Equilibrium Analysis in Wireless Networks Walrasian Markets: A Distributed Approach

A Walrasian Market can be modeled as a distributed system consisting a set of independent buyers and sellers. The Walrasian equilibrium theorem proves the existence of the optimal price that results in the market clean state or Walrasian Equilibrium where the sum of absolute excess demand is zero. It is proved that finding this equilibrium price is an NP-hard problem. In this paper, we present an efficient distributed control-theoretic approach for finding the Walrasian equilibrium in an exchange economy. We have modeled the price adjustment process as a closed-loop control system where the sum of absolute excess demand is measured as the system error that is fed to commodity moderators in a distributed schema simultaneously, and then each commodity moderator adjusts the price of its related commodity. We devised a controller algorithm with low complexity and fast convergence that iteratively moves the error value to zero. The proposed scheme, finds the equilibrium price and Pareto efficient allocation without knowing the shape of user utility functions or their preferences. It is scalable and is usable for exchange economies with multiple goods and many types of users.