We present a formal model of haggling between a name-your-own-price retailer and a set of individual buyers. Rather than posting a price, the retailer waits for potential buyers to submit offers for a given product and then chooses to either accept or reject them. Consumers whose offers have been rejected can invest in additional haggling effort and increment their offers. This pricing model allows the name-your-own-price retailer to engage in price discrimination: As haggling is costly for the potential buyer, customers with a high willingness to haggle will achieve lower transaction prices. However, because haggling is costly, it reduces overall welfare and diminishes the benefits of price discrimination. Our study is motivated by several name-your-own-price retailers that have recently emerged on the Internet. Based on detailed transaction data of a large German name-your-own-price retailer, we present a model of consumer haggling. We then show how this model can be used to improve the decision making of the retailer, who needs to choose a threshold price above which all offers are accepted. Another decision variable for the retailer lies in the user interface design, which allows the retailer to either facilitate or to hinder the haggling of the consumer.