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Fig. 4. The evolution of system productivity for different numbers of agents and tasks:
a) 3 agents and 10 tasks; b) 100 agents and 1000 tasks
(1000), at the expense of a greater computing time. Therefore, the model can
easily scale to any (reasonable) number of agents and tasks.
When dealing with more agents, it can be seen that the fluctuations are re-
duced, as there are far more possibilities to achieve a good allocation deal. When
the number of agents is small, the initial variation is more apparent, as agents
quickly shift from one role to another. As stated before, the difference between
the Nash and the utilitarian solution also reflect in the overall system produc-
tivity converging to slightly different values.
The increase and stabilization of the total productivity is an emergent prop-
erty of the system, because the explicit aim of the agents is to adapt and max-
imize their own individual utilities, not to solve tasks more quickly. The shape
of the productivity evolution function is very similar to that of productivity
evolution measured in actual human working environments [7].
4
Conclusions
The paper presents a method by which agents can self-organize their roles by
changing their individual utilities to fit the particularities of task distributions.
This is achieved by reaching a (near-)optimal negotiation outcome, computed
by means of an evolutionary algorithm with hybrid encoding. The adaptive be-
haviour is based on the main idea of cognitive dissonance theory. Knowledge
dynamic effects such as learning and forgetting are also taken into account.
Over repeated trials, the system is shown to stabilize and the agents converge
to specific roles by handling tasks defined by particular complexity levels of
their attributes. As an emergent property of this behaviour, the overall system
productivity increases and eventually stabilizes, following a typical shape also
revealed by studies about the human worker performance.
Compared to E-GAP [10], the present method does not address roles explicitly,
but implicitly, based on the changes of the agents' individual utilities. Also,
rather than treating task allocation as a constraint optimization problem, it
uses negotiation as a mechanism to achieve emergent coordination.
Several future directions of research have been identified. The investigation of
using direct multilateral negotiation techniques (e.g. [4]) to reach the desired out-
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