On the Trustee’s Side: Trust As Relational Capital - Trust Theory: A Socio-Cognitive and Computational Model - page 282

Unilateral Dependence
(where T is a tool for g 1 and
g 1 is not included in G'')

T T

G''

g 1

Reciprocal Dependence
(where T is a tool for g 1
and R is a tool for g 2 )

T T

R R

g 1 g 2

Mutual Dependence
(where T and R are tools for g 3 )

T T

R R

g 3 g 3

Figure 10.3 Unilateral, Reciprocal and Mutual Dependence

If the world knowledge were perfect for all the agents, the above described objective
dependence would be a common belief about the real state of the world (Figure 10.1). In fact,
the important relationship is the network of dependence believed by each agent (see Figures
10.2A and 10.2B). In other words, we cannot only associate a set of goals, actions, plans and
resources with each agent, but we have to evaluate these sets as believed by each agent (the
subjective point of view) and also take into consideration that they would be partial, different
from each other, sometimes wrong, and so on. In more practical terms, each agent will have
a different (subjective) representation of the dependence network as exemplified in Figures
10.1, 10.2A, and 10.2B.
For this reason we introduce the formula Bel k G z that represents Ag z 's goal set as believed by
Ag k . The same for Bel k Az z , Bel k z , and Bel k R z , respectively, for actions, plans and resources.
In practice, the dependence relationships should be re-modulated on the basis of the agents'
subjective interpretation. The really operative part of the resulting interactions among the
agents is due to their beliefs about the reciprocal dependences rather than the objective
dependences; although, the final results of those interactions are also due to the 'objective'
powers and dependence relations, even if ignored by the agents.
We call Subj-Dependence(Ag j ,Ag i ,g jk ) when representing Ag j 's point of view with respect
its dependence relationships with Ag i about its k-th goal g jk . Analogously, we call Obj-
Dependence(Ag j ,Ag i ,g jk ) for representing the objective dependence relationship of Ag j with
Ag i about its k-th goal g jk . In the first place, each agent should correctly believe what is true
of their own goals, actions, plans, resources; while they could mismatch the sets of other
agents.