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Inertia and reactivity in decision making as cognitive variational inequalities. (English) Zbl 1138.91370
Summary: In this paper, we modelize a decision process of an agent where inertia and reactivity aspects help to converge to stable routines. A decision is a move. We consider an agent who can only take incremental decisions, moving step by step on an unknown landscape, due to limited knowledge of his environment, resources, efforts, energy, money or time constraints. The agent explores around to be able to compare incremental advantages and costs of moving (changing). The agent reaches a stable routine, stops moving, and prefers to stay there, when advantages to move are lower than costs to move. Inertia is modelized by costs to move quickly (reactivity is the learned ability to move quickly in a cheap way). We apply our `worthwhile to move approach’ [H. Attouch and A. Soubeyran, “From procedural rationality to routines: a `worthwhile to move’ approach of satisficing with not too much sacrificing”, \url{http://www.gate.cnrs.fr/seminaires/2006_2007/Soubeyran_a.pdf}] to build `cognitive versions of variational inequalities’ for `second-order dynamical gradients systems with inertia’ (`HBF’ differential equations). In this model, we have mainly focused on the costs of moving. The advantages of moving (the other side of the balance, which drives a `worthwhile to move decision’) are detailed in [loc. cit.]. To save space the annex concentrates only on the costs of moving.

MSC:
91B06Decision theory
34A60Differential inclusions
49J40Variational methods including variational inequalities
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