On the Efficiency of the Walrasian Mechanism

TL;DR

This paper analyzes the efficiency of the Walrasian mechanism in markets with strategic agents, proving that even in equilibrium, welfare is at least 25% of optimal under certain valuation conditions, regardless of market size.

Contribution

It establishes a universal lower bound on equilibrium welfare for the Walrasian mechanism with gross substitute valuations, independent of market size.

Findings

Pure Nash equilibria guarantee at least 25% of optimal welfare.

Efficiency bounds hold without large market assumptions.

Results apply to markets with gross substitute valuations and no overbidding.

Abstract

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price t\^{a}tonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market.