  We consider the dynamics of particles undergoing the reaction $A+A \to
\emptyset$ in one dimension with a dynamic bias. Here the particles move
towards their nearest neighbour with probability $0.5+\epsilon$ where $-0.5
\leq \epsilon < 0$. $\epsilon_c = -0.5$ is the deterministic limit where the
nearest neighbour interaction is strictly repulsive. We show that the negative
bias changes drastically the behaviour of the fraction of surviving particles
$\rho(t)$ and persistence probability $P(t)$ with time $t$. $\rho(t)$ decays as
$a/ (\log t)^b$ where $b$ increases with $\epsilon - \epsilon_c$. $P(t)$ shows
a stretched exponential decay with non-universal decay parameters. The
probability $\Pi(x,t)$ that a tagged particle is at position $x$ from its
origin is found to be Gaussian for all $\epsilon<0$; the associated scaling
variable is $x/t^\alpha$ where $\alpha$ approaches the known limiting value
$1/4$ as $\epsilon \to \epsilon_c$, in a power law manner. Some additional
features of the dynamics by tagging the particles are also studied. The results
are compared to the case of positive bias, a well studied problem.
