Social lending

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 ai they want to lend, and bid on the interest rate, bi, 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? The Prosper mechanism is exactly the same as the VCG mechanism applied to a modified instance of the problem, where lender i is replaced by ai dummy lenders, each willing to lend one unit at interest rate bi. 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 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.