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other hand, the
anticipated expectation
(AE)
1
reflects an agent's estimation of other
agents' expectations towards its own behavior.
The EC is calculated based on a modified version of the standard deviation, estimat-
ing an agent's certainty over the possible reactions to its next message
m
sent
[3, sec. 2.1
and 9.5]:
|
1
|
m
j
)
2
1
m
j
∈
M
|
EC
m
sent
=
|
−
lookup
(
MEM
alter
,
m
sent
,
(3)
|
M
|−
M
M
This linear function returns a value of 0 for uniformly distributed probability estima-
tions over the others' possible reactions to an agent's message. Contrastingly, the most
inhomogenous distribution of those estimated probabilities leads to a value of 1. Thus,
the function reflects the certainty of the agent expecting a particular response to its mes-
sage. However, note that the
lookup
of each value for the possible reactions of the MAS
is used with the sent message as its first argument. This is because
MEM
alter
contains
ego's observations of himself from alter's perspective. Thus, as ego's
m
sent
is what alter
receives from him, it is treated as the received message in
MEM
alter
.
On the other hand, the AE is calculated directly using the
lookup
-function as the
estimated probability of the agent's next message
m
sent
in response to the last received
message
m
received
[3, sec. 2.1]:
AE
m
sent
=
lookup
(
MEM
ego
,
m
received
,
m
sent
)
(4)
As
MEM
ego
stores all observations of ego's responses to received messages, Equation 4
reflects ego's anticipation of alter's perception of his behavior. Hence, the AE denotes
an agent's estimation of what is expected from itself by the community of its fellow
agents.
Finally, a weighted sum combines both types of expectations to a selection value
V
for each possible next message
m
sent
∈
M
. This value represents the potential of a given
message to stabilize the interaction flows within the MAS. High selection values repro-
duce themselves when an agent chooses a corresponding message and thereby feeds it
back into the control loop. This leads to an emergence of interaction patterns (repeat-
edly occurring communication flows between the agents) which represent the social
structures in a MAS. However, differing from Luhmann's theory and the model by
Dittrich et al. [3], goal-directed agent interaction requires social structures which facil-
itate the fulfillment of the agents' objectives. Therefore, at this stage, a utility function
utility
:
M
−→
+
is additionally introduced. This function enables
V
not only to reflect
communicative stability within the system, but also directs the agent's behavior towards
domain dependent performance criteria. Thus,
V
m
sent
is given by the following equation.
c
f
V
m
sent
=
(
α
EC
m
sent
+
(1
−α
)AE
m
sent
)
·
utility
(
m
sent
)
+
(5)
|
M
|
1
Dittrich et al. [3] call this
expectation-expectation
(EE), literally translating Luhmann's orig-
inal German term. Luhmann, however, uses
anticipated expectation
in the English edition of
his main work [11].
