Abstract:

Prosper, the largest online social lending marketplace with nearly a million members and $\$178$ million in funded loans, uses an auction amongst lenders to finance each loan. In each auction, the borrower specifies $D$, the amount he wants to borrow, and a maximum acceptable interest rate $R$. Lenders specify the amounts $a_i$ they want to lend, and bid on the interest rate, $b_i$, they're willing to receive. Given that a basic premise of social lending is cheap loans for borrowers, how does the Prosper auction do in terms of the borrower's payment, when lenders are {\em strategic agents} with private true interest rates? The Prosper mechanism is exactly the same as the VCG mechanism applied to a {\em modified instance} of the problem, where lender $i$ is replaced by $a_i$ dummy lenders, each willing to lend one unit at interest rate $b_i$. However, the two mechanisms behave very differently --- the VCG mechanism is truthful, whereas Prosper is not, and the total payment of the borrower can be vastly different in the two mechanisms. We first provide a complete analysis and characterization of the Nash equilibria of the Prosper mechanism. Next, we show that while the borrower's payment in the VCG mechanism is {\em always} within a factor of $O(\log D)$ of the payment in any equilibrium of Prosper, even the cheapest Nash equilibrium of the Prosper mechanism can be as large as a factor $D$ of the VCG payment; both factors are tight. Thus, while the Prosper mechanism is a simple uniform price mechanism, it can lead to much larger payments for the borrower than the VCG mechanism. Finally, we provide a model to study Prosper as a dynamic auction, and give tight bounds on the price for a general class of bidding strategies.