We consider an online retailer's joint pricing and contingent free-shipping (CFS) decisions in both monopoly and duopoly structures, which is an important marketing-operations interface problem. We begin by investigating the impacts of a retailer's decisions on consumers' purchase behaviors, and show that the CFS strategy is useful to acquire the consumers with large order sizes. Then, we compute the probability of repeated purchases, and construct an expected profit function for an online retailer in the monopolistic setting. We find that the fixed shipping fees may have the largest impact on the retailer's profit among all shipping-related parameters, and the retailer can benefit more from homogeneous markets than from heterogeneous ones. Next, we consider the competition between two retailers in the duopoly structure, and analytically show that, if two retailers have identical fixed and variable shipping fees, then their equilibrium decisions are equal. In order to numerically find a Nash equilibrium for two retailers, we develop a simulation approach using Arena and OptQuest. Our simulation-based examples suggest that, as a result of the competition, the two retailers should decrease their profit margins but increase their CFS cutoff levels if they have the same fixed and also the same variable shipping fees.