The notion of complementarity is fundamental to economics, as reflected in the large and growing number of studies that invoke alternate conceptions of this idea. Though complementarity has been studied for many years, its connection with theory of supermodularity is far more recent. Taking advantage of these techniques, the first three chapters of this dissertation study aspects of interest in network markets; endogenous information acquisition; and some insights into the comparison of player's equilibrium strategies. The last chapter applies this methodology to econometric identification.Chapter one provides a thorough analysis of oligopolistic markets with positive demand-side network externalities and perfect compatibility. With a general complementarity structure on the model primitives allowing for products with low or high stand-alone values, a nontrivial fulfilled-expectations equilibrium exists. We formalize the concept of industry viability, investigate its determinants, and show that viability is always enhanced by having more firms in the market and/or by technological progress.The second chapter studies covert information acquisition in common value Bayesian games of strategic complementarities. Using the supermodular stochastic order to arrange the structures of information increasingly in terms of preferences, we provide novel, easily interpretable conditions under which the value of information is globally convex, and study the implications in terms of the equilibrium configuration. Our analysis also enlightens the effect of information on players' behavior.Chapter three proposes a simple approach to compare players' equilibrium choices in asymmetric games with strategic complementarities. We offer three applications of our idea to industrial organization and behavioral economics.The last chapter studies (nonparametric) partial identification of treatment response with social interactions. It imposes economically driven monotone conditions to the primitives of the model, i.e., the structural equations, and shows that they imply shape restrictions on the distribution of potential outcomes by means of monotone comparative statics. We propose precise conditions that validate counterfactual predictions in models with multiple equilibria. Under three sets of assumptions, we identify sharp distributional bounds (in terms of stochastic dominance) on the potential outcomes given observable data. We illustrate our results by studying the effect of police per-capita on crime rates in New York state.