Nonlinear Dynamics in Economics, Finance and the Social Sciences

Essays in Honour of John Barkley Rosser Jr

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Reviewed by Segismundo S. Izquierdo
University of Valladolid

This book presents a collection of twenty papers analysing non-linear dynamic models in economics and finance. The papers were selected from an international workshop held at the University of Urbino, Italy, in 2008.

Covering a wide range of economic applications, the book is especially useful as a source of inspiration for new ideas and research themes, as well as a repository of methodological references on the analysis of different kinds of dynamical systems: continuous and discrete, chaotic and non-chaotic, deterministic and stochastic.

The range of applications includes a large spectrum of issues on microeconomics, macroeconomics and finance. According to the editors, the variety of applications and methods "is intended to give some perspective on the growing literature in this field" (non linear dynamics). The main applications or motivating issues that can be found in the papers are: environment and resource conservation, sustainable economic growth, wealth distribution, stability of international agreements or coalitions, R&D investment decisions, duopoly competition, spatial distribution of firms, auctions, business cycles, macroeconomic models with imperfect competition and learning, macroeconomic disequilibrium, elections and behaviour of politicians, portfolio choice with disappointment aversion, financial market models, capital asset pricing with heterogeneous beliefs, and credit policy of commercial banks.

In most cases, the structure of the papers in the book is:

1. A modelling and formalisation of a dynamic social or economic issue, leading to a system of non-linear difference or differential equations.
   Several of the papers, especially those on microeconomics, analyse situations of social interactions in which the decisions of one individual agent has some non negligible influence on the results obtained by the other agents. Consequently, the modelling process often follows a game-theoretical formalisation approach, including differential games (as in "International Environmental Agreement: A Dynamical Model of Emissions Reduction" by Biancardi). In several cases, the agents are assumed to follow optimising behaviours given their available information, which can pose an interesting problem by itself. In many other cases, aligned with a bounded rationality approach, the agents are assumed to follow some "simple", "sensible" or "logically appealing" learning, imitation, adaptation or reproduction rule. Most of the models lead to deterministic equations, but one can also find examples of continuous-time stochastic dynamic modelling (as in "Political Accountability: A Stochastic Control Approach" by Longo and Mainini).
2. An analysis of the dynamics of the obtained system of equations.
   In general, the dynamic system of equations depends on some control parameter(s) and the study characterises the existence and the stability of fixed points, limit cycles and quasi periodic or chaotic orbits as a function of the control parameters, showing trajectories and bifurcation diagrams. Most often, the analytical results (where possible) are complemented and extended with numerical simulations.
3. A discussion of the implications and the relevance of the findings made about the dynamics of the model.

Among the papers with a more theoretical or methodological focus, Matsumoto and Szidarovszky ("Delay Differential Nonlinear Economic Model") present theoretical findings and illustrative examples on the effects of information delays on the behaviour of dynamic economic systems, and Huang ("Issues in Strategy-Switching Dynamics") analyses a particular revision protocol in finite populations in an evolutionary game theory context.

In summary, the book is specially interesting for researchers in economics and in the social sciences who want to approach and explore the field of applications of non linear dynamics, who are looking for ideas to develop new papers in this field, or who would like to have at their disposal a varied collection of practical methodological examples of analysis of models made up of systems of non linear difference or differential equations.

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© Copyright Journal of Artificial Societies and Social Simulation, 2010