A Domain Theory for Task Oriented Negotiation

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1 Distributed Information Processing Course EPFL A Domain Theory for Task Oriented Negotiation Gilad Zlotkin & Jeffrey S.Rosenschein (1993) Computer Science Department Hebrew University, Jerusalem, Israel Presented by LUU Vinh-Toan

2 Goals of Paper Present a general theory that captures the relationship between certain domains and negotiation mechanisms Categorize precisely the kinds of domain in which agents can find themselves Use category to choose appropriate negotiation 2

mechanisms Categorize precisely the kinds of domain in which

3 Task Oriented Domains (TOD) Describes a certain class of scenarios for multi-agent encounters. TOD is a Tuple <T, A, c> T: (finite) set of all possible tasks A = (A1, A2,.., An), an ordered list of Agent c: c(x) is the cost of executing all the tasks in X (subset of T) by single Agent. C (ø) = 0 An Encounter is set of tasks <T 1, T 2,, T n > such that T k is a set of tasks from T that A k needs to achieve 3

., An), an ordered list of Agent c: c(x) is the cost of executing all the tasks in X (subset of T) by

4 Examples(1) Postmen domain 1 2 Task Set: Set of all addresses in the graph Cost Function (of subset X): Length of minimal path from post office, visits all members of X, ends at the Post office Ex: C(X 1 ) = 5, C(X 2 ) =

Length of minimal path from post office, visits all

5 Examples(2) Database Queries Agents have to access to a common DB and each has to carry out a set of queries Agents can exchange results of queries and sub-queries The Fax Domain Agents are sending faxes to locations on a telephone network. Multiple faxes can be sent one the connection is established with receiving node The Agents can exchange message to be faxed 1 1,2 1,2 2 5

are sending faxes to locations on a telephone network.

6 Attributes(1)- Subadditivity c(x U Y) c(x) + c(y) By combining sets of task, we may reduce (no increase) the total cost, as compared with the cost of achieving the sets alone. 6

7 Attributes(2)- Concavity c(y U Z) c(y) c(x U Z) c(x) The cost of tasks Z adds to set of tasks Y cannot be greater than the cost Z add to a subset of Y The general Postmen domain is not Concave (unless restricted to trees) Example: Z adds 0 to X but adds 2 to its superset Y (all blue nodes) Concavity implies sub-additivity 7

Postmen domain is not Concave (unless restricted to trees) Example: Z adds 0 to X

8 Attributes(3)- Modularity c(x U Y) = c(x) + c(y) c(x Y) The cost of the combination of 2 sets of tasks is exactly the sum of their individual costs minus the cost of their intersection Only Fax Domain is modular Modularity implies concavity 8

sum of their individual costs minus the cost of their

9 Mechanisms for Subadditive TOD s An encounter (T 1, T 2 ) within a 2 agent. We have: Pure Deal (D 1,D 2 ): redistribution of tasks among 2 agents D 1 U D 2 = T 1 U T 2, A k execute D k Mixed Deal (D 1,D 2 ):p Pure Deal (D 1,D 2 ) and probability p. With p, A 1 executes D 1, A 2 executes D 2. With 1- p, A 1 executes D 2, A 2 executes D 1 Cost k ((D 1,D 2 ):p) = p*c(d k )+(1-p)*c(D 3-k ) All-or-Nothing Deal (T 1 UT 2, 0):p A 1 has a p chance of executing all the tasks T 1 U T 2 and has 1-p chance of doing nothing. 9

):p Pure Deal (D 1,D 2 ) and probability p. With p, A 1 executes D 1, A 2 executes D 2.

10 Deal and Utility in 2 Agents TOD Deal δ is a pair (D 1,D 2 ) Deal Θ Ξ(T 1,T 2 ) is called the conflict deal Utility i (δ)= Cost(T i )-Cost(D i ) A deal δ is called individual rational if δ Θ A deal δ is called pareto optimal if there does not exist another deal δ such that δ > δ Set of all deals that are individual rational and pareto optimal is called the Negotiation Set (NS). 10

Θ A deal δ is called pareto optimal if there does not exist another deal δ such that δ > δ Set

11 Incentive Compatible Mechanisms Agents do not have full information about one another s goals=> Agents can benefit from concealing goals, or manufacturing artificial goals. 3 types of lies: Hiding tasks Phantom tasks Decoy tasks A negotiation mechanism is called Incentive compatible when the strategy of telling the truth is in equilibrium 11

3 types of lies: Hiding tasks Phantom tasks Decoy tasks A negotiation mechanism is

12 3-dimensional table of Characterization of Relationship L T T/P Implied relationship between cells Implied relationship with same domain attribute. means lying may be beneficial means telling the truth is always beneficial refers to lies which are not beneficial because they may always be discovers 12

means lying may be beneficial means telling the truth is always beneficial

13 Incentive Compatible Fixed Points (FP) FP1: in Subadditive TOD, any optimal negotiation mechanism (ONM) over A-or-N deals, every hiding lie is not beneficial Ex:A 1 hides letter to c, his utility doesn t increase. FP2: in Subadditive TOD, any ONM over Mixed deals, every phantom lie has a positive probability of being discovered. FP3: in Concave TOD, any ONM over Mixed deals, every decoy lie is not beneficial. FP4: in Modular TOD, any ONM over Pure deals, every decoy lie is not beneficial. c 1 a b 2 1,2 13

FP2: in Subadditive TOD, any ONM over Mixed deals, every phantom lie has a positive probability of being discovered.

14 Non-incentive Compatible Fixed Points Post Office FP5: in Concave TOD, any ONM over Pure deals, every Phantom lie is beneficial. Ex1:A 1 creates Phantom letter at node c, his utility has risen from 3 to 4 2 a (A1, A2) 1 b (A1, A2) 3 FP6: in Subadditive TOD, any ONM over A- or- N deals, every Decoy lie is beneficial. Ex2:A 1 lies with decoy letter to h, his utility has risen from 1.5 to 1.72 (A1) (A1) (A1) g f e h d (A1) b c (A2) (A2) c (A1) 14

Ex1:A 1 creates Phantom letter at node c, his utility has risen from 3 to 4 2 a (A1, A2) 1 b (A1, A2) 3 FP6: in

15 Non-incentive Compatible Fixed Points FP7: a in Modular TOD, any ONM over Pure deals, every Hide lie is beneficial. f Ex3: A 1 hides his letter node b =>Max Utility is that sends A 1 to node b! 2 1 e d b c (A1,A2) FP8: in Modular TOD, any ONM over Mixed deals, every Hide lie is beneficial. Ex4: A 1 hideshis letter to node a A 1 s Utility is 4.5 > 4 (Utility of telling the truth) (A1,A2) (A1) f e (A1,A2) a b c (A2) (A1,A2) d (A1,A2) (A1,A2) 15

2 1 e d b c (A1,A2) FP8: in Modular TOD, any ONM over Mixed deals, every Hide lie is beneficial.

16 Conclusion In order to use Negotiation Protocols, it is necessary to know when protocols are appropriate TOD s cover an important set of Multiagent interaction 16

A Domain Theory for Task Oriented Negotiation 4

A Domain Theory for Task Oriented Negotiation 4 Gilad Zlotkin Jeffrey S. Rosenschein Computer Science Department Hebrew University Givat Ram, Jerusalem, Israel Abstract We present a general theory that