On the Efficiency of the Walrasian Mechanism

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

Pricing Multi-Unit Markets

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices

Efficiency Guarantees in Auctions with Budgets

In settings where players have a limited access to liquidity, represented in the form of budget constraints, efficiency maximization has proven to be a challenging goal. In particular, the social welfare cannot be approximated by a better factor then the number of players. Therefore, the literature has mainly resorted to Pareto-efficiency as a way to achieve efficiency in such settings. While successful in some important scenarios, in many settings it is known that either exactly one incentive-compatible auction that always outputs a Pareto-efficient solution, or that no truthful mechanism can always guarantee a Pareto-efficient outcome. Traditionally, impossibility results can be avoided by considering approximations. However, Pareto-efficiency is a binary property (is either satisfied or not), which does not allow for approximations. In this paper we propose a new notion of efficiency, called \emph{liquid welfare}. This is the maximum amount of revenue an omniscient seller would be able to extract from a certain instance. We explain the intuition behind this objective function and show that it can be 2-approximated by two different auctions. Moreover, we show that no truthful algorithm can guarantee an approximation factor better than 4/3 with respect to the liquid welfare, and provide a truthful auction that attains this bound in a special case. Importantly, the liquid welfare benchmark also overcomes impossibilities for some settings. While it is impossible to design Pareto-efficient auctions for multi-unit auctions where players have decreasing marginal values, we give a deterministic $O(\log n)$-approximation for the liquid welfare in this setting

Financial Stability and Monetary Policy - A Framework

The paper presents a stylised framework to analyse conditions under which monetary policy contributes to amplified movements in the housing market. Extending work by Hyun Shin (2005), the paper analyses self enforcing feedback mechanisms resulting in amplifier effects in a credit constrained economy. The paper characterizes conditions for asymmetric effects, causing systemic crises. By injecting liquidity, monetary policy can prevent a meltdown. Anticipating such a response, private agents are encouraged to take higher risks. Provision of liquidity works as a public good, but it may create potential conflicts with other policy objectives and may give incentives to build up leverage with a high systemic exposure to small probability events

Explorations in Evolutionary Design of Online Auction Market Mechanisms

This paper describes the use of a genetic algorithm (GA) to find optimal parameter-values for trading agents that operate in virtual online auction “e-marketplaces”, where the rules of those marketplaces are also under simultaneous control of the GA. The aim is to use the GA to automatically design new mechanisms for agent-based e-marketplaces that are more efficient than online markets designed by (or populated by) humans. The space of possible auction-types explored by the GA includes the Continuous Double Auction (CDA) mechanism (as used in most of the world’s financial exchanges), and also two purely one-sided mechanisms. Surprisingly, the GA did not always settle on the CDA as an optimum. Instead, novel hybrid auction mechanisms were evolved, which are unlike any existing market mechanisms. In this paper we show that, when the market supply and demand schedules undergo sudden “shock” changes partway through the evaluation process, two-sided hybrid market mechanisms can evolve which may be unlike any human-designed auction and yet may also be significantly more efficient than any human designed market mechanism

Fee-Setting Mechanisms: On Optimal Pricing by Intermediaries and Indirect Taxation

Mechanisms according to which private intermediaries or governments charge transaction fees or indirect taxes are prevalent in practice. We consider a setup with multiple buyers and sellers and two-sided independent private information about valuations. We show that any weighted average of revenue and social welfare can be maximized through appropriately chosen transaction fees and that in increasingly thin markets such optimal fees converge to linear fees. Moreover, fees decrease with competition (or the weight on welfare) and the elasticity of supply but decrease with the elasticity of demand. Our theoretical predictions fit empirical observations in several industries with intermediaries

Envy Freedom and Prior-free Mechanism Design

We consider the provision of an abstract service to single-dimensional agents. Our model includes position auctions, single-minded combinatorial auctions, and constrained matching markets. When the agents' values are drawn from a distribution, the Bayesian optimal mechanism is given by Myerson (1981) as a virtual-surplus optimizer. We develop a framework for prior-free mechanism design and analysis. A good mechanism in our framework approximates the optimal mechanism for the distribution if there is a distribution; moreover, when there is no distribution this mechanism still performs well. We define and characterize optimal envy-free outcomes in symmetric single-dimensional environments. Our characterization mirrors Myerson's theory. Furthermore, unlike in mechanism design where there is no point-wise optimal mechanism, there is always a point-wise optimal envy-free outcome. Envy-free outcomes and incentive-compatible mechanisms are similar in structure and performance. We therefore use the optimal envy-free revenue as a benchmark for measuring the performance of a prior-free mechanism. A good mechanism is one that approximates the envy free benchmark on any profile of agent values. We show that good mechanisms exist, and in particular, a natural generalization of the random sampling auction of Goldberg et al. (2001) is a constant approximation