MUNM127 Теория на игрите и динамичните системи (SECS...S/06)


The course aims to define and apply some mathematical methods and tools, in particular the theory of dynamical systems and the theory of games, to model the time evolution of social and economic systems. The systems considered are often adaptive systems, influenced by the presence of boundedly rationa, heterogeneous and interacting agents. Some lessons will be devoted to a deeper analysis of some mathematical concepts already introduced in the framework of the course in General Mathematics in order to use them in more advanced applications. The formal methods studied in this course will give a general understanding of the setup of a mathematical model in economics and how the results obtained should be critically analyzed. This is obtained both through the analysis of some models given in the literature and by examples and exercises proposed in classrooom notes.

At the end of the course the students should be able to built and analyze mathematical models expressed by the formalism of dynamical systems and/or the theory of games, and a sufficient capability of using mathematical and logical tools to describe in a schematic way the behaviour of complex situations. These mathematical tools should enhance the approach towards the description and the management of time evolving complex economic systems, and favour the ability to interface with experts in mathematics and computer science in order to study the behaviour of economic systems by an interdisciplinary approach.

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Управление и икономика на устойчивото развитие (на български и английски език)


проф. Джан Итало Бисчи  

Описание на курса:


Предварителни изисквания:

Форми на провеждане:

Учебни форми:

Език, на който се води курса:

Теми, които се разглеждат в курса:

Part 1. Dynamical systems in discrete and continuous time.

One-dimensional and two-dimensional linear dynamical systems with constant coefficients in continuous time and discrete time. Classification of equilibrium points. Eigenvalues and eigenvectors, phase diagrams. Basins of attraction.

Nonlinear dynamical systems: equilibrium points and their stability through linear approximations. Local bifurcations. Periodic solutions, Limit cycles.

Logistic map, period doubling route to chaos. Features of deterministic chaos.

Elements of dynamical systems in more than two dimensions.

Part 2. Introduzione to decision theory and game theory.

Representations of games in normal form and extensive form. Dominated strategies, best reply, Nash equilibrium in pure and mixed strategies. Examples and problems of inefficiency, multiplicity of Nash equilibria. Case of zero-sum games. Evolutionary games with one population and two populations of players. Replicator dynamics.

Part 3. Examples and applications.

Cobweb model, endogenous business cycle models, Cournot, Bertrand and Stackelberg games, models of financial markets with heterogeneous agents, dynamic oligopoly games, models of population dynamics, hawk-dove games with replicator dynamics, adaptive models in dynamic games with boundedly rational agents

Литература по темите:

Textbooks: G.I. Bischi, D. Radi "Lecture notes on Dynamical Systems in Economics and Finance"