Auctions for Social Lending: A Theoretical Analysis

Prosper, the largest online social lending marketplace with over a million members and $207 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[subscript i] they want to lend, and bid on the interest rate, b[subscript 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 strategic agents with private true interest rates? We first provide an analysis of the complete information game and fully characterize the Nash equilibria of the Prosper mechanism. Next, we show that while the borrower's payment in the VCG mechanism is always within a factor of O(logD) 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 consider an incomplete information setting and derive the Bayesian optimal auction for the borrower, which, perhaps surprisingly, may prefer to assign the loan to lenders with high interest-rates over lenders with lower interest rates, when lenders' budgets and interest-rates are correlated.