Adverse Selection with Quality Variance: A Maximum-Entropy Approach

Abstract

The adverse-selection mechanism in markets explains how asymmetric information between buyers and sellers can drive high-quality goods out of the market, thereby causing market deterioration. In its simplest formulation, only the mean quality is used to describe the market, and this is insufficient to determine how fast the market deteriorates or how the quality distribution evolves. To resolve the two problems, we describe the adverse selection as a dynamic truncation of the quality distribution: buyers set an upper bound proportional to the mean quality by a rate $\xi$ that is larger than unity, and sellers whose quality exceeds this upper bound reject an offer and exit the market. The retained market is then characterized by the conditional distribution obtained after this truncation, and the corresponding evolution process is iterated until market quality reaches a stable state. This statistical approach gives three results. (i) We identify a mechanism for preventing complete adverse selection, defined as the process where the quality of the market is driven down to the minimum quality floor. (ii) A larger quality variance or a smaller price premium, defined as the amount by which the payment upper bound exceeds the current mean quality, raises the upper bound on the deterioration in mean quality. (iii) A maximum-entropy benchmark shows numerically how quality variance and the payment rate jointly determine market deterioration and the final stable quality platform. This approach also clarifies how market interventions can slow adverse selection: they may raise buyers' payment rate, reduce quality variance, or increase the minimum quality floor.