Differentially Private Mechanism for the Equiribrium Price under Quadratic Cost Functions and Quadratic Utility Functions

Abstract

An algorithm which protects consumers’ privacy is considered for a tatonnement model which determines the equilibrium price such that demand and supply coincide. In this model, consumers bid their demands and a firm bids her supply for the price given by an auctioneer, which is iterated until the total demands and the supply are balanced. Instead of bidding the demands exactly, noise is added to these values, which introduces differential privacy into the iterative algorithm. A definition of adjacency between two privacy information is provided and sensitivity of the algorithm is investigated. The main advantage of the algorithm is to protect consumers’ privacy and to guarantee that the price converges to the equilibrium one in a probabilistic sense.