  Heterogeneous wireless networks with small-cell deployments in licensed and
unlicensed spectrum bands are a promising approach for expanding wireless
connectivity and service. As a result, wireless service providers (SPs) are
adding small-cells to augment their existing macro-cell deployments. This added
flexibility complicates network management, in particular, service pricing and
spectrum allocations across macro- and small-cells. Further, these decisions
depend on the degree of competition among SPs. Restrictions on shared spectrum
access imposed by regulators, such as low power constraints that lead to
small-cell deployments, along with the investment cost needed to add small
cells to an existing network, also impact strategic decisions and market
efficiency. If the revenue generated by small-cells does not cover the
investment cost, then there will be no deployment even if it increases social
welfare. We study the implications of such spectrum constraints and investment
costs on resource allocation and pricing decisions by competitive SPs, along
with the associated social welfare. Our results show that while the optimal
resource allocation taking constraints and investment into account can be
uniquely determined, adding those features with strategic SPs can have a
substantial effect on the equilibrium market structure.
