A Quest Towards a Mathematical Theory of Living Systems by Nicola Bellomo Abdelghani Bellouquid Livio Gibelli & Nisrine Outada

Author:Nicola Bellomo, Abdelghani Bellouquid, Livio Gibelli & Nisrine Outada
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In some cases, large deviations break out the macroscopic (qualitative) characteristics of the dynamics, whence substantial modifications can be observed. These deviations can be interpreted as the requisites for events that can be classified as a “Black Swan” [230]. Particularly important is the detection of early signals to predict the onset of such sudden large deviations [23].

5.2.2 Mathematical tools toward modeling social dynamics

Social systems are prominent examples of complex systems and, in recent years, a growing interest has arisen to study their collective emerging behaviors such as cooperation, cultural conflicts, and problems of social consensus.

Two complementary ways of modeling social systems can be roughly distinguished.

The first approach involves the design and analysis of simplified mathematical models that do not try to mimic the real behavior of individuals but abstract the most important qualitative aspects so as to gain insight into the system dynamics. The rationale behind this approach is that, in analogy with the “universality” concept in statistical physics, certain aspects of complex behavior are supposed to be independent on the specific dynamical details.

The second approach consists in designing more comprehensive and realistic models, usually in the form of numerical simulations, which represent the interacting parts of a complex system, often down to minute details. The border between these two approaches is not sharply defined, and tools of each of them are always more often applied together.

The first approach has been mainly adopted to investigate social systems using methods of the statistical physics. Two research fields have been rapidly grown referring specifically to as econophysics [247] and sociophysics [78, 121, 241]. Although the principles of both fields have much in common, econophysics focuses on the narrower subject of economic behavior while sociophysics studies a broader range of social issues, including social networks, language evolution, population dynamics, epidemic spreading, terrorism, voting, coalition formation, and opinion dynamics.

A more realistic description of real-world social interactions can be build within game-theoretical models. In its original formulation, game theory has been used to analyze situations of conflict or cooperation in economics [176, 183]. Two major streams of extensions of classical game theory have been developed as early as in the sixties of the last century, namely, differential games [212] and games with incomplete information [136]. The former are characterized by continuously time-varying strategies and payoffs with a dynamical system governed by ordinary differential equations, while in the latter players are supposed to ignore information about the others players for what strategies and payoffs are concerned.

An important breakthrough of game theory is behavioral game theory, also called experimental game theory [76, 129]. The main idea is that, instead of analyzing games theoretically, experimenters get real people to play them and record results. The remarkable finding is that in many situations people respond instinctively and play according to heuristic rules and social norms rather than adopting the strategies indicated by rational game theory.

Evolutionary game theory is an extension of the classical paradigm toward this concept of bounded rationality. Unlike classical game theory, the focus is on large

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