  Power-law tails are ubiquitous in income distributions and in the energy
distributions of diluted relativistic gases. We analyze the conceptual link
between these two cases. In economic interactions fat tails arise because the
richest individuals enact some protection mechanisms ("saving propensity")
which allow them to put at stake, in their interactions, only a small part of
their wealth. In high-energy particle collisions something similar happens, in
the sense that when particles with very large energy collide with slow
particles, then as a sole consequence of relativistic kinematics (mass
dilation), they tend to exchange only a small part of their energy; processes
like the frontal collision of two identical particles, where the exchanged
energy is 100%, are very improbable, at least in a diluted gas. We thus show
how in two completely different systems, one of socio-economic nature and one
of physical nature, a certain feature of the binary microscopic interactions
leads to the same consequence in the macroscopic distribution for the income or
respectively for the energy.
