This thesis contains three chapters, each of which covers a different topic in experimental economics.The first chapter investigates power and power analysis in economics experiments. Power is the probability of detecting an effect when a true effect exists, which is an important but under-considered concept in empirical research. Power analysis is the process of selecting the number of observations in order to avoid issues with low power. However, it is often not clear ex-ante what the required parameters for a power analysis, like the effect size and standard deviation, should be. This chapter considers the use of Quantal Choice/Response (QR) simulations for ex-ante power analysis, as it maps related data-sets into predictions for novel environments. The QR can also guide optimal design decisions, both ex-ante as well as ex-post for conceptual replication studies. This chapter demonstrates QR simulations on a wide variety of applications related to power analysis and experimental design.The second chapter considers a question of interest to computer scientists, information technology and security professionals. How do people distribute defenses over a directed network attack graph, where they must defend a critical node? Decision-makers are often subject to behavioral biases that cause them to make sub-optimal defense decisions. Non-linear probability weightingis one bias that may lead to sub-optimal decision-making in this environment. An experimental test provides support for this conjecture, and also other empirically important biases such as naive diversification and preferences over the spatial timing of the revelation of an overall successful defense. The third chapter analyzes how individuals resolve an exploration versus exploitation trade-off in a laboratory experiment. The experiment implements the single-agent exponential bandit model. The experiment finds that subjects respond in the predicted direction to changes in the prior belief, safe action, and discount factor. However, subjects also typically explore less than predicted. A structural model that incorporates risk preferences, base rate neglect/conservatism, and non-linear probability weighting explains the empirical findings well.