Abstract
Socio-economic networks describe collective phenomena through constraints relating actions of several agents, coalitions of these agents 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 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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Aubin, JP. (2003). Evolution of complex economic systems and uncertain information. In: Lesage, C., Cottrell, M. (eds) Connectionist Approaches in Economics and Management Sciences. Advances in Computational Management Science, vol 6. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3722-6_1
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DOI: https://doi.org/10.1007/978-1-4757-3722-6_1
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