What are game theory and chaos theory

a) What does chaos mean in systems and how did it come to be discovered?

Dynamic systems do not behave linearly, in certain system constellations one can describe system behavior approximately with the help of linearity. However, this only applies locally in certain “stable” areas.

In certain situations in systems, the non-linear behavior leads to unexpected system behavior and can possibly get out of control (see also catastrophe theory).

The description of non-linear structures and their behavior led to the development of chaos theory. A maxim of this theory is the recognition that even simple structures in systems highlight complex behavior patterns.

The mathematical description of system behavior led to the development of chaos theory in systems. The geometric description of such systems led to the discovery of fractal geometry. The core message of this fractal geometry is the knowledge that not only integer dimensions exist in reality, but also so-called broken dimensions. Their identification feature is the concept of "self-similarity", which is best found geometrically in the representation of the so-called almond brojt set.

b) What are chaos theory keywords and what is their meaning?

The following keywords can be found when studying chaos theory or the topic of fractal geometry:

- fractal or self-similar structures

- dissipative structures

- attractors

- disasters

Their meaning is as follows:

- fractal structure:

A geometric structure that reproduces this structure as a section of itself is called a fractal or self-similar structure.

- dissipative structure:

A structure in a system is called dissipative if it shows stable behavior again in an unstable system area.

- Attractors:

Attractors are geometric structures in system behavior that represent the long-term behavior of system states.

- disasters:

Disasters describe abrupt changes (or changes) with which a system suddenly reacts to minor changes in system sizes.

c) What is the significance of chaos theory for business management in companies?

With the scientification of business administration at the end of the 19th century / beginning of the 20th century, attempts were made to functionally represent business management relationships. One of the basic approaches was the representation of cause / effect relationships, whereby one based on the linearity as a basic maxim. However, the developments in companies in the 1980s showed that the previous models for explaining business management relationships were not sufficient to explain the instabilities in companies due to changes in the market, structural changes in companies and the introduction of new technologies.

From this developed, inter alia. 2 new branches in business administration that have become increasingly important to this day, namely game theory and systems theory. While game theory tries to define and simulate models for strategies from the knowledge of stochastics and probability theory via random variables, distributions and measures, systems theory is used to map economic processes as dynamic systems and their system behavior.

In the course of the analysis of economic processes with the focus on dynamic systems, new knowledge and models have developed over the last few years, such as fractal organizations, dissipative rationalization and attractors of strategic corporate planning.