Ranking Mechanism Design for Price-setting Agents in E-commerce

Ranking algorithms of e-commerce sites take the buyer's search query and information of the corresponding sellers' items as input, and output a ranking of sellers' items that maximizes sites' objectives. However, the conversion rate of each item (i.e., the probability of a completed transaction) not only depends on the ranking given by the site (which controls click-through rates), but also depends on the item price set by its seller(which controls the buyer's willingness to buy). As a result, a ranking algorithm is in fact a mechanism that deals with sellers who strategically set item prices. An interesting fact about this setting, at least the status quo for the largest e-commerce sites such as Taobao, Amazon, and eBay, is that sellers are usually not given the option to report their private costs but can only communicate with the site by setting item prices. In terms of mechanism design, this is a setting where the designer is restricted to design a specific type of indirect mechanisms. We follow the framework of implementing optimal direct mechanisms by indirect mechanisms to tackle this optimal indirect ranking mechanism design problem. We firstly define a related optimal direct ranking mechanism design setting and use Myerson's characterization to optimize in that setting. We then characterize the class of direct mechanisms which could be implemented by indirect mechanisms, and construct a mapping that maps the mechanisms designed in the previous direct setting to indirect mechanisms in the original setting where sellers are allowed only to set item prices. We show that, using this technique, one can obtain mechanisms in the indirect setting that maximize expected total trading volume. We then present the mechanism employed by one of the largest e-commerce websites currently, get a Bayesian Nash Equilibrium of it and obtain the gap of the volume of the site's mechanism and the optimal mechanism. Given real dataset from the site, we also simulate our optimal mechanism and the site's mechanism, and it shows that our mechanism outperforms the site's mechanism significantly.