Betrayal or cooperation? Analytical investigation of behavior drivers
Using game magnetization and susceptibility in an analytic investigation
of cooperation with infinite numbers of people

Date:
September 8, 2020
Source:
American Institute of Physics
Summary:
At the macroscopic level, there are numerous examples of people
cooperating to form groupings. Yet at the basic two-person level,
people tend to betray each other, as found in games like the
prisoner's dilemma, even though people would receive a better payoff
if they cooperated among themselves. The topic of cooperation and
how and when people start trusting one another has been studied
numerically, and researchers investigate what drives cooperation
analytically.



FULL STORY ==========================================================================
When looking at humanity from a macroscopic perspective, there are
numerous examples of people cooperating to form societies, countries, religions, and other groupings.


==========================================================================
Yet at the basic two-person level, people tend to betray each other, as
found in social dilemma games like the prisoner's dilemma, even though
people would receive a better payoff if they cooperated among themselves.

The topic of cooperation and how and when people start trusting one
another has been studied by various researchers who have addressed this
problem numerically. In a paper in Chaos, by AIP Publishing, researchers investigate what drives cooperation analytically.

In order to investigate what happens when an infinite number of people,
instead of two people, play a game like the prisoner's dilemma, the
researchers mapped the two-player game to a two-spin ID Ising model,
which is a 1D line of interacting spins in the presence of an external
magnetic field.

Spins can either point clockwise, which is up, or counterclockwise, which
is down. The net difference between the fraction of spins pointing up
to those pointing down provides the analytic result for the magnetization.

"Game magnetization is an excellent measure of how in the overall scheme
of things the total number of players respond to different payoffs,"
said Colin Benjamin, one of the authors. "In our work, we go beyond
game magnetization and look at game susceptibility, too." An analytical
result for susceptibility probes the net change in the fraction of players adopting a certain strategy for both classic and quantum social dilemmas
and pinpoints the real drivers of cooperative behavior, which can vary
given the situation.

The findings in this research can be applied to analytical solutions
to numerous other social dilemma games, such as rock-paper-scissors,
Battle of the Sexes, or Stag Hunt. The mapping to ID Ising model can help understand cooperative behavior in many other social dilemmas as well.

"One future area to explore is that of recent COVID-19 infection
dynamics," said Benjamin. "A lot of numerical work has been done to
explore COVID-19 infection dynamics using tools of evolutionary game
theory. An analytical model, however, is lacking."

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


========================================================================== Journal Reference:
1. Colin Benjamin, Aditya Dash. Thermodynamic susceptibility as a
measure of
cooperative behavior in social dilemmas. Chaos: An Interdisciplinary
Journal of Nonlinear Science, 2020; 30 (9): 093117 DOI:
10.1063/5.0015655 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/09/200908113235.htm

--- up 2 weeks, 1 day, 6 hours, 50 minutes
* Origin: -=> Castle Rock BBS <=- Now Husky HPT Powered! (1337:3/111)