Relationship between uniqueness and competition ability

In our previous paper (Feng A X, Xu X L, He D R 2009 Chin. Phys. Lett. 26 058901) we proposed quantitative definitions of uniqueness and competition ability. Their trivial linear relationship was analytically discussed. In this letter, we present analytical discussion on the more interesting anomalous cases. The analytical result shows that, instead of the trivial linear relationship, the relationship between uniqueness and competition ability obeys a power law. The competition between Beijing restaurants is taken as an example. The empirical investigation results show a strong support to the analytical conclusion.