Differentially Private Mechanism for Determining the Equilibrium Price under Strongly Convex Cost Functions and Strongly Concave Utility Functions

Abstract

An algorithm for finding the equilibrium price such that demand and supply coincide is proposed. In the algorithm, the auctioneer publishes a noisy price in order to protect consumers' privacy, while the consumers and the firm bid their optimal demands and the supply at given noisy price. In a conventional work, it is assumed that utility functions and a cost function are quadratic concave and quadratic convex, respectively. In this paper, the assumption is relaxed to strictly concave and strictly convex. Then, it is shown that the algorithm protects consumers' privacy and the candidate price converges to the equilibrium price in a weak sense.