  In this paper, we discover that the class of random polynomials arising from
the equilibrium analysis of random asymmetric evolutionary games is
\textit{exactly} the Kostlan-Shub-Smale system of random polynomials, revealing
an intriguing connection between evolutionary game theory and the theory of
random polynomials. Through this connection, we analytically characterize the
statistics of the number of internal equilibria of random asymmetric
evolutionary games, namely its mean value, probability distribution, central
limit theorem and universality phenomena. Moreover, comparing symmetric and
asymmetric random games, we establish that symmetry in the group interaction
increases the expected number of internal equilibria. Our research establishes
new theoretical understanding of asymmetric evolutionary games and why
symmetry/asymmetry of group interactions matters.
