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82 Artificial Intelligence for the Internet of Everything

adapt. We also analyzed different behaviors at the root node (CEO agent) in
the hierarchy: “active” refers to the agent that passes indirect messages
among subordinate agents and “passive” accounts for ignoring those mes-
sages completely.
From the average payoff values in Fig. 4.8, we concluded that organiza-
tions with stronger subordinates (“lateral” and “fully connected”) performed
better, while the relative benefit of such teams is highest for medium depen-
dencies between decisions (K¼2–3). In these situations the benefit of lateral
coordination appears to outweigh the cost of managing multiple communi-
cations. The relative benefit of fully connected networks reduces as the
dependencies become more complex (K >3), mostly due to the suboptim-
ality of a distributed solution when there are many dependencies (i.e., large
K) among the decision variables.

4.4.4 Impact of Decision Decomposition

Finally, we studied the effect of decision decomposition (the assignment of
decision and factor nodes to agents) on team performance. We computed a
score on the quality of a current decision as the value of an objective function
^
^

at the max-marginal vector d ¼ d i , where,
^ ðÞ:
d i ¼ arg maxb i d i
We found that using optimized versus random decomposition improved
the solutions achieved by a team, with a larger effect for lateral structures
(Fig. 4.9).
Due to space limitations we omitted an analysis of (a) how team struc-
tures affect performance; (b) correlation between free energy and the reward
function improvement; (c) internal/external workload metrics and how
they impact the decision quality; and (d) measures of resilience. These will
be included in a future manuscript.

Fig. 4.7 Considered team structures.