Uncontrolled competitions for freely accessible
resources such as fish stocks or water can have fatal consequences not only for
the resources themselves. In such competitions, investors, too, are ultimately
driven to their subsistence level, a new game-theoretical study by Professor
Claudius Gros, theoretical physicist at Goethe University, shows.
FRANKFURT.
Without regulations for their use, the condition of freely accessible resources
such as fish stocks, water or air can deteriorate dramatically. In economics,
this is referred to as the "Tragedy of the Commons". In 2009, Elinor
Ostrom became the first woman to win the Nobel Prize in Economics for her
studies on this topic. Ostrom's question of how to prevent this
"tragedy" is just as relevant today as it was some 20 years ago.
Game theory deals with situations in which
a number of agents compete with each other, with each participant trying to
maximize his or her own profit individually. One speaks of a "Nash
equilibrium" if players cannot increase their returns further. The
"Tragedy of the Commons" is a game theoretical scenario in which the
actors do not compete directly, but indirectly: If someone takes a piece of a
common pie, there will be less for everybody else.
Instead of investigating how to avoid the
"Tragedy of the Commons", Claudius Gros from Goethe University’s
Institute for Theoretical Physics examined the resulting Nash equilibrium, with
unexpected results: If a common good is divided more or less equally among N
interested parties, then each receives a share of the order 1/N. However, the
respective investment costs still need to be deducted. Gros' calculations show
that, in equilibrium, the actors increase their engagement until the resulting
investment costs almost reach the value of the resources the individual
investor can secure for her- or himself. Mathematically, the theoretical physicist
was able to show that the final profit of the individual investor scales as
1/N².
The original expectation, that investors
each receive a proportional share from the resource, remains correct, as Gros'
research shows. However, this does not translate into an overall return of the
same proportion, which is smaller by a power in the number of investors. Gros
denotes the dramatic deterioration of the net profit as "catastrophic
poverty", as it implies that unregulated competition drives the individual
actor close to the profitability limit, viz to the subsistence level.
Similarly, Gros was able to show that catastrophic poverty can be avoided when
the actors cooperate with each other. Cooperation leads to a net profit
corresponding to the number of investors in simple power, the classical result.
The result of the investigations is
therefore that the "Tragedy of the Commons" can cause substantially
more damage than previously assumed. Uncontrolled access not only leads to a
potentially excessive exploitation of the resource, a topic that has been the
focus of many previous studies. In addition, investors suffer themselves when
only maximizing their own profits. Mathematically, Gros was able to show that
technological progress intensifies this process and that either all, or the
vast majority of participating investors are ultimately affected by
catastrophic poverty. If anything, only a few investors – the oligarchs – stand
to gain more.
Publication:
Claudius Gros, “Generic catastrophic
poverty when selfish investors exploit a degradable common resource”, Royal
Society Open Science (2023) https://royalsocietypublishing.org/doi/10.1098/rsos.221234
Images
for download:
https://www.uni-frankfurt.de/131929975
Caption:
Professor Claudius Gros, Goethe University
Frankfurt. Credit: Uwe Dettmar for Goethe University
Further
information
Professor Claudius Gros
Institute for Theoretical Physics
Goethe University Frankfurt, Germany
Tel. +49 (0)69 798-47818
gros07@itp.uni-frankfurt.de
https://itp.uni-frankfurt.de/~gros/
