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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.

MSC:

91B55 Economic dynamics
37N40 Dynamical systems in optimization and economics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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