This dissertation consists of three essays on sequential games of cooperation, competition, and experimentation. Chapter 1 is the introduction. Chapter 2, Equilibrium and Sequential Structure in Collective Action Problems, uses dynamic tragedy of the commons and dynamic public good games, as metaphors for intertemporal social cooperation and competition, to study how a society could arrange decision-making sequences to elicit the highest levels of efficiency. Chapter 3, Prizes and Incentives in Sequential Exploration, investigates incentives and the order of play in a dynamic experimentation model of collaboration. I propose a simple model of innovation and demonstrate that high efforts are achieved when collaborating agents are of medium ability. I ask how a principal should sequence agents, structure teams, promote collaboration, and set prizes to best elicit efforts. Chapter 4, Intergenerational Exploitation and Catastrophic Risk, proposes a novel approach to modeling the problem of climate change. Using the framework of strategic experimentation with overlapping generations as players, I show that there is a continuum of equilibria and that an efficient equilibrium exists at intermediate social discount rates.