Regulation of the evolution of the architecture of a network by tensors operating on coalitions of actors |
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Authors: | Jean-Pierre Aubin |
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Institution: | 1.Réseau de Recherche Viabilité, Jeux, Contr?le, 14, rue Domat, 75005 Paris, France (e-mail: J.P.Aubin@wanadoo.fr)
,FR |
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Abstract: | Socio-economic networks, neural networks and genetic networks describe collective phenomena through constraints relating
actions of several actors, coalitions of these actors and multilinear connectionist operators acting on the set of actions
of each coalition. We provide a class of control systems governing the evolution of actions, coalitions and multilinear connectionist
operators under which the architecture of the network remains viable. The controls are the “viability multipliers” of the
“resource space” in which the constraints are defined. They are involved as “tensor products” of the actions of the coalitions
and the viability multiplier, allowing us to encapsulate in this dynamical and multilinear framework the concept of Hebbian
learning rules in neural networks in the form of “multi-Hebbian” dynamics in the evolution of connectionist operators. They
are also involved in the evolution of coalitions through the “cost” of the constraints under the viability multiplier regarded
as a price. |
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Keywords: | : Dynamic network – Evolutionary economics – Viability multipliers – Fuzzy coalitions – Connectionist operators |
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