  We investigate a dynamic model of network marketing in a small-world network
structure artificially constructed similarly to the Watts-Strogatz network
model. Different from the traditional marketing, consumers can also play the
role of the manufacturer's selling agents in network marketing, which is
stimulated by the referral fee the manufacturer offers. As the wiring
probability $\alpha$ is increased from zero to unity, the network changes from
the one-dimensional regular directed network to the star network where all but
one player are connected to one consumer. The price $p$ of the product and the
referral fee $r$ are used as free parameters to maximize the profit of the
manufacturer. It is observed that at $\alpha=0$ the maximized profit is
constant independent of the network size $N$ while at $\alpha \neq 0$, it
increases linearly with $N$. This is in parallel to the small-world transition.
It is also revealed that while the optimal value of $p$ stays at an almost
constant level in a broad range of $\alpha$, that of $r$ is sensitive to a
change in the network structure. The consumer surplus is also studied and
discussed.
