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Oligopoly
The book focuses classical oligopoly theory as developed in 1840-1940. By the end of this period oligopoly came under the spell of game theory in its probabilistic equilibrium format. Work by Cournot, von Stackelberg, Palander, and Hotelling, causal and dynamic in essence, but ignored, is reconsidered in the light of modern dynamics using topology and numerics. As particular features, von Stackelberg leadership is included in the dynamic Cournot model, the Hotelling problem is solved with elastic demand, thus skipping the absurd idea of quadratic transportation costs. Further, it is shown that the celebrated destabilisation of Cournot equilibrium under increased competition is due to mistakenly assuming constant returns, and that the whole idea of rational expectations is untenable in dynamic oligopoly. Early original ideas in oligopoly theory, such as coexistence and multiplicity of attractors are focused again after many undeserved decades of oblivion.
Qualitative Theory of Dynamical Systems, Tools and Applications for Economic Modelling
The book presents the lectures delivered during a short course held at Urbino University in summer 2015 on qualitative theory of dynamical systems, included in the activities of the COST Action IS1104 “The EU in the new economic complex geography: models, tools and policy evaluation”. It provides a basic introduction to dynamical systems and optimal control both in continuous and discrete time, as well as some numerical methods and applications in economic modelling. Economic and social systems are intrinsically dynamic, characterized by interdependence, nonlinearity and complexity, and these features can only be approached using a qualitative analysis based on the study of invariant set...
Arts, Sciences, and Economics
This book deals with the economic aspects of changing attitudes in arts and sciences. The effects of the public good character of culture, along with the very long production period and lifetime for its products, are emphasized, since both contribute to the failure of normal market solutions. Embodiment of ideas and the consequences of modern reproduction technology for protection of property rights are closely examined. The evolution within arts and sciences, which often seems to return to previously scrapped ideals, is illustrated by detailed case studies, in which the importance of changing tastes, rather than progress proper, is emphasized. The author attempts an understanding for this using Darwinian evolution in combination with modern mathematical complexity theory, expressed in terms accessible to the general reader. The second edition is extended and updated especially as regards the illustration material.
Complexity and Geographical Economics
The uneven geographical distribution of economic activities is a huge challenge worldwide and also for the European Union. In Krugman’s New Economic Geography economic systems have a simple spatial structure. This book shows that more sophisticated models should visualise the EU as an evolving trade network with a specific topology and different aggregation levels. At the highest level, economic geography models give a bird eye’s view of spatial dynamics. At a medium level, institutions shape the economy and the structure of (financial and labour) markets. At the lowest level, individual decisions interact with the economic, social and institutional environment; the focus is on firms’ decision on location and innovation. Such multilevel models exhibit complex dynamic patterns – path dependence, cumulative causation, hysteresis – on a network structure; and specific analytic tools are necessary for studying strategic interaction, heterogeneity and nonlinearities.
Disequilibrium Economics
This book discusses mathematical models for various applications in economics, with a focus on non-linear dynamics. Based on the author’s over 50 years of active work in the field, the book has been inspired by models from the period between 1920 and 1950. Following a brief introduction to economics for mathematicians and other modelers, it assembles a repository of useful specific functions for global dynamic modeling. Furthermore, twelve “research stubs” – outlined research agendas that have not yet been fully worked on – are suggested for further study and could even be expanded to entire research projects. The book is a valuable resource, particularly for young scientists who are skilled in mathematical and computational techniques and are looking for applications in economics.
Continuous And Discontinuous Piecewise-smooth One-dimensional Maps: Invariant Sets And Bifurcation Structures
The investigation of dynamics of piecewise-smooth maps is both intriguing from the mathematical point of view and important for applications in various fields, ranging from mechanical and electrical engineering up to financial markets. In this book, we review the attracting and repelling invariant sets of continuous and discontinuous one-dimensional piecewise-smooth maps. We describe the bifurcations occurring in these maps (border collision and degenerate bifurcations, as well as homoclinic bifurcations and the related transformations of chaotic attractors) and survey the basic scenarios and structures involving these bifurcations. In particular, the bifurcation structures in the skew tent ...
Nonlinearity, Bounded Rationality, and Heterogeneity
This book pursues a nonlinear approach in considering both chaotic dynamical models and agent-based simulation models of economics, as well as their dynamical behaviors. Three key concepts arising in this context are “nonlinearity,” “bounded rationality” and “heterogeneity,” which also make up the title of the book. Nonlinearity is the warp that runs throughout all models because systems that exhibit chaotic or other complex behavior in the absence of any exogenous disturbances are absolutely nonlinear. Bounded rationality constitutes the woof, because economic systems do not exhibit complex behavior if all agents are perfectly rational, as is usually assumed in neoclassical economics. Agents who are boundedly rational have to struggle to do their best with limited information and tend to adapt to their economic environment without knowing what is the best. Furthermore, the heterogeneity of firms or consumers dyes the fabric of complex dynamics woven from the warp and woof.
