  We present a network influence game that models players strategically seeding
the opinions of nodes embedded in a social network. A social learning dynamic,
whereby nodes repeatedly update their opinions to resemble those of their
neighbors, spreads the seeded opinions through the network. After a fixed
period of time, the dynamic halts and each player's utility is determined by
the relative strength of the opinions held by each node in the network
vis-a-vis the other players. We show that the existence of a pure Nash
equilibrium cannot be guaranteed in general. However, if the dynamics are
allowed to progress for a sufficient amount of time so that a consensus among
all of the nodes is obtained, then the existence of a pure Nash equilibrium can
be guaranteed. The computational complexity of finding a pure strategy best
response is shown to be NP-complete, but can be efficiently approximated to
within a (1 - 1/e) factor of optimal by a simple greedy algorithm.
