The ubiquity of smartphones has fueled content consumption worldwide, leading to an ever-increasing demand for a better Internet experience. This has necessitated an upgrade of the capacity of the access network. The Internet service providers (ISPs) have been demanding that the content providers (CPs) share the cost of upgrading access network infrastructure. A \emph{public investment} in the infrastructure of a neutral ISP will boost the profit of the CPs, and hence, seems a rational strategy. A CP can also make a \emph{private investment} in its infrastructure and boost its profits. In this paper, we study the trade-off between public and private investments by a CP when the decision is made under different types of interaction between them. Specifically, we consider four interaction models between CPs -- centralized allocation, cooperative game, non-cooperative game, and a bargaining game -- and determine the public and private investment for each model. Via numerical results, we evaluate the impact of different incentive structures on the utility of the CPs. We see that the bargaining game can result in higher public investment than the non-cooperative and centralized models. However, this benefit gets reduced if the CPs are incentivized to invest in private infrastructure.

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