  We study a model for cascade effects over finite networks based on a
deterministic binary linear threshold model. Our starting point is a networked
coordination game where each agent's payoff is the sum of the payoffs coming
from pairwise interactions with each of the neighbors. We first establish that
the best response dynamics in this networked game is equivalent to the linear
threshold dynamics with heterogeneous thresholds over the agents. While the
previous literature has studied such linear threshold models under the
assumption that each agent may change actions at most once, a study of best
response dynamics in such networked games necessitates an analysis that allows
for multiple switches in actions. In this paper, we develop such an analysis
and construct a combinatorial framework to understand the behavior of the
model. To this end, we establish that the agents behavior cycles among
different actions in the limit and provide three sets of results.
  We first characterize the limiting behavioral properties of the dynamics. We
determine the length of the limit cycles and reveal bounds on the time steps
required to reach such cycles for different network structures. We then study
the complexity of decision/counting problems that arise within the context.
Specifically, we consider the tractability of counting the number of limit
cycles and fixed-points, and deciding the reachability of action profiles. We
finally propose a measure of network resilience that captures the nature of the
involved dynamics. We prove bounds and investigate the resilience of different
network structures under this measure.
