RSRG Seminar

In this talk, we present a case where ideas from data compression, namely those from quantization, are used to solve open problems regarding mechanism design with limited information in the field of microeconomics.  Specifically, we analyze a nonlinear economic pricing model with limited information. A seller offers a menu with a finite number n of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we present necessary conditions that the optimal finite menus for the socially efficient and revenue-maximizing mechanisms, respectively, must satisfy.  In both cases, we provide an estimate of the loss resulting from the use of finite n-class menus.  We show that the losses converge to zero at a rate proportional to 1/n^² as n becomes large.  We then extend our nonlinear pricing model to the multi-product environment, where vector quantization can be used to jointly design finite menus for social welfare and revenue maximization in multiple dimensions.  We show that losses resulting from the use of d-dimensional M-class menus converge to zero at a rate proportional to d/M^(^2/d) as M becomes large.  

Joint work with Dirk Bergemann (Yale), Yun Xu (Yale), and Ji Shen (London School of Economics).