  Social inequalities are ubiquitous and here we show that the values of the
Gini ($g$) and Kolkata ($k$) indices, two generic inequality indices, approach
each other (starting from $g = 0$ and $k = 0.5$ for equality) as the
competitions grow in various social institutions like markets, universities,
elections, etc. It is further showed that these two indices become equal and
stabilize at a value (at $g = k \simeq 0.87$) under unrestricted competitions.
We propose to view this coincidence of inequality indices as a generalized
version of the (more than a) century old 80-20 law of Pareto. Furthermore, the
coincidence of the inequality indices noted here is very similar to the ones
seen before for self-organized critical (SOC) systems. The observations here,
therefore, stand as a quantitative support towards viewing interacting
socio-economic systems in the framework of SOC, an idea conjectured for years.
