Auction hosting site pricing and market equilibrium with endogenous bidder and seller participation

This paper characterizes the payoffs and pricing policies of auction hosting sites when both the bidders' and the sellers' participation is endogenous. Sellers have heterogeneous opportunity costs and make a listing decision depending on the listing fee and the expected revenue from the sale. On the other side of the market, factors such as facility in navigating an interface layout and prior bidding experience result in bidder heterogeneity with respect to participation costs. Bidders participate if their ex ante expected payoff from searching the site exceeds their participation costs. The auction site earns revenue by setting positive listing fees, trading off the increased revenue per seller resulting from a higher fee with the revenue reduction from the loss of sellers. Though this appears to be a classic monopoly problem, there are important differences. The reduction in the number of sellers participating in a site has feedback effects, as it affects the number of bidders who choose to visit that site, which in turn again affects the attractiveness of the site to sellers, and thus further reduces seller participation. In this environment the monopolist's ability to extract rents is severely limited, even if one considers rent extraction from the seller side of the market only. It is demonstrated that the inverse demand curve is flatter than the demand curve obtained from the (inverse) distribution of seller costs. Moreover, the inverse demand curve has at least one and possibly multiple flat segments, leading to discontinuities in the profit function. Thus, small changes in the environment can lead to large changes in the optimal fee and market participation.