  Caching and multicasting are two promising methods to support massive content
delivery in multi-tier wireless networks. In this paper, we consider a random
caching and multicasting scheme with caching distributions in the two tiers as
design parameters, to achieve efficient content dissemination in a two-tier
large-scale cache-enabled wireless multicasting network. First, we derive
tractable expressions for the successful transmission probabilities in the
general region as well as the high SNR and high user density region,
respectively, utilizing tools from stochastic geometry. Then, for the case of a
single operator for the two tiers, we formulate the optimal joint caching
design problem to maximize the successful transmission probability in the
asymptotic region, which is nonconvex in general. By using the block successive
approximate optimization technique, we develop an iterative algorithm, which is
shown to converge to a stationary point. Next, for the case of two different
operators, one for each tier, we formulate the competitive caching design game
where each tier maximizes its successful transmission probability in the
asymptotic region. We show that the game has a unique Nash equilibrium (NE) and
develop an iterative algorithm, which is shown to converge to the NE under a
mild condition. Finally, by numerical simulations, we show that the proposed
designs achieve significant gains over existing schemes.
