This thesis considers one problem in contract theory and one problem in learning and pricing.

The contract theory problem studies a game between two providers with fixed capacities that compete for customers through a broker. The broker works on commission margins and can influence customers choice. We study the effects of requiring minimum sale volumes, or thresholds, to trigger an increase in commissions. This setting is similar to quantity discount contracts, when suppliers require minimum purchase volumes to give discounts on the total purchase. We show that the equilibrium results in less revenue for the smaller provider and more revenue for the broker, with the revenue for the larger provider remaining unchanged. However, if commission margins are fixed at least one provider has an incentive to impose minimum sale volumes to trigger commissions, usually at the expense of the broker.

The problem in learning and pricing studies a capacity provider who offers multiple versions of a single product, such as different seat locations for an event. We assume that the different versions share an unknown core value and command a known premium or discount relative to the core value. Customers arrive at an unknown arrival rate during a finite sales horizon. We assume that the provider has a prior knowledge about the arrival rate which is updated using Bayesian rule. Estimates of the core value are updated using maximum likelihood estimation. We show how to simultaneously estimate the unknown parameters as the sales evolve and how to price the products to maximize revenues under a rolling horizon framework.

Key Words: Provider-Broker Competition, Game Theory, Nash Equilibrium, Stackelberg Equilibrium, Leader-Follower, Repeated Games, Demand Learning, Dynamic Pricing, Multinomial Logit Choice, Bayesian Update, Maximum Likelihood Estimation