Envy coupled with competition divides society into an upper and lower
class, game theoretical study shows

Date:
June 17, 2020
Source:
Goethe University Frankfurt
Summary:
Can class differences come about endogenously, i.e. independent
of birth and education? Researchers pursued this issue in a game
theoretical study. They were able to show that the basic human
need to compare oneself with others may be the root cause of the
formation of social classes.



FULL STORY ==========================================================================
Can class differences come about endogenously, i.e. independent of birth
and education? Professor Claudius Gros from the Institute for Theoretical Physics at Goethe University pursued this issue in a game theoretical
study. He was able to show that the basic human need to compare oneself
with others may be the root cause of the formation of social classes.


==========================================================================
It's generally recognized that differences in background and education
cement class differences. It is less clear when and under what
circumstances individual psychological forces can drive an initially
homogenous social group apart and ultimately divide it. Claudius Gros, professor for theoretical physics at Goethe University, investigated this question in a mathematical precise way using game theory methods. "In
the study, societies of agents - - acting individuals -- are simulated
within game theory, which means that everybody optimises her/his success according to predetermined rules. I wanted to find out whether social differences can emerge on their own if no one starts off with advantages
-- that is, when all actors have the same skills and opportunity,"
the physicist explains.

The study is based on the assumption that there are things in every
society that are coveted but limited -- such as jobs, social contacts
and positions of power. An inequality is created if the top position is
already occupied and someone must therefore accept the second-best job
-- but not, however, a societal division. With the help of mathematical calculations Gros was able to demonstrate that envy, which arises from
the need to compare oneself with others, alters individual behaviour and consequently the agents' strategies in characteristic ways. As a result
of this changed behaviour, two strictly separate social classes arise.

Game theory provides the mathematical tools necessary for the modelling
of decision situations with several participants, as in Gros' study. In general, constellations in which the decision strategies of the individual actors mutually influence each other are particularly revealing. The
success of the individual depends then not only on his or her own actions,
but on others' actions as well, which is typical of both economic and
social contexts. Game theory is consequently firmly anchored in the
economy. The stability condition of game theory, the "Nash equilibrium,"
is a concept developed by John Forbes Nash in his dissertation in 1950,
using the example of poker players. It states that in equilibrium no
player has anything to gain by changing their strategy if the other
players do not change theirs either. An individual only tries out new
behaviour patterns if there is a potential gain. Since this causal chain
also applies to evolutionary processes, the evolutionary and behavioural sciences regularly fall back on game theoretical models, for example
when researching animal behaviours such as the migratory flight routes
of birds, or their competition for nesting sites.

Even in an envy-induced class society there is no incentive for an
individual to change his or her strategy, according to Gros. It is
therefore Nash stable.

In the divided envy society there is a marked difference in income
between the upper and lower class which is the same for all members of
each social class.

Typical for the members of the lower class is, according to Gros, that
they spend their time on a series of different activities, something game theory terms a "mixed strategy." Members of the upper class, however, concentrate on a single task, i.e., they pursue a "pure strategy." It is
also striking that the upper class can choose between various options
while the lower class only has access to a single mixed strategy. "The
upper class is therefore individualistic, while agents in the lower
class are lost in the crowd, so to speak," the physicist sums up.

In Claudius Gros' model, whether an agent lands in the upper or lower
class is ultimately a matter of coincidence. It is decided by the dynamics
of competition, and not by origin. For his study, Gros developed a new
game theoretical model, the "shopping trouble model" and worked out a
precise analytical solution. From it, he derives that an envy-induced
class society possesses characteristics that are deemed universal in
the theory of complex systems. The result is that the class society is
beyond political control to a certain degree. Political decision-makers
lose a portion of their options for control when society spontaneously
splits into social classes. In addition, Gros' model demonstrates that
envy has a stronger effect when the competition for limited resources
is stronger. "This game theoretical insight could be of central
significance. Even an 'ideal society' cannot be stably maintained in
the long term -- which ultimately makes the striving for a communistic
society seem unrealistic," the scientist remarks.


========================================================================== Story Source: Materials provided by Goethe_University_Frankfurt. Note:
Content may be edited for style and length.


========================================================================== Journal Reference:
1. Claudius Gros. Self-induced class stratification in competitive
societies
of agents: Nash stability in the presence of envy. Royal Society
Open Science, 2020; 7 (6): 200411 DOI: 10.1098/rsos.200411 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/06/200617121514.htm

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