Learning Transient Relationships Through Observations

Table 6.3 shows a summary of which signals have been observed byavom1from the interactions

that agentavom2has had with each of the service providers thatavom1is considering forming a

VO with. By observing a signal in an interaction episode between two agents,avom1 is able to

create a picture of what transient relationship (Lˆavom2,asp1_{) exists between those two agents in} that one episode. However, to do this the agent has to be configured with some prior knowledge. Therefore, we assume thatavom1 has conditional probability tables that allows it to obtain the

probability of observing a signal given the presence of a particular type of relationship, as shown in Table 6.4.

Now, using the mechanism described in Section 5.4.3, we show howavom1is able to calculate

Relationship p(Signal|Relationship) S1 S2 S3 S4 Competes 0.5 0.1 0.2 0.3 Cooperates 0.2 0.6 0.1 0.1 Depends on 0.2 0.2 0.5 0.1 Depended upon 0.1 0.1 0.2 0.4

TABLE 6.4: Agentavom1’s conditional probability tables showing the probability of a signal

given the presence of a certain type of relationship.

specifically, we illustrate the use of this mechanism by considering a certain interaction episode betweenavom2andasp1that led to a signal of typeS1being produced.8

ˆ Lavom2,asp1 _P(Lˆavom2,asp1₎ ˆ Lavom2,asp1 com 0.25 ˆ Lavom2,asp2 cop 0.25 ˆ Lavom2,asp3 dep 0.25 ˆ Lasp4,avom2 dep 0.25

TABLE6.5: The prior distribution ofLˆavom2,asp1_{. The distribution representsa}

vom1’s beliefs

about what type of transient relationship exists betweenavom2andasp1in a particular interac-

tion episode.

In this case, before observing the signal,avom1believes that each type of transient relationship

betweenavom2andasp1is equally likely. Therefore,avom1starts with a uniform distribution for

ˆ

Lavom2,asp1 _{as shown in Table 6.5. We denote this the prior distribution.}

After observing a signal of type S1, avom1 is able to calculate the posterior distribution for

ˆ

Lavom2,asp1_{, and modify its beliefs about the transient relationship. This calculation involves} using Table 6.4:

Using Table 6.4:p(S1|Lˆavom2,asp1 _{= ˆL}avom2,asp1

com ) = 0.5

Using Table 6.5:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

com ) = 0.25

Using Equation 5.1:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

com )∝0.25×0.5 = 0.125

Using Table 6.4:p(S1|Lˆavom2,asp1 _{= ˆL}avom2,asp1

cop ) = 0.2

Using Table 6.5:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

cop ) = 0.25

Using Equation 5.1:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

cop )∝0.25×0.2 = 0.05

Using Table 6.4:p(S1|Lˆavom2,asp1 _{= ˆL}avom2,asp1

dep ) = 0.2

Using Table 6.5:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

dep ) = 0.25

Using Equation 5.1:p( ˆLavom2,asp1 _{= ˆL}avom2,asp1

dep )∝0.25×0.2 = 0.05

Using Table 6.4:p(S1|Lˆavom2,asp1 _{= ˆL}asp1,avom2

dep ) = 0.1

Using Table 6.5:p( ˆLavom2,asp1 _{= ˆL}asp1,avom2

dep ) = 0.25

Using Equation 5.1:p( ˆLavom2,asp1 _{= ˆL}asp1,avom2

dep )∝0.25×0.1 = 0.025

8

Table 6.3 shows that in total there were six occasions on whichavom1observed a signal of typeS1from an

Finally, after normalising the answers we obtain the posterior distribution: ˆ Lavom2,asp1 _P(Lˆavom2,asp1₎ ˆ Lavom2,asp1 com 0.5 ˆ Lavom2,asp2 cop 0.2 ˆ Lavom2,asp3 dep 0.2 ˆ Lasp4,avom2 dep 0.1

From the calculations above we can see that the posterior distribution is significantly different from the (uniform) prior. The most likely value forLˆavom2,asp1 _{from the posterior distribution} (after observing signalS1) isLˆavom2,asp1

com with a probability of0.5. For this reason, agentavom1

believes that in this particular interaction episode agentavom2 andasp1 shared a transient re-

lationship of type competitive. We do not show the calculations for the other observations of signals from interactions of the different SPs withavom2, and instead we simply state that:

• Agentavom1believes that on six occasionsavom2was competing withasp1. • Agentavom1believes that on five occasionsavom2was cooperating withasp2. • Agentavom1believes that on six occasionsavom2was depending onasp3. • Agentavom1believes that on nine occasionsasp4was depending onavom2.

The next section illustrates how, at the end of each observed episode, agentavom1 can use its

beliefs about the type of transient relationship to modify its belief about the permanent relation- ship.