  We determine exactly the short-distance effective potential between two
"guest" charges immersed in a two-dimensional two-component charge-asymmetric
plasma composed of positively ($q_1 = +1$) and negatively ($q_2 = -1/2$)
charged point particles. The result is valid over the whole regime of
stability, where the Coulombic coupling (dimensionless inverse temperature)
$\beta <4$. At high Coulombic coupling $\beta>2$, this model features
like-charge attraction. Also, there cannot be repulsion between
opposite-charges at short-distances, at variance with large-distance
interactions.
