Complex economic nonlinear dynamics endogenously do not converge to a point, a limit cycle, or an explosion. Their study developed out of earlier studies of cybernetic, catastrophic, and chaotic systems. Complexity analysis stresses interactions among dispersed agents without a global controller, tangled hierarchies, adaptive learning, evolution, and novelty, and out-of-equilibrium dynamics. Complexity methods include interacting particle systems, self-organized criticality, and evolutionary game theory, to simulate artificial stock markets and other phenomena. Theoretically, bounded rationality replaces rational expectations. Complexity theory influences empirical methods and restructures policy debates.

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On the Complexities of Complex Economic Dynamics

A robust rational route to randomness in a simple asset pricing model

http://cermsem.univ-paris1.fr/cornet-english/cornet1988a-jme.pdf

General Equilibrium-theory and Increasing Returns - Presentation

This paper provides a detailed description of the Eurace@Unibi model, which has been developed as a versatile tool for macroeconomic analysis and policy experiments. The model explicitly incorporates the decentralized interaction of heterogeneous agents across different sectors and regions. The modeling of individual behavior is based on heuristics with empirical microfoundations. Although Eurace@Unibi has been applied successfully to different policy domains, the complexity of the structure of the model, which is similar to other agent-based macroeconomic models, makes it hard to communicate to readers the exact working of the model and enable them to check the robustness of obtained results. This paper addresses these challenges by describing the details of all decision rules, interaction protocols and balance sheet structures used in the model. Furthermore, we discuss the use of a virtual appliance as a tool allowing third parties to reproduce the simulation results and to replicate the model. The paper illustrates the potential use of the virtual appliance by providing some sensitivity analyses of the simulation output carried out using this tool.

Macroeconomics with heterogeneous agent models: fostering transparency, reproducibility and replication

We consider a price adjustment process in a model of monopolistic competition. Firms have incomplete information about the demand structure. When they set a price they observe the amount they can sell at that price and they observe the slope of the true demand curve at that price. With this information they estimate a linear demand curve. Given this estimate of the demand curve they set a new optimal price. We investigate the dynamical properties of this learning process. We find that, if the cross-price effects and the curvature of the demand curve are small, prices converge to the Bertrand-Nash equilibrium. The global dynamics of this adjustment process are analyzed by numerical simulations. By means of computational techniques and by applying results from homoclinic bifurcation theory we provide evidence for the existence of strange attractors.

A price adjustment process in a model of monopolistic competition

It is well known that adjustment processes like tatonnement can show erratic dynamic behavior. The prices can make big jumps and vary over a wide range. A discrete tatonnement process in a simple two goods economy is studied with only one price adjusted. It is shown that the interval in which the price varies can be restricted to a neighborhood of an equilibrium price with big jumps excluded, if the relative price adjustment is restricted by a maximal rate of increase or decrease of the price. Within the interval any type of erratic dynamics remains possible.

A cautious price adjustment mechanism: chaotic behavior

In this paper we study the dynamics of discrete price adjustment processes. We show that gross substitutability leads to a kind of stability of the process: it guarantees that all prices converge to some bounded region that contains the unique equilibrium price. The dynamics inside this region is by no means trivial. We demonstrate that as the speed of adjustment increases the process undergoes several bifurcations, and the dynamics may become quite complex. Our approach differs from other literature on tâtonnement processes in that our systems are not necessarily one-dimensional.

Stability and complex dynamics in a discrete tâtonnement model

Supply-constrained equilibria in economies with indexed prices

Fixed price equilibria in a multifirm model

We study fixed price temporary equilibria (with rationing) and sequences of temporary equilibria in a three commodities (goods, labor, bonds) overlapping generations model with endogenous investment. Young consumers, living two periods, work, consume, and buy bonds for financing next period's consumption. New firms, existing for two periods, make a production plan for the next period, taking into account expected rationing, assumed similar to present rationing. The plan determines the amount of goods to buy as capital, financed by bonds. Old firms produce, using labor and the previously bought capital. Different regimes exist and expectations can be self-fulfilling and self-destroying.

Claus Weddepohl

Papers

A cautious price adjustment mechanism: chaotic behavior

Stability and complex dynamics in a discrete tâtonnement model

Supply-constrained equilibria in economies with indexed prices

Fixed price equilibria in a multifirm model

Fixed price equilibria in an overlapping generations model with investment