We study the problem of optimally investing in nodes of a social network in a competitive setting, wherein two camps attempt to drive the average opinion of the population in their favor. Using DeGroot-Friedkin model of opinion dynamics, we formulate the problem as a zero-sum game with its players being the two camps. We derive optimal investment strategies for both camps, and show that a random investment strategy is optimal when the underlying network follows a popular class of weight distributions. We study a broad framework, where we consider several settings of the problem, namely, when the influence of a camp on a node is a concave function of its investment on that node, when a camp aims at maximizing competitor's investment or deviation from its desired investment, and when one of the camps has uncertain information about the values of the model parameters. We also study the problem under common coupled constraints on the combined investments by the camps and derive optimal strategies of the two camps, and hence quantify the first-mover advantage. For a quantitative and illustrative study, we conduct simulations on real-world datasets and provide results and insights.