This thesis is composed of two parts. Part I contributes to the matching literature and Part II contributes to the contest literature. Part I: A set of indivisible objects must be allocated among a group of agents, or agents from one side of the market must be matched to agents on the other. Each agent has their own preference over these objects, or over the agents on the other side. These preferences exhibit an underlying structure, motivated by real-world examples such as the refugee settlement problem, the job rotation problem and others. We study design of procedures to match agents to objects/agents, without resorting to randomization devices or monetary transfers. Three concerns play a central role in this design: incentive compatibility, efficiency and fairness. For each setting we consider, we appropriately formalise what we mean by these terms. Part II: A competitive league coach (team manager) must manage the energy pool of players in the team over the course of the entire season. High energy usage increases the chance of winning the current game, but also increases the risk of developing accumulated fatigue or injuries in later games. We explore this “winning in the short term” vs “saving energy for the future” dilemma that the coach faces over a long season
