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This thesis comprises four essays that belong to different strands of the theoretical economic literature. Chapter 1 and Chapter 2 study two-sided one-to-one matching markets with quasi-linear utility and multi-dimensional heterogeneity. Chapter 1 investigates the efficiency properties of two-sided investments and in particular the sources and limitations of potential investment coordination failures in large two-sided economies with competitive post-investment market. Chapter 2 scrutinizes a novel two-sided matching model with a finite number of agents and two-sided private information about exogenously given attributes. Chapter 3 is a note on the optimal size of fixed-prize research tournaments that seeks to fill two important gaps in an influential paper by Fullerton and McAfee (1999), and Chapter 4 studies the impact of incomplete information on the problem of maximizing revenue in a dynamic version of the knapsack problem, which is a classical combinatorial resource allocation problem with numerous economic applications.