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Stability, chaos and multiple attractors: a single agent makes a difference. (English) Zbl 1178.91105
Summary: This paper provides an example in which a slight behavioral heterogeneity may fundamentally change the dynamical properties of a nonlinear cobweb market with a quadratic cost function and an isoelastic demand function. We consider two types of producers; cautious adapters and naive optimizers. In a market of naive optimizers a single cautious adapter stabilizes the otherwise exploding market. In a market of cautious adapters a single naive optimizer may destabilize the market; without him there exists at most one periodic attractor in the market but with him there may appear many (and even infinitely many) coexisting periodic attractors.
91B55Economic dynamics
37N40Dynamical systems in optimization and economics
37D45Strange attractors, chaotic dynamics