– Might be a reachable state which satisfies both, but

may be too expensive – unwilling to expend effort.

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Example

Suppose there are two states that satisfy both agents.

State 1: There are two roles: one has a cost of 6 for one agent and 2 for the other.

State 2: Two roles, but both cost 5.

State 1 is cheaper (overall), but state 2 is more equal. How handle?

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Mixed joint plans

Instead of picking the plan that is unfair to one agent (but better overall), use a lottery.

Assign a probability that one would get a certain plan.

Called a mixed joint plan – plan with probability. Expected utility is the same for both (as their costs/benefits are symmetric)

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Cost

If = (J:p) is a deal, then

costi() = p*c(J)i + (1-p)*c(J)k where k is i’s opponent -the role i plays with (1-p) probabilityUtility is simply difference between cost of achieving goal alone and expected utility of joint planA symmetric mechanism that is in equilibrium if no one is motivated to change strategies. We choose to use one which maximizes the product of utilities (as is a fairer division). Try dividing a utility of 10 various ways to see when product is maximized.

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Examples: Cooperative

Slotted blocks world: initially white block is at 1 and black block at 2. Agent 1 wants black in 1. Agent 2 wants white in 2. (Both goals are compatible.)Assume pick up is cost 1 and set down is one.Mutually beneficial – each can pick up at the same time, costing each 2 – Win – as didn’t have to move other block out of the way!If done by one, cost would be four – so utility to each is 2.

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Examples: Compromise

Slotted blocks world: initially white block is at 1 and black block at 2, two gray blocks at 3. Agent 1 wants black in 1, but not on table. Agent 2 wants white in 2, but not directly on table.

Alone, agent 1 could just pick up black and place on white. Similarly, for agent 2.

But together, all blocks must be picked up and put down. Best plan: one agent picks up black, while other agent rearranges (cost 6 for one, 2 for other)

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Compromise, continued

Who should get to do the easier role?Look at worth. If A1 assigns worth of 3 and A2 assigns worth of 6, we could use probability to make it “fair”. Assign A1to cost-2 task 7/8 of the time.Then expected utility for A1 = 7/8*2+1/8(6) = 5/2 (which is less than worth)Assign A2 to cost-2 task 1/8 of timeExpected utility for A2 =7/8*6+1/8*2 = 11/2 (which is less than worth)Note we have split the utility, each ½ under worth, but person who valued it more, did more work. Lying?

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Example: conflictI want black on white (in slot 1)You want white on black (in slot 1)Can’t both win. Could flip a coin to decide who wins. Better than both losing. Weightings on coin needn’t be 50-50.May make sense to have person with highest worth get his way – as utility is greater. (Would accomplish his goal alone) Efficient but not fair?What if we could transfer half of the gained utility to the other agent?For more complicated goals, could also work together to accomplish joint part of goal, and then flip coin for rest. (so loser would have negative utility)

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Example:semi-cooperative

Both agents want contents of slots 16 and 17 swapped.Both have different goals for other slots – but they could BOTH be achieved (at greater expense to both)Do accomplish one Agent’s goal by oneself is 26: 8 for each swap and 10 for rest.Cooperative swap is 4.Idea, work together to swap, and then flip coin to see who gets his way for rest.

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Example: semi-cooperative, cont

Winning agent: utility: 26-4-10 = 12Losing agent: utility: -4So with ½ probability: 12*1/2 -4*1/2 = 4If they would have both been satisfied, assume cost for each is 24. Then utility is 2.Note, they double their utility, if they are willing to risk not achieving the goal.Note, kept just the joint part of the plan that was more efficient, and gambled on the rest (to remove the need to satisfy the other)

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Worth Oriented Domain

Rates the acceptability of final states

Allows partially completed goals

Negotiation : a joint plan, schedules, and goal relaxation. May reach a state that might be a little worse that the ultimate objective

Example – Multi-agent Tile world (like airport shuttle) – isn’t just a specific state, but the value of work accomplished

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Domain Definitions

Graph (City Map) G = G(V,E)– v V => nodes (address / Post office)– e => edges (roads)

Weight function (Distance of road)– W : EIN

Letters for agent A : LA

Agent Li : I – Letters (LA LB) =

Cost(L) IN => weight of minimum weight cycle that starts at PO and visits all vertices of L and ends at PO

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Negotiation Protocol() – Product of the two agent utilities from product maximizing negotiation protocol One step protocol

– Concession protocol

At t >= 0, A offers (A,t) and B offers (B,t), such that– Both deals are from the negotiation set i andt >0, Utilityi((i,t)) <= Utilityi((i,t-1)) – (I am making concessions, so my utility is going down)

Negotiation ending– Conflict – no one will change offer –for all i, Utilityi((i,t)) = Utilityi((i,t-1))– Agreement, j !=i Utilityj((i,t)) >= Utilityj((j,t))

» Only A => agree (B,t)» Only B => agree (A,t)» Both A,B => agree (k,t) such that ((k))=max{((A)),((B))} of those that both accept, pick one with higher product» Both A,B and ((A))=((B)) => flip a coin

Pure deals

Mixeddeal

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Mixed deal

Element of probability – Agents will perform (DA,DB) with probability p or (DB,DA) with probability 1-pCosti([(DA,DB):p]) = pCost(Di) + (1-p)Cost(Dj)

(an expected cost)Utilityi([:p]) = Cost(Li) – Costi([:p])

(cost of doing it alone minus expected cost of mixed deal)All or nothing deal – 0<=p<=1 such that – mixed deal m = [({LA,LB}, ):p] NS (m) = maxNS(d)

Mixed deal makes the solution space of deals continuous, rather than discrete as it was before

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Hidden lettersUtility (figured as if b didn’t exist)– May decide to have A2 deliver both, it doesn’t cost him anything,

but there is no benefit to him either. Doesn’t seem fair. But if we saw b, we might decide to have A1 do both (as on his way).

– Pure deal (one person delivers all) – expected cost=[(,] = 4

– Mixed deal – expected cost= [(,] = 3 for A1, 5 for A2

– Splits the utility• if truth and work alone, A1

cost 10, A2 cost 8• If lie and work alone, A1 cost

6, and A2 cost 8.• Pure deal doesn’t split utility

equally• Compute p mathematically• Util1 = 6-8p = 8-8(1-p) = util2• p = 3/8

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Hidden letters – but it was a lieUtility for Agent 1– Pure deal (one person delivers all) – expected cost=[(,]

– ½(2) + ½(10) = 6 (as my empty deal still requires b’s deliver)

– Mixed deal – expected cost= [(,] = 3/8*10 + 5/8*2 = 5

– Splits the utility

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Phantom lettersUtility for agent 1– Expected(on telling the truth) = both win equally (as flip coin)

– Pure deal – [(c,b)] both win, but 1 gets more because of lie

– Mixed deal – possibility of being caught as may discover the letter is bogus (all or nothing deal). A1 is given higher chances of doing all deliveries as he had the most original work to do.

– Mixed deal helps penalize person who is lying

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Subadditive Task Oriented Domain

the cost of the union of tasks is less than or equal to the sum of the costs of the separate sets – adds to a sub-cost

for finite X,Y in T, c(X U Y) <= c(X) + c(Y)).

Example of subadditive: – Deliver to one, saves distance to other (at right angles, say)

Example of non subadditive TOD– deliver in opposite directions –doing both saves nothing

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Incentive compatible Mechanism

L lying is beneficial

T Honesty is better

T/P Lying can be beneficial, but chances of being caught

70

Concave Task Oriented Domain

We have 2 tasks X and Y, where X is a subset of Y

Another set of task Z is introduced– c(X U Z) - c(X) >= c(Y U Z) - c(Y).

71MAS Compromise: Negotiation process for conflicting goals

Identify potential interactions

Modify intentions to avoid harmful interactions or create cooperative situations

Techniques required– Representing and maintaining belief models

– Reasoning about other agents beliefs

– Influencing other agents intentions and beliefs

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PERSUADER

Program to resolve problems in labor relations domainAgents– Company– Union– Mediator

Tasks– Generation of proposal– Generation of counter proposal based on feedback from dissenting

party– Persuasive argumentation

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Persuasive argumentation

Argumentation goals– Ways that an agent’s beliefs and behaviors can be affected by an

argument

Increasing payoff– Change importance attached to an issue

– Changing utility value of an issue

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Narrowing differences

Gets feed back from rejecting party– Objectionable issues

– Reason for rejection

– Importance attached to issues

Increases payoff of rejecting party by greater amount than reducing payoff for agreed parties.

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Experiments

Without Memory – 30% more proposals

Without argumentation – lesser proposals and better solutions

No failure avoidance – more proposals with objections

No preference analysis – Oscillatory condition

No feedback – communication overhead by 23%

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Multiple Attribute: Example

2 agents are trying to set up a meeting. The first agent wishes to meet

later in the day while the second wishes to meet earlier in the day.

Both prefer today to tomorrow. While the first agent assigns highest

worth to a meeting at 16:00hrs, s/he also assigns progressively smaller

worths to a meeting at 15:00hrs, 14:00hrs….

By showing flexibility and accepting a sub-optimal time, an agent can

accept a lower worth which may have other payoffs, (e.g. reduced

travel costs).

Worth function for first agent

0

100

9 12 16

Ref: Rosenschein & Zlotkin, 1994

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How can we calculate Utility?

Weighting each attribute

– Utility = {Price*60 + quality*15 + support*25}

Rating/ranking each attribute

– Price : 60, quality : 20, support : 20

– INSPIRE uses rating

Using constraints on an attribute

– Price[5,100], quality[0-10], support[1-5]

– Try to find the pareto optimum

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Utility Graphs 1

Each agent concedes in every round of negotiation

Eventually reach an agreement

time

Utility

No. of negotiations

Agentj

Agenti

Point of acceptance

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Utility Graphs 2

•No agreement

Agentj finds offer unacceptable

time

Utility

Agentj

Agenti

No. of negotiations

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Argumentation 1

The process of attempting to convince others of

something.

Why argument-based negotiations:

– Limitations of game-theoretic approaches

» Positions cannot be justified – Why did the agent pay so much

for the car?

» Positions cannot be changed – Initially I wanted a car with a

sun roof. But I changed preference during the buying process.

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Argumentation 2

4 modes of argument (Gilbert 1994):

1. Logical - ”If you accept that A and A implies B, then

you must accept that B”

2. Emotional - ”How would you feel if it happened to

you?”

3. Visceral - One argumentation participant stamps their

feet and show the strength of their feelings

4. Kisceral - Appeals to the intuitive

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Logic Based Argumentation

Basic form of argumentation

Database ├ (Sentence,Grounds)Where

Database: is a (possibly inconsistent) set of logical formulae

Sentence is a logical formula know as the conclusion

Grounds is a set of logical formula

grounds database

sentence can be proved from grounds

(we give reason for our conclusions)

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Attacking arguments

Two fundamental kinds of attack:– A undercuts B = A invalidates premise of B– A rebuts B = A contradicts B

Derived notions of attack used in Literature:

– A attacks B = A u B or A r B

– A defeats B = A u B or (A r B and not B u A)

– A strongly attacks B = A a B and not B u A

– A strongly undercuts B = A u B and not B u A

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Proposition: Hierarchy of attacks

Undercuts = u

Strongly undercuts = su = u - u -1

Strongly attacks = sa = (u r ) - u -1

Defeats = d = u ( r - u -1)

Attacks = a = u r