On the relationship between discounting and complicated behavior in dynamic optimization models

Article Abstract:

An inverse relationship was found between discounting and complicated behavior in dynamic optimization models. Specifically, the inverse relationship exists between a dynamic optimization model's discount factor and the corresponding optimal policy function's topological entropy. The generalization implied by an aggressive model was found to be highly necessary in the creation of topological chaos in aggregative dynamic optimization models.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Economic research, Entropy (Information theory), Mathematical optimization, Optimization theory

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A note on controlling a chaotic tatonnement

Article Abstract:

A technique was employed to control a chaotic tatonnement process with the help of a Walrasian auctioneer. The control technique involved the creation of a parametric class of exchange economies that will produce the logistic family of dynamical systems. The approach was proven effective in identifying a given neighborhood of competitive equilibrium that is directed for a large subgroup of parametric class of economies.

Chaos theory, Chaotic systems, Walrasian model

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Stability and complex dynamics in a discrete tatonnement model

Article Abstract:

A stability was established under a discrete tatonnement process in which all goods are classified as gross substitutes. The existence of stability was concluded after a convergence point among prices was identified which is located in a region where equilibrium is found. The discrete tatonnement process has the tendency to experience several bifurcations and become complex when price adjustment is increased.

Pricing, Nonlinear theories

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